[ { "q_id": "9819_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5769999027252197, 0.03356465697288513, 0.010978542268276215, 0.00452147051692009 ], [ 0.8298473358154297, 0.037757255136966705, 0.02098417840898037, 0.006075126584619284 ], [ 0.82984459400177, 0.04026848450303078, 0.013482671231031418, 0.0033238583710044622 ], [ 0.8009470105171204, 0.014168955385684967, 0.08289019763469696, 0.01878838613629341, 0.006782629992812872 ], [ 0.8009545207023621, 0.04545792192220688, 0.019006235525012016, 0.006006479263305664, 0.012207183055579662 ], [ 0.4751850664615631, 0.031890787184238434, 0.9940963983535767, 0.9964283108711243 ], [ 0.264405220746994, 0.032552801072597504, 0.2704659104347229, 0.9393421411514282, 0.9950615763664246 ], [ 0.8009499311447144, 0.038383372128009796, 0.015446017496287823, 0.005211330484598875 ], [ 0.8298442959785461, 0.036640286445617676, 0.25192728638648987, 0.012381931766867638, 0.004137275740504265 ], [ 0.8009518980979919, 0.03513395041227341, 0.026906896382570267, 0.009334159083664417 ], [ 0.8009487986564636, 0.03501121327280998, 0.015644339844584465, 0.00563594838604331 ], [ 0.8298473358154297, 0.038409531116485596, 0.01966826431453228, 0.006021886132657528 ], [ 0.8298506140708923, 0.1405288428068161, 0.04256117716431618, 0.025915602222085, 0.00853130966424942 ], [ 0.8298442959785461, 0.05084263160824776, 0.01722024753689766, 0.0118113337084651, 0.0046580093912780285 ], [ 0.4914642572402954, 0.0352368988096714, 0.018843961879611015, 0.006839357782155275 ], [ 0.8592957854270935, 0.043682534247636795, 0.025941435247659683, 0.005700007546693087 ] ] }, { "q_id": "9580_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06844941526651382, 0.146108478307724, 0.49274447560310364, 0.376189649105072, 0.03760528564453125, 0.07035104930400848, 0.006774937734007835, 0.12116535753011703, 0.03215097263455391, 0.03224867582321167, 0.05776474252343178, 0.009649870917201042, 0.006835359148681164 ], [ 0.0778646245598793, 0.16421937942504883, 0.46362248063087463, 0.04320754483342171, 0.1482686698436737, 0.03257687762379646, 0.047435399144887924, 0.014151143841445446, 0.008251310326159 ], [ 0.07012034207582474, 0.20678506791591644, 0.5807425379753113, 0.07059506326913834, 0.028189411386847496, 0.011940265074372292, 0.009133751504123211 ], [ 0.38684162497520447, 0.053633466362953186, 0.07497389614582062, 0.1921415776014328, 0.2715228497982025, 0.03632520139217377, 0.061886776238679886, 0.006088517606258392, 0.1041586771607399, 0.031757090240716934, 0.029805343598127365, 0.05059872195124626, 0.011983413249254227, 0.00599575275555253 ], [ 0.38684386014938354, 0.07011589407920837, 0.27839499711990356, 0.0015704018296673894, 0.5229623317718506, 0.10838446021080017, 0.09843701124191284, 0.02228023298084736, 0.009867082349956036 ], [ 0.2570686936378479, 0.0392945371568203, 0.22881315648555756, 0.3223751187324524, 0.216477170586586, 0.18331460654735565, 0.04685826972126961, 0.034617308527231216, 0.03658927232027054, 0.01868501491844654, 0.01185019500553608 ], [ 0.019980594515800476, 0.03135426715016365, 0.03965897485613823, 0.09956827759742737, 0.1770860105752945, 0.019643394276499748, 0.04294651746749878, 0.05313536524772644, 0.043821804225444794, 0.018703989684581757 ], [ 0.15861180424690247, 0.011450188234448433, 0.014646888710558414, 0.026958394795656204, 0.03839920833706856, 0.026868445798754692, 0.015237197279930115, 0.025879202410578728, 0.00943743996322155, 0.0035523553378880024, 0.02405858039855957, 0.09703981876373291, 0.05485861748456955, 0.0444917194545269, 0.032452333718538284, 0.012433975003659725 ], [ 0.3868427276611328, 0.01404664572328329, 0.02284706011414528, 0.02108950726687908, 0.03742632642388344, 0.009242046624422073, 0.14338168501853943, 0.09483939409255981, 0.16835178434848785, 0.03467845916748047, 0.024263348430395126 ], [ 0.23339863121509552, 0.043730445206165314, 0.05894767493009567, 0.016298305243253708, 0.011273852549493313 ], [ 0.25706687569618225, 0.03554388880729675, 0.19440484046936035, 0.028064200654625893, 0.13890185952186584, 0.03765595704317093, 0.0673438012599945, 0.018427414819598198, 0.009717709384858608 ], [ 0.24710750579833984, 0.03926223888993263, 0.0836416706442833, 0.01811552420258522, 0.04670295864343643, 0.01046638935804367, 0.00277966377325356 ], [ 0.018975267186760902, 0.03012780100107193, 0.02819778211414814, 0.10915371030569077, 0.06518340110778809, 0.17049627006053925, 0.035243161022663116, 0.10789261013269424, 0.030294721946120262, 0.19886738061904907, 0.060768768191337585, 0.021708108484745026, 0.010815775953233242 ], [ 0.03602192923426628, 0.017860058695077896, 0.6373505592346191, 0.44584208726882935, 0.06304334849119186, 0.02787119150161743, 0.008738260716199875, 0.8793842196464539 ], [ 0.15459772944450378, 0.034361474215984344, 0.0332171730697155, 0.007439452223479748, 0.0022109118290245533 ], [ 0.4681842625141144, 0.3805462718009949, 0.04000798240303993, 0.020970983430743217, 0.009770400822162628 ] ] }, { "q_id": "10024_mmlu_physics", "cot_ids": [ 0, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15 ], "rewards": [ [ 0.3939475119113922, 0.2206164002418518, 0.0013254943769425154, 0.00522227305918932 ], [ 0.29836907982826233, 0.18302205204963684, 0.046383269131183624 ], [ 0.2338714599609375, 0.14314770698547363, 0.06446728855371475, 0.3309885859489441, 0.005188093055039644 ], [ 0.419372022151947, 0.3294519782066345, 0.0042401812970638275 ], [ 0.36434534192085266, 0.17806462943553925, 0.08472175151109695, 0.22771351039409637, 0.004504589829593897 ], [ 0.3904974162578583, 0.3702296018600464, 0.1705477237701416, 0.0018657546024769545 ], [ 0.03493528440594673, 0.001250311266630888 ], [ 0.07390712201595306, 0.17793647944927216, 0.07761506736278534, 0.14738252758979797, 0.004924201872199774 ], [ 0.3548807203769684, 0.257189005613327, 0.9892988204956055, 0.9957005381584167 ], [ 0.39663997292518616, 0.2817233204841614, 0.0043234070762991905 ], [ 0.05234841629862785, 0.01918927952647209, 0.028735345229506493, 0.007258817553520203, 0.0012022588634863496 ], [ 0.49702852964401245, 0.992172122001648, 0.9977084398269653 ] ] }, { "q_id": "9903_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06957315653562546, 0.06675392389297485, 0.03628116101026535, 0.13211655616760254, 0.08468734472990036, 0.19425800442695618, 0.1981906145811081, 0.11707857251167297 ], [ 0.06957195699214935, 0.0005530384369194508, 3.07397531287279e-05, 0.00247154850512743, 2.8648917577811517e-05, 9.425728057976812e-05, 0.014411620795726776, 0.13179229199886322 ], [ 0.06957253813743591, 0.015242972411215305, 0.07428759336471558, 0.017846815288066864, 0.06959874927997589, 0.04534875974059105, 0.03198964148759842, 0.0005374217871576548, 0.1674393117427826, 0.08005556464195251, 0.48628076910972595, 0.6069577932357788 ], [ 0.0695730596780777, 0.0011797717306762934, 0.20899160206317902, 0.01409488171339035, 0.026930654421448708, 0.005054470617324114, 0.006071709096431732, 0.008431040681898594, 0.0012821825221180916 ], [ 0.06957365572452545, 0.0013741978909820318, 0.30459529161453247, 0.008181878365576267, 0.030119987204670906, 0.004934466909617186 ], [ 0.06957278400659561, 0.0013741807779297233, 0.047257229685783386, 0.10121646523475647, 0.006009021308273077, 0.06620422005653381, 0.22661226987838745, 0.7426651120185852 ], [ 0.06957139819860458, 0.0013741953298449516, 0.16137585043907166, 0.005032096523791552, 0.20729447901248932, 0.013305031694471836, 0.13459157943725586, 0.007137975189834833 ], [ 0.06957211345434189, 0.007928776554763317, 0.0499073788523674, 0.008424322120845318, 0.07234981656074524, 0.028231553733348846, 0.07844249904155731, 0.0032141932751983404 ], [ 0.06957365572452545, 0.001080291927792132, 0.22550053894519806, 0.005757341627031565, 0.07291188091039658, 0.005189427174627781, 0.1315036118030548, 0.1144949272274971 ], [ 0.05347030982375145, 0.11575108021497726, 0.15542390942573547, 0.13150295615196228, 0.0834827870130539, 0.0005207830108702183, 0.21534791588783264, 0.1431889832019806, 0.3316386044025421, 0.18515029549598694 ], [ 0.06957244873046875, 0.0014848666032776237, 0.17496712505817413, 0.003731090808287263, 0.0858987346291542, 0.005859385710209608, 0.03898010402917862, 0.08075076341629028, 0.08156146854162216 ], [ 0.06957365572452545, 0.0013741978909820318, 0.036858487874269485, 0.004586603958159685, 0.2770082354545593, 0.019962618127465248, 0.030578378587961197, 0.0036698265466839075 ], [ 0.0695730447769165, 0.01557946391403675, 0.07448447495698929, 0.014215841889381409, 0.14833605289459229, 0.5445269346237183, 0.0035027211997658014 ], [ 0.05155737325549126, 0.05196460336446762, 0.2307235300540924, 0.08696584403514862, 0.15413856506347656, 0.2383393496274948, 0.11714345961809158, 0.1323041021823883, 0.13306866586208344, 0.1439443826675415, 0.10108276456594467, 0.1426960676908493 ], [ 0.05281626433134079, 0.0784229189157486, 0.04329640045762062, 0.10403545200824738, 0.050276078283786774, 0.16248728334903717, 0.16201269626617432, 0.09723135083913803, 0.0004685877065639943, 0.13348887860774994, 0.01002978254109621, 0.13385051488876343, 0.05280894413590431, 0.05268878489732742 ] ] }, { "q_id": "9111_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.3643622100353241, 0.10511810332536697, 0.061111677438020706, 0.0021781618706882, 0.41386252641677856, 0.9964141249656677 ], [ 0.9874134063720703, 0.9925234913825989, 0.764755368232727, 0.41548076272010803, 0.9971784353256226 ], [ 0.2022208571434021, 0.08798711746931076, 0.27140915393829346, 0.9924749732017517, 0.9975482821464539 ], [ 0.20222048461437225, 0.9340230822563171, 0.3085748553276062, 0.40642380714416504, 0.9969146251678467 ], [ 0.3643597960472107, 0.9347177743911743, 0.3568854033946991, 0.583720862865448, 0.9965001344680786 ], [ 0.36435946822166443, 0.05744002014398575, 0.13456174731254578, 0.19351860880851746, 0.00400213897228241, 0.9424338936805725, 0.9954918026924133 ], [ 0.40354323387145996, 0.7629255652427673, 0.11731888353824615, 0.0026087749283760786, 0.7760624289512634, 0.996087908744812 ], [ 0.2022217959165573, 0.15711764991283417, 0.1870669722557068, 0.3669660687446594, 0.8664019703865051, 0.996418833732605 ], [ 0.20221932232379913, 0.9249556660652161, 0.5115900635719299, 0.47647401690483093, 0.9978207349777222, 0.9982684850692749 ], [ 0.2022225558757782, 0.8563446402549744, 0.3748054504394531, 0.44492676854133606, 0.996626615524292 ], [ 0.2022193968296051, 0.16334909200668335, 0.5706977248191833, 0.0050826845690608025, 0.8324277997016907, 0.003982756286859512, 0.9609001278877258, 0.9977049231529236 ], [ 0.936612606048584, 0.9945026636123657, 0.9861547350883484, 0.9979265928268433 ], [ 0.3643622100353241, 0.038483619689941406, 0.10356644541025162, 0.04105677455663681, 0.001577670918777585, 0.043579865247011185, 0.9499033689498901, 0.9972214698791504 ], [ 0.202219620347023, 0.3464077115058899, 0.5678126811981201, 0.9829443097114563, 0.951258659362793, 0.997302770614624 ], [ 0.20222339034080505, 0.9728540182113647, 0.8916041851043701, 0.9967505931854248 ], [ 0.9879189133644104, 0.9920532703399658, 0.9973729848861694 ] ] }, { "q_id": "9852_mmlu_physics", "cot_ids": [ 1, 2, 3, 5, 6, 8, 9, 10, 14, 15 ], "rewards": [ [ 0.961740255355835, 0.01841537095606327, 0.009253391996026039, 0.01738477684557438, 0.00032572296913713217, 0.06187037006020546, 0.012276848778128624, 0.006194592919200659, 0.037175968289375305, 0.031489722430706024, 0.1055670902132988, 0.02305254153907299, 0.02670987695455551, 0.18403343856334686, 0.03528011217713356, 0.16866444051265717, 0.023117847740650177, 0.06601998209953308, 0.9936324954032898, 0.9999490976333618 ], [ 0.09449605643749237, 0.05670509859919548, 0.09036263823509216, 0.011275703087449074, 0.07837141305208206, 0.07813660055398941, 0.19565479457378387, 0.038340236991643906, 0.059298075735569, 0.11312953382730484, 0.05641208589076996, 0.022510645911097527, 0.01771220751106739, 0.04005100578069687, 0.019283823668956757, 0.9977193474769592, 0.999914288520813 ], [ 0.12245535105466843, 0.04085500165820122, 0.0019531575962901115, 0.04973507672548294, 0.002603048924356699, 0.02744285762310028, 0.04877660423517227, 0.002771556144580245, 0.022289209067821503, 0.019717829301953316, 0.03564777225255966, 0.017866702750325203, 0.0012410370400175452, 0.0003876957925967872 ], [ 0.9617401361465454, 0.01046905666589737, 0.04026045277714729, 0.00041765047353692353, 0.040862832218408585, 0.009109143167734146, 0.020566828548908234, 0.007580623030662537, 0.0398518331348896, 0.004365127068012953, 0.012233886867761612, 0.009960022754967213, 0.003419147338718176, 0.0003438152198214084 ], [ 0.12245550751686096, 0.03806565701961517, 0.03979899734258652, 0.019792985171079636, 0.057814259082078934, 0.05720711499452591, 0.12782599031925201, 0.0712525025010109, 0.12072303146123886, 0.006315480452030897, 0.010362482629716396, 0.00730943214148283, 0.0021365515422075987, 0.0002919651451520622 ], [ 0.9617403149604797, 0.01898091472685337, 0.002830335171893239, 0.023016925901174545, 0.027173995971679688, 0.019865263253450394, 0.01301257498562336, 0.049134399741888046, 0.014638576656579971, 0.02886705845594406, 0.1369948834180832, 0.034653980284929276, 0.07111378014087677, 0.0038345828652381897, 0.0010105068795382977, 0.013330409303307533, 0.009844272397458553, 0.007634095381945372, 0.004053573589771986, 0.00036378594813868403 ], [ 0.12245878577232361, 0.03861510753631592, 0.04134537652134895, 0.04102573171257973, 0.004689719062298536, 0.018861565738916397, 0.03266231343150139, 0.0050394912250339985, 0.030988570302724838, 0.03175943344831467, 0.03221699222922325, 0.008899468928575516, 0.20934930443763733, 0.17726007103919983, 0.9975231289863586, 0.9998966455459595 ], [ 0.9617400169372559, 0.007627653889358044, 0.033000752329826355, 0.0009549996466375887, 0.036116499453783035, 0.018579358235001564, 0.03230513632297516, 0.07349811494350433, 0.07970824092626572, 0.008671938441693783, 0.04209180176258087, 0.029102126136422157, 0.031061934307217598, 0.008484628982841969, 0.008228013291954994, 0.00244444003328681, 0.000334526295773685 ], [ 0.03427994251251221, 0.052121229469776154, 0.10328708589076996, 0.0045053656212985516, 0.04917772859334946, 0.1874653548002243, 0.8191145062446594, 0.9998979568481445 ], [ 0.09516392648220062, 0.04687539115548134, 0.059522487223148346, 0.04868827387690544, 0.00525406189262867, 0.020488660782575607, 0.017500709742307663, 0.044819436967372894, 0.01710517145693302, 0.02362002618610859, 0.011943821795284748, 0.011957171373069286, 0.002594554331153631, 0.0003149900585412979 ] ] }, { "q_id": "9222_mmlu_physics", "cot_ids": [ 0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 15 ], "rewards": [ [ 0.2724718749523163, 0.023523753508925438, 0.026880979537963867, 0.019089719280600548, 0.02686489373445511, 0.035477474331855774, 0.029203075915575027, 0.06028389185667038, 0.040800269693136215, 0.02631639875471592, 0.9876304268836975, 0.9953821301460266 ], [ 0.6600064635276794, 0.0395992174744606, 0.008217142894864082, 0.0004784352204296738, 0.015105028636753559, 0.015259881503880024, 0.13955610990524292, 0.1132822036743164, 0.17092140018939972, 0.05871594324707985, 0.08916252851486206, 0.031336888670921326, 0.025493551045656204, 0.0014150120550766587, 0.006761031690984964, 0.0032769409008324146, 0.02584984339773655, 0.17214220762252808, 0.9869716763496399 ], [ 0.2912522852420807, 0.019147343933582306, 0.02551466040313244, 0.06739189475774765, 0.021606843918561935, 0.03802315890789032, 0.04407225921750069, 0.05518949031829834, 0.04948069527745247, 0.09650329500436783, 0.11914046108722687, 0.0015898485435172915, 0.013280848041176796, 0.013898991979658604, 0.19119034707546234, 0.9900525212287903 ], [ 0.2643581032752991, 0.02281506173312664, 0.002672135131433606, 0.050518106669187546, 0.02481735683977604, 0.08992712199687958, 0.07879626750946045, 0.12196740508079529, 0.0012699274811893702, 0.005723034963011742, 0.28251126408576965, 0.2835392653942108 ], [ 0.21607638895511627, 0.019416317343711853, 0.02463536337018013, 0.02816222421824932, 0.13178324699401855, 0.011193019337952137, 0.09105931222438812, 0.03607279807329178, 0.09328567236661911, 0.021008789539337158, 0.10860616713762283, 0.21555595099925995, 0.04550636187195778, 0.03139299526810646, 0.026111941784620285, 0.000198591107618995, 0.3461655080318451, 0.02169632725417614, 0.03383801877498627, 0.005025489721447229 ], [ 0.21607574820518494, 0.02552558109164238, 0.03158504515886307, 0.027086813002824783, 0.08753855526447296, 0.04338384419679642, 0.08561333268880844, 0.022404804825782776, 0.03480813279747963, 0.007302524987608194, 0.06192820891737938, 0.008394794538617134, 0.022382037714123726, 0.9867292642593384, 0.996852457523346 ], [ 0.012457769364118576, 0.019273553043603897, 0.30775997042655945, 0.10353484004735947, 0.029324525967240334, 0.04680981487035751, 0.041537173092365265, 0.04198557138442993, 0.026706693693995476, 0.12312103807926178, 0.08283029496669769, 0.31884872913360596, 0.013916872441768646, 0.03470404073596001, 0.005138338543474674 ], [ 0.2160782366991043, 0.025525404140353203, 0.030225040391087532, 0.019804663956165314, 0.0792558565735817, 0.043790027499198914, 0.08556238561868668, 0.009674884378910065, 0.033644899725914, 0.01257307454943657, 0.0550713837146759, 0.017708366736769676, 0.011483748443424702, 0.0015134996501728892, 0.40336498618125916, 0.9924964904785156 ], [ 0.2160767912864685, 0.0255256500095129, 0.03158504515886307, 0.027086665853857994, 0.08753874152898788, 0.058951061218976974, 0.06320270895957947, 0.004532752092927694, 0.0634300485253334, 0.11559129506349564, 0.1595062017440796, 0.010498053394258022, 0.9817326664924622, 0.9950746893882751 ], [ 0.27247294783592224, 0.022314120084047318, 0.005545014049857855, 0.023466065526008606, 0.007048009894788265, 0.022075291723012924, 0.03406887128949165, 0.03391522541642189, 0.05267767608165741, 0.027198009192943573, 0.05700625106692314, 0.1550437957048416, 0.05644826591014862, 0.0196093562990427 ], [ 0.20185431838035583, 0.026590613648295403, 0.03386501222848892, 0.03073817491531372, 0.106969453394413, 0.04142756760120392, 0.09223723411560059, 0.027021221816539764, 0.036503154784440994, 0.010137844830751419, 0.0914713442325592, 0.10131543129682541, 0.006295502185821533, 0.06259793788194656, 0.9832831621170044, 0.9948070645332336 ], [ 0.2643546760082245, 0.012725931592285633, 0.005054575856775045, 0.026877738535404205, 0.02485848218202591, 0.17154891788959503, 0.14421498775482178, 0.02164820022881031, 0.015461158938705921, 0.4250674545764923, 0.2905585467815399 ] ] }, { "q_id": "9404_mmlu_physics", "cot_ids": [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15 ], "rewards": [ [ 0.9416717886924744, 0.14257419109344482, 0.7151188254356384, 0.0042484225705266 ], [ 0.9770612120628357, 0.21353569626808167, 0.3077438175678253, 0.48618215322494507, 0.9995275735855103, 0.9997256398200989 ], [ 0.9319882392883301, 0.5332580208778381, 0.5405092835426331, 0.1863950490951538, 0.9976503252983093, 0.9985058307647705 ], [ 0.9416709542274475, 0.15964709222316742, 0.3775753974914551, 0.2941884398460388, 0.6959558725357056, 0.00294968718662858 ], [ 0.941670298576355, 0.3904931843280792, 0.07311639189720154, 0.07718602567911148, 0.06757886707782745, 0.04711819067597389, 0.07961463183164597, 0.15662434697151184, 0.1222170740365982, 0.028793346136808395 ], [ 0.9319875240325928, 0.696857213973999, 0.4259970784187317, 0.9512758255004883, 0.0027854458894580603 ], [ 0.9319875240325928, 0.2622561454772949, 0.19501636922359467, 0.998534083366394, 0.9990412592887878 ], [ 0.9337870478630066, 0.16230203211307526, 0.6929121613502502, 0.0027291777078062296 ], [ 0.9326401948928833, 0.6310349106788635, 0.18738901615142822, 0.38747528195381165, 0.22044460475444794, 0.9985394477844238, 0.9991569519042969 ], [ 0.9310681223869324, 0.243724524974823, 0.3060259521007538, 0.9993983507156372, 0.9996211528778076 ], [ 0.941670835018158, 0.1412249058485031, 0.638020396232605, 0.004473352804780006 ], [ 0.9416712522506714, 0.25906485319137573, 0.19568781554698944, 0.9982215762138367, 0.9994083642959595 ], [ 0.9326401948928833, 0.5859531164169312, 0.18427695333957672, 0.2797991931438446, 0.99872225522995, 0.9993999004364014 ] ] }, { "q_id": "9939_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.17661736905574799, 0.055385395884513855, 0.9598015546798706, 0.9975270628929138 ], [ 0.6172390580177307, 0.07810325920581818, 0.30993929505348206, 0.05472390726208687, 0.9837707281112671, 0.9985675811767578 ], [ 0.5261013507843018, 0.17332817614078522, 0.07819566130638123, 0.9918894171714783, 0.9991724491119385 ], [ 0.5260976552963257, 0.04750745743513107, 0.3497714698314667, 0.06334911286830902, 0.9840348958969116, 0.9988962411880493 ], [ 0.5260987281799316, 0.04750732332468033, 0.09513653069734573, 0.7573127746582031, 0.7076082229614258, 0.9981921315193176 ], [ 0.7003049850463867, 0.08561161160469055, 0.2579781413078308, 0.10061600804328918, 0.9937612414360046, 0.9993127584457397 ], [ 0.7175858616828918, 0.052476443350315094, 0.06441847234964371, 0.014843798242509365, 0.0017386317485943437 ], [ 0.7036712765693665, 0.13713166117668152, 0.0685342326760292, 0.9673410058021545, 0.9985431432723999 ], [ 0.5260990858078003, 0.055634044110774994, 0.13803929090499878, 0.6474919319152832, 0.9322099685668945, 0.9974517226219177, 0.9993482232093811 ], [ 0.6027393341064453, 0.048121657222509384, 0.05542562156915665, 0.16588719189167023, 0.9741312861442566, 0.9989516735076904 ], [ 0.5389500856399536, 0.08349118381738663, 0.08967488259077072, 0.1357395052909851, 0.9239475131034851, 0.9979069232940674, 0.999370276927948 ], [ 0.5331947803497314, 0.029308324679732323, 0.19012543559074402, 0.04960617050528526, 0.05341237038373947, 0.9979628324508667, 0.9994688630104065 ], [ 0.7573356032371521, 0.05759703367948532, 0.9960154891014099, 0.9993426203727722 ], [ 0.7573351860046387, 0.060316722840070724, 0.10007542371749878, 0.022188551723957062, 0.9972323775291443, 0.9991699457168579 ], [ 0.6574417948722839, 0.04157707840204239, 0.34845414757728577, 0.9911839962005615, 0.9988623857498169 ], [ 0.6799519658088684, 0.07964488863945007, 0.07469698041677475, 0.020999955013394356, 0.0018018219852820039 ] ] }, { "q_id": "9224_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14 ], "rewards": [ [ 0.026441115885972977, 0.03738242760300636, 0.016904545947909355, 0.0011834437027573586 ], [ 0.12201280146837234, 0.21972499787807465, 0.0009673762251622975, 0.1368386447429657, 0.062276024371385574, 0.2985084652900696, 0.002683571306988597, 0.0010495554888620973 ], [ 0.13075251877307892, 0.15415409207344055, 0.3256193697452545, 0.06314003467559814, 0.06940308958292007, 0.06435249000787735, 0.3616744577884674, 0.04769284278154373, 0.10787695646286011, 0.006630997639149427 ], [ 0.1345282644033432, 0.15902824699878693, 0.1887454241514206, 0.03446536511182785, 0.9680812358856201, 0.9953071475028992 ], [ 0.18239174783229828, 0.01127096638083458, 0.008852779865264893 ], [ 0.13075263798236847, 0.061497725546360016, 0.0013299330603331327, 0.02812986634671688, 0.031734153628349304, 0.12313004583120346, 0.051457345485687256, 0.018388349562883377, 0.11384948343038559, 0.031406644731760025, 0.09232986718416214, 0.15897798538208008, 0.012272431515157223, 0.021425360813736916, 0.01936095952987671 ], [ 0.045880258083343506, 0.02121799997985363, 0.03152310103178024, 0.03649274259805679, 0.07186755537986755, 0.02555263787508011 ], [ 0.13075263798236847, 0.11574835330247879, 0.07684547454118729, 0.060918085277080536, 0.14659865200519562, 0.07027923315763474, 0.005156241357326508 ], [ 0.13075409829616547, 0.11056560277938843, 0.1019623726606369, 0.05588198080658913, 0.15991556644439697, 0.01018090546131134, 0.1390978842973709, 0.13716235756874084, 0.03741799667477608, 0.09602735936641693, 0.9887064695358276, 0.9970070719718933 ], [ 0.12845706939697266, 0.4571034610271454, 0.13077755272388458, 0.15498170256614685, 0.028325963765382767, 0.027414949610829353, 0.00520728062838316 ], [ 0.13075409829616547, 0.09034739434719086, 0.07402264326810837, 0.0497172586619854, 0.13380347192287445, 0.037138454616069794, 0.05172402411699295, 0.005416703876107931, 0.12375684082508087, 0.2429642677307129, 0.337638795375824, 0.002401451114565134 ], [ 0.12023156136274338, 0.11580702662467957, 0.10263774544000626, 0.07165029644966125, 0.1702924221754074, 0.0791444405913353, 0.055392585694789886, 0.14998091757297516, 0.10454639792442322, 0.17663012444972992, 0.1294432282447815, 0.03371436521410942, 0.013546713627874851 ], [ 0.2048984169960022, 0.015822606161236763, 0.11222485452890396, 0.0005042931297793984, 0.10546942800283432, 0.06501418352127075, 0.13284704089164734, 0.0023086261935532093, 0.0269822608679533, 0.5954472422599792, 0.8233489990234375, 0.15326125919818878 ], [ 0.207235649228096, 0.22592464089393616, 0.15158404409885406, 0.15884427726268768, 0.027603862807154655, 0.03378666937351227, 0.005969115532934666 ] ] }, { "q_id": "9614_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.3459581434726715, 0.10159771889448166, 0.3020916283130646, 0.04656459018588066, 0.023992789909243584, 0.005539757199585438 ], [ 0.29976949095726013, 0.010180390439927578, 0.1068878099322319, 0.003488194430246949, 0.01220429316163063, 0.02796170860528946, 0.056231435388326645, 0.061298150569200516, 0.3837197721004486, 0.05649920925498009, 0.11211682111024857, 0.04900619015097618, 0.39886346459388733, 0.02393716759979725, 0.013079560361802578 ], [ 0.13167710602283478, 0.0008156235562637448, 0.015070830471813679, 0.0033753816969692707, 0.05171903967857361, 0.08845366537570953, 0.0016763355815783143, 0.04495219513773918, 0.016213372349739075, 0.36407536268234253, 0.034656912088394165, 0.01226687803864479 ], [ 0.13167768716812134, 0.028917495161294937, 0.007522372528910637, 0.03292899951338768, 0.0010556172346696258, 0.2873852550983429, 0.0010182211408391595, 0.3911626636981964, 0.08839432150125504, 0.17723412811756134, 0.3896399736404419, 0.003681575646623969, 0.3333336412906647, 0.943450391292572, 0.017951130867004395 ], [ 0.2964901030063629, 0.07592205703258514, 0.2360938936471939, 0.006512749008834362, 0.15296509861946106, 0.04439684748649597, 0.29892927408218384, 0.011623737402260303, 0.004769180901348591 ], [ 0.13167987763881683, 0.009799146093428135, 0.01652822457253933, 0.051309216767549515, 0.021419711410999298, 0.016976743936538696, 0.2106831967830658, 0.02428542636334896, 0.06133514642715454, 0.13024728000164032, 0.018696611747145653, 0.039047952741384506, 0.30680766701698303, 0.0015068149659782648, 0.39785388112068176, 0.14702163636684418, 0.2009516954421997, 0.026917839422822, 0.012209484353661537 ], [ 0.13167768716812134, 0.011590750887989998, 0.017295140773057938, 0.045750826597213745, 0.03404320776462555, 0.03192637488245964, 0.027824681252241135, 0.06621495634317398, 0.012029675766825676, 0.08163319528102875, 0.2575884759426117, 0.5018339157104492, 0.022221757099032402, 0.03138205409049988, 0.3727377653121948, 0.0022046787198632956, 0.000904708809684962, 0.1450730264186859, 0.27703335881233215, 0.7782326340675354 ], [ 0.1316790133714676, 0.0011654779082164168, 0.02868841588497162, 0.002179910195991397, 0.015955880284309387, 0.2679082453250885, 0.002689705230295658, 0.06464553624391556, 0.023439254611730576, 0.836681604385376, 0.0003237157070543617, 0.9807108044624329, 0.9875620603561401 ], [ 0.1316790133714676, 0.028073346242308617, 0.01730155572295189, 0.07590559124946594, 0.001399880857206881, 0.299925833940506, 0.022904060781002045, 0.3713645935058594, 0.10742861032485962, 0.3029578924179077, 0.054660964757204056, 0.013408414088189602 ], [ 0.13167928159236908, 0.019337361678481102, 0.04599722474813461, 0.3530353903770447, 0.5426810383796692, 0.18711622059345245, 0.6343754529953003 ], [ 0.3686564564704895, 0.07903289049863815, 0.4081155061721802, 0.1871330440044403, 0.04837662726640701, 0.02335590310394764 ], [ 0.13167880475521088, 0.01150333322584629, 0.1121659204363823, 0.037403654307127, 0.17712152004241943, 0.15759752690792084, 0.6589621305465698, 0.7406969666481018 ], [ 0.13167792558670044, 0.0015858398983255029, 0.011899632401764393, 0.0020082369446754456, 0.005511714145541191, 0.011049753054976463, 0.0005791497533209622, 0.20088554918766022, 0.05538177862763405, 0.031046973541378975, 0.1398303210735321, 0.8253303170204163, 0.008795165456831455 ], [ 0.13167934119701385, 0.0065601896494627, 0.007069721352308989, 0.03874276578426361, 0.0004475019813980907, 0.10462624579668045, 0.033116698265075684, 0.02372118830680847, 0.023142067715525627, 0.001620573690161109, 0.03813473507761955, 0.012709890492260456, 0.07110012322664261, 0.356921523809433, 0.03962936997413635, 0.6873605251312256, 0.002292061923071742 ], [ 0.1316773146390915, 0.020100675523281097, 0.026580100879073143, 0.028696579858660698, 0.0967971459031105, 0.11146094650030136, 0.32179126143455505, 0.05296890437602997, 0.01873880997300148, 0.24109308421611786, 0.0007482967339456081, 0.09619366377592087, 0.02486877329647541, 0.013704563491046429 ] ] }, { "q_id": "9911_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9927365779876709, 0.3267390727996826, 0.07893933355808258, 0.11680208146572113, 0.9776546359062195, 0.8210737109184265 ], [ 0.9473927021026611, 0.8330520987510681, 0.9816856384277344, 0.01871926710009575, 0.0006127063534222543 ], [ 0.9962170720100403, 0.6028274297714233, 0.06436294317245483, 0.35451173782348633, 0.0038739428855478764 ], [ 0.9967049956321716, 0.05455273017287254, 0.05866112560033798, 0.04973987862467766, 0.13267070055007935, 0.018431425094604492, 0.0008667897200211883, 0.0011537149548530579 ], [ 0.9966642260551453, 0.5898409485816956, 0.33884596824645996, 0.05591431260108948, 0.9835113286972046, 0.0010233825305476785 ], [ 0.9851598143577576, 0.9728690385818481, 0.16363145411014557, 0.11643160134553909, 0.0791906788945198, 0.08762554079294205, 0.7672540545463562, 0.16560965776443481 ], [ 0.9921802282333374, 0.3950240910053253, 0.10046219825744629, 0.06270034611225128, 0.0006596124148927629 ], [ 0.9962286949157715, 0.7673599123954773, 0.008481168188154697, 0.00054279895266518 ], [ 0.9846166372299194, 0.9348498582839966, 0.7918009161949158, 0.01657978445291519, 0.0005077137611806393 ], [ 0.9966642260551453, 0.7122995257377625, 0.016816627234220505, 0.0005469432799145579 ], [ 0.9961546063423157, 0.6530531048774719, 0.013144650496542454, 0.000585319590754807 ], [ 0.9961546063423157, 0.47864747047424316, 0.048858821392059326, 0.049637433141469955, 0.44147592782974243, 0.2235359251499176 ], [ 0.9966642260551453, 0.9761456251144409, 0.0171901173889637, 0.0005547870532609522 ], [ 0.9949285984039307, 0.06086214259266853, 0.10062093287706375, 0.1066446527838707, 0.9842150807380676 ], [ 0.9710729718208313, 0.8783941864967346, 0.28822240233421326, 0.15576867759227753, 0.07760287821292877, 0.981661856174469, 0.05746346712112427 ], [ 0.9957472681999207, 0.8679688572883606, 0.05475464463233948, 0.00040849499055184424 ] ] }, { "q_id": "9206_mmlu_physics", "cot_ids": [ 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.2810358703136444, 0.1422351598739624, 0.08039028197526932, 0.24643592536449432, 0.18285797536373138, 0.7320594787597656, 0.8319501876831055, 0.0034699272364377975 ], [ 0.18729303777217865, 0.09323809295892715, 0.1050475686788559, 0.17447826266288757, 0.03723447397351265, 0.6487389206886292, 0.032041650265455246, 0.28314197063446045, 0.11220266669988632, 0.9969488978385925 ], [ 0.39831307530403137, 0.1632959395647049, 0.3285900354385376, 0.07064357399940491, 0.16577304899692535, 0.48767244815826416, 0.03960784897208214, 0.7263562083244324, 0.3113974332809448, 0.023722467944025993, 0.021225132048130035, 0.5367258787155151, 0.005602832417935133 ], [ 0.14052779972553253, 0.06256820261478424, 0.050341326743364334, 0.27881601452827454, 0.47990545630455017, 0.001972290687263012, 0.04482172802090645, 0.9748266935348511, 0.9983686804771423 ], [ 0.28103363513946533, 0.14015153050422668, 0.1064152717590332, 0.06900603324174881, 0.11198887228965759, 0.13362053036689758, 0.048393573611974716, 0.06092049181461334, 0.04119814559817314, 0.5789922475814819, 0.015323253348469734, 0.017736291512846947, 0.5815265774726868, 0.12009989470243454, 0.1277853101491928, 0.003374264342710376 ], [ 0.13585644960403442, 0.02946215495467186, 0.030225109308958054, 0.05396494269371033, 0.05884307250380516, 0.01663067750632763, 0.002447964856401086 ], [ 0.04418271780014038, 0.1863093078136444, 0.13881534337997437, 0.2335600107908249, 0.09560738503932953, 0.022752411663532257, 0.0988926962018013, 0.9482417106628418, 0.0027594587299972773 ], [ 0.14691637456417084, 0.10062067210674286, 0.6123482584953308, 0.1234961524605751, 0.014166299253702164, 0.0023123896680772305 ], [ 0.021835297346115112, 0.01524741854518652, 0.7164060473442078, 0.003674453590065241, 0.5863743424415588, 0.09232711046934128, 0.8453794121742249, 0.004867680836468935, 0.7631562352180481, 0.0038119941018521786 ], [ 0.031810637563467026, 0.10713741928339005, 0.3311953544616699, 0.048438917845487595, 0.05090080946683884, 0.09633304923772812, 0.25781452655792236, 0.03409181535243988, 0.8750374913215637, 0.057124845683574677, 0.018667299300432205, 0.34304508566856384, 0.9955138564109802, 0.9987167119979858 ], [ 0.03528748080134392, 0.03255713731050491, 0.6570223569869995, 0.028918351978063583, 0.6136174201965332, 0.01603960618376732, 0.03913348168134689, 0.34351933002471924, 0.0066475640051066875, 0.07449263334274292, 0.0037655786145478487 ], [ 0.03181033954024315, 0.005897307302802801, 0.041351817548274994, 0.05986877903342247, 0.02438846044242382, 0.1254452019929886, 0.17509052157402039, 0.5192270874977112, 0.052741099148988724, 0.034572940319776535, 0.05385586619377136, 0.010341095738112926, 0.732157826423645, 0.016382334753870964, 0.40915071964263916, 0.10991118848323822, 0.006147538777440786, 0.016225576400756836, 0.2168964296579361, 0.03222677484154701, 0.022426454350352287, 0.007667703088372946, 0.00013594853226095438, 0.026158872991800308, 0.9889201521873474 ], [ 0.23523283004760742, 0.2517493963241577, 0.11554820835590363, 0.6507453918457031, 0.296337366104126, 0.054685335606336594, 0.02883165143430233, 0.4178506135940552, 0.14857736229896545, 0.3098166286945343, 0.003489706665277481 ], [ 0.13175438344478607, 0.08355309069156647, 0.686705470085144, 0.17043475806713104, 0.2866872549057007, 0.0725652351975441, 0.9813024401664734, 0.0031884005293250084 ] ] }, { "q_id": "9516_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5466778874397278, 0.946690022945404, 0.9998879432678223 ], [ 0.6141335964202881, 0.8647826313972473, 0.9998303651809692 ], [ 0.6141335964202881, 0.8647826313972473, 0.9998303651809692 ], [ 0.6540903449058533, 0.9695531725883484, 0.9187583327293396, 0.45323729515075684, 0.006922504864633083, 0.7238064408302307, 0.9057682752609253, 0.9994934797286987, 0.9999550580978394 ], [ 0.840323269367218, 0.0011415471090003848, 0.5372185111045837, 0.9393408894538879, 0.2993859648704529, 0.11580150574445724, 0.9997391104698181, 0.999923825263977 ], [ 0.5813723802566528, 0.9413027763366699, 0.9557645916938782, 0.5043939352035522, 0.7441312074661255, 0.9998044371604919, 0.9999423027038574 ], [ 0.5813789963722229, 0.9490745663642883, 0.9635635614395142, 0.701348066329956, 0.996936559677124, 0.9999465942382812 ], [ 0.9194260835647583, 0.41706883907318115, 0.7856505513191223, 0.36664268374443054, 0.9995933175086975, 0.9999459981918335 ], [ 0.8403225541114807, 0.015719328075647354, 0.6887436509132385, 0.9461066126823425, 0.19474844634532928, 0.3933347165584564, 0.35039252042770386, 0.9999151229858398 ], [ 0.6141293048858643, 0.85802161693573, 0.7526888251304626, 0.6434409618377686, 0.9997904896736145, 0.9999401569366455 ], [ 0.6540896892547607, 0.7728302478790283, 0.6158625483512878, 0.36283954977989197, 0.0068307057954370975, 0.7289485931396484, 0.9998683929443359, 0.9999481439590454 ], [ 0.9860625863075256, 0.9948269724845886, 0.9998574256896973 ], [ 0.5813760757446289, 0.7512755393981934, 0.8202547430992126, 0.654430091381073, 0.9998617172241211 ], [ 0.9937129616737366, 0.9994756579399109, 0.9998971223831177 ], [ 0.8530811667442322, 0.005733831319957972, 0.5521050095558167, 0.73243647813797, 0.31625479459762573, 0.24088531732559204, 0.9990283250808716, 0.9999396800994873 ], [ 0.8750552535057068, 0.0010919017950072885, 0.9271724224090576, 5.620859519694932e-05, 0.3038021922111511, 0.9997296929359436, 0.9999520778656006 ] ] }, { "q_id": "9411_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4626888036727905, 0.00038775178836658597, 0.35005006194114685, 0.030897876247763634, 0.16129648685455322, 0.01089627668261528, 0.9843077063560486, 0.9970133304595947 ], [ 0.4626833200454712, 0.017827868461608887, 0.5473182797431946, 0.10109558701515198, 0.16129598021507263, 0.29155316948890686, 0.0597325898706913, 0.9848227500915527, 0.9974164962768555 ], [ 0.468484491109848, 0.00044820259790867567, 0.32621151208877563, 0.0022871829569339752, 0.13503658771514893, 0.00825427658855915, 0.2336868792772293, 0.008472622372210026, 0.9979998469352722, 0.9998093247413635 ], [ 0.46848487854003906, 0.018773289397358894, 0.5924538373947144, 0.09079557657241821, 0.1737203449010849, 0.0006960757309570909, 0.35409653186798096, 0.06039401516318321, 0.9848533868789673, 0.9974856376647949 ], [ 0.46848568320274353, 0.0004482030344661325, 0.7049930691719055, 0.021282583475112915, 0.0405927374958992, 0.9785929918289185, 0.9953521490097046 ], [ 0.462687611579895, 0.0003877576964441687, 0.35004764795303345, 0.005172137636691332, 0.12720142304897308, 0.015680421143770218, 0.07070232182741165, 0.26704421639442444, 0.009170121513307095, 0.9776309132575989, 0.9940335154533386 ], [ 0.05943960323929787, 0.037263303995132446, 0.767192542552948, 0.08931933343410492, 0.9984946250915527, 0.9998262524604797 ], [ 0.6477566361427307, 0.593899130821228, 0.08015293627977371, 0.22979232668876648, 0.3666156530380249, 0.08153396099805832, 0.987644374370575, 0.9978505373001099 ], [ 0.8314526677131653, 0.05169752612709999, 0.8907641768455505, 0.11005920171737671, 0.2458714097738266, 0.4593655467033386, 0.050795964896678925, 0.9849637150764465, 0.9974314570426941 ], [ 0.46268606185913086, 0.019374417141079903, 0.673101544380188, 0.09872645884752274, 0.15170501172542572, 0.0007383275660686195, 0.30951347947120667, 0.06269089877605438, 0.9861544966697693, 0.9972178936004639 ], [ 0.4684849679470062, 0.017301004379987717, 0.5804636478424072, 0.10811877250671387, 0.14584970474243164, 0.3244266211986542, 0.06462171673774719, 0.9859495759010315, 0.9972981810569763 ], [ 0.5343125462532043, 0.08818172663450241, 0.13093380630016327, 0.03153623268008232, 0.8428491353988647, 0.08594536036252975, 0.9869487285614014, 0.9978594183921814 ], [ 0.46268215775489807, 0.0003877544077113271, 0.3500469923019409, 0.03321252018213272, 0.058572448790073395, 0.010640003718435764, 0.9848400950431824, 0.9967073202133179 ], [ 0.46848440170288086, 0.0005537610850296915, 0.905430018901825, 0.01598539762198925, 0.06997109204530716, 0.5358530282974243, 0.013351831585168839, 0.028967225924134254, 0.001028939033858478 ], [ 0.46268296241760254, 0.017827918753027916, 0.5473189949989319, 0.1010957658290863, 0.1612977832555771, 0.2915512025356293, 0.049924585968256, 0.9847812652587891, 0.9974367022514343 ], [ 0.46268442273139954, 0.0003877566196024418, 0.3500446379184723, 0.03089727647602558, 0.16444464027881622, 0.010432555340230465, 0.984376072883606, 0.9970697164535522 ] ] }, { "q_id": "9461_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4124690294265747, 0.011970078572630882, 0.09327095001935959, 0.16870911419391632, 0.02183636836707592, 0.025733502581715584, 0.003967626020312309, 0.997736930847168, 0.9999172687530518 ], [ 0.9112352728843689, 0.3136705160140991, 0.024718856438994408, 0.9973794221878052, 0.9999046325683594 ], [ 0.6494573354721069, 0.1268262416124344, 0.20947520434856415, 0.03827209770679474, 0.010704356245696545, 0.1539020836353302, 0.9998598098754883 ], [ 0.9112361073493958, 0.06075987219810486, 0.29895955324172974, 0.03712817654013634, 0.04760369658470154, 0.1929219514131546, 0.9998935461044312 ], [ 0.8985586166381836, 0.04574931040406227, 0.0819016695022583, 0.3411448299884796, 0.02487357147037983, 0.031795527786016464, 0.006672950461506844, 0.9974552989006042, 0.999923825263977 ], [ 0.8670691847801208, 0.37344446778297424, 0.0868690088391304, 0.236673504114151, 0.04698014631867409, 0.07897037267684937, 0.11856568604707718, 0.9998258948326111 ], [ 0.9112343788146973, 0.06845072656869888, 0.11323200166225433, 0.16705134510993958, 0.032205987721681595, 0.026432916522026062, 0.11793266981840134, 0.9998553991317749 ], [ 0.971315860748291, 0.30517351627349854, 0.4227150082588196, 0.0005552687216550112 ], [ 0.8739936947822571, 0.36535218358039856, 0.046360474079847336, 0.07229677587747574, 0.2106441706418991, 0.01694844663143158, 0.04094430059194565, 0.06413520127534866, 0.07055184245109558, 0.3496828079223633, 0.999913215637207 ], [ 0.8670695424079895, 0.3293760120868683, 0.2713695466518402, 0.03009258396923542, 0.022378208115696907, 0.04539475589990616, 0.053121935576200485, 0.9959277510643005, 0.9999169111251831 ], [ 0.867068886756897, 0.32259300351142883, 0.07075109332799911, 0.19682665169239044, 0.23204781115055084, 0.045468997210264206, 0.019233323633670807, 0.016601279377937317, 0.9977741837501526, 0.9999128580093384 ], [ 0.7283871173858643, 0.32601040601730347, 0.09240090101957321, 0.9998323917388916 ], [ 0.667193591594696, 0.10432203859090805, 0.023668702691793442, 0.05636487156152725, 0.19790488481521606, 0.016420025378465652, 0.05476975068449974, 0.009985441341996193, 0.13444297015666962, 0.1032525897026062, 0.997313916683197, 0.9999417066574097 ], [ 0.7080978751182556, 0.4378024935722351, 0.2933540940284729, 0.026456180959939957, 0.019825806841254234, 0.5615702271461487, 0.999859094619751 ], [ 0.7889230847358704, 0.29378098249435425, 0.024048974737524986, 0.028973599895834923, 0.9969618916511536, 0.9999288320541382 ], [ 0.951783299446106, 0.07654677331447601, 0.0941593274474144, 0.00040648647700436413, 0.18627700209617615, 0.017099086195230484, 0.04854859411716461, 0.16104218363761902, 0.9999058246612549 ] ] }, { "q_id": "10143_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15 ], "rewards": [ [ 0.3978842794895172, 0.1839248538017273, 0.63707435131073, 0.0005798846832476556, 0.05088137090206146, 0.0067333620972931385, 0.014950552955269814, 0.16314080357551575, 0.03909415751695633, 0.0014515380607917905 ], [ 0.10463616251945496, 0.03935643658041954, 0.047499578446149826, 0.05166506767272949, 0.00589497946202755, 0.03494354337453842, 0.03176877647638321, 0.19397693872451782, 0.002834273036569357 ], [ 0.10463589429855347, 0.04506034031510353, 0.051340702921152115, 0.00044896031613461673, 0.1817619502544403, 0.006576471030712128, 0.0784418061375618, 0.027683237567543983, 0.0008610031800344586 ], [ 0.3201155960559845, 0.04717978462576866, 0.00042697504977695644, 0.09279490262269974, 0.008006486110389233, 0.05758577212691307, 0.0816899761557579, 0.06757502257823944, 0.10210046172142029, 0.23434872925281525, 0.005259275436401367 ], [ 0.8495842814445496, 0.014623363502323627, 0.01857064664363861, 0.04190355911850929, 0.0014641915913671255, 0.05088229849934578, 0.005864100996404886, 0.0404888354241848, 0.011347202584147453, 0.06081004440784454, 0.052528396248817444, 0.0658508911728859, 0.0377766452729702, 0.053092800080776215, 0.0011466427240520716 ], [ 0.42380812764167786, 0.015352599322795868, 0.00014769757399335504, 0.052570149302482605, 0.007478244602680206, 0.061422090977430344, 0.04646628722548485, 0.06891924142837524, 0.08899015933275223, 0.031019655987620354, 0.060917679220438004, 0.01571161299943924 ], [ 0.3493907153606415, 0.07261679321527481, 0.00033442425774410367, 0.014282806776463985, 0.10325939208269119, 0.027532454580068588, 0.008226217702031136, 0.34568390250205994, 0.01844736374914646, 0.026113880798220634, 0.08842381089925766, 0.0017998797120526433 ], [ 0.32011178135871887, 0.06390425562858582, 0.07068678736686707, 0.6028593182563782, 0.00647276546806097, 0.04534931853413582, 0.07212129235267639, 0.11054787784814835, 0.003249489003792405 ], [ 0.10463643074035645, 0.04543192312121391, 0.0003318925155326724, 0.05284194275736809, 0.00034620967926457524, 0.03514948859810829, 0.006087796296924353, 0.02136465162038803, 0.002287741284817457 ], [ 0.10463643074035645, 0.049382299184799194, 0.23037992417812347, 0.029690710827708244, 0.006921472027897835, 0.12810172140598297, 0.004150796215981245, 0.0017940268153324723 ], [ 0.11934493482112885, 0.05964071303606033, 0.0003410624631214887, 0.08219899982213974, 0.006789359729737043, 0.06233084201812744, 0.03310251608490944, 0.0008005228592082858 ], [ 0.3303605318069458, 0.09291310608386993, 0.013217566534876823, 0.0695248693227768, 0.04916686564683914, 0.14965268969535828, 0.11437688022851944, 0.04021303355693817, 0.005070458631962538 ], [ 0.09710907936096191, 0.0007749596261419356, 0.0589325986802578, 0.0015320064267143607, 0.03305931016802788, 0.11849123984575272, 0.30597665905952454, 0.012151972390711308, 0.001632346073165536 ], [ 0.32829585671424866, 0.060112643986940384, 0.0002470012695994228, 0.06069864705204964, 0.11606208980083466, 0.009812133386731148, 0.050794634968042374, 0.05265357717871666, 0.02363339066505432, 0.002222206676378846 ] ] }, { "q_id": "9796_mmlu_physics", "cot_ids": [ 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.12810412049293518, 0.10063356906175613, 0.07919991761445999, 0.06418943405151367, 0.0006099037127569318 ], [ 0.1351122409105301, 0.03051825985312462, 0.1036996841430664, 0.11905050277709961, 0.0005452090408653021 ], [ 0.17442861199378967, 0.015618733130395412, 0.03670777380466461, 0.06025456264615059, 0.0871976912021637, 0.0006271597230806947 ], [ 0.12622585892677307, 0.029065074399113655, 0.04367564618587494, 0.000507134071085602, 0.027226269245147705, 0.3892170786857605, 0.0004770844825543463 ], [ 0.14988233149051666, 0.02399348095059395, 0.07591686397790909, 0.0005996607942506671 ], [ 0.17195725440979004, 0.010105080902576447, 0.03665592893958092, 0.015601638704538345, 0.013706807047128677, 0.0210894662886858, 0.13807092607021332 ], [ 0.15736694633960724, 0.0030969795770943165, 0.06805218756198883, 0.03849603235721588, 0.09325683861970901, 0.16406524181365967, 0.014144678600132465 ], [ 0.1771954596042633, 0.03413156792521477, 0.01998400315642357, 0.06535990536212921, 0.02523314766585827 ], [ 0.07282797992229462, 0.03506620600819588, 0.024536870419979095, 0.026742910966277122, 0.0007398492889478803, 0.029712148010730743, 0.05569399893283844, 0.10390578210353851 ], [ 0.17188400030136108, 0.014099237509071827, 0.020000943914055824, 0.0005191368982195854 ], [ 0.18999353051185608, 0.048855677247047424, 0.05628596991300583, 0.04549820348620415, 0.01831580139696598, 0.131376713514328, 0.00041678716661408544 ], [ 0.174428328871727, 0.07698655128479004, 0.10467525571584702, 0.00046576306340284646 ], [ 0.3113817572593689, 0.05545928701758385, 0.1970556080341339, 0.0005043750861659646 ], [ 0.10559559613466263, 0.006104759406298399, 0.06714941561222076, 0.05252017825841904, 0.01788325421512127, 0.05714896693825722, 0.34688034653663635, 0.11761339753866196 ], [ 0.15736636519432068, 0.014478758908808231, 0.14578557014465332, 0.07859979569911957, 0.06815149635076523, 0.0005932188942097127 ] ] }, { "q_id": "9710_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9217544794082642, 0.4289562702178955, 0.9965819716453552, 0.007192340213805437 ], [ 0.6467812061309814, 0.8413758277893066, 0.891495406627655, 0.5173607468605042, 0.10539239645004272, 0.3059690296649933, 0.003621714422479272 ], [ 0.9217545390129089, 0.39711982011795044, 0.9857433438301086, 0.006634833291172981 ], [ 0.307513564825058, 0.7800887823104858, 0.504761815071106, 0.9912137389183044, 0.010365578345954418 ], [ 0.5191293358802795, 0.5882786512374878, 0.32780739665031433, 0.007335382048040628, 0.5887377858161926, 0.12298818677663803, 0.04308594390749931, 0.009041095152497292 ], [ 0.9079287648200989, 0.36150825023651123, 0.9961484670639038, 0.006515976972877979 ], [ 0.5535487532615662, 0.6092858910560608, 0.0005649756640195847, 0.9700837135314941, 0.2611595690250397, 0.9825676083564758, 0.004190549254417419 ], [ 0.7008001804351807, 0.8126937747001648, 0.8782175183296204, 0.48470115661621094, 0.13621124625205994, 0.959276020526886, 0.006919224280864 ], [ 0.30751538276672363, 0.6259334087371826, 0.35555973649024963, 0.012080770917236805, 0.5718428492546082, 0.041311949491500854, 0.1948750913143158, 0.011252500116825104 ], [ 0.7303717732429504, 0.023687830194830894, 0.41911548376083374, 0.9810342192649841, 0.17879718542099, 0.08834949135780334, 0.004589722491800785 ], [ 0.9589797258377075, 0.3724859058856964, 0.997565746307373, 0.0056281909346580505 ], [ 0.8179625868797302, 0.027536705136299133, 0.3424138128757477, 0.9774752855300903, 0.17756660282611847, 0.975975751876831, 0.004988935310393572 ], [ 0.4842708706855774, 0.5362327098846436, 0.0006260906811803579, 0.9565092325210571, 0.204595685005188, 0.987457811832428, 0.005096178501844406 ], [ 0.6988255381584167, 0.12920930981636047, 0.36421412229537964, 0.988352358341217, 0.004370300564914942 ], [ 0.4594690799713135, 0.20178788900375366, 0.9936501383781433, 0.004809394478797913 ], [ 0.9474819302558899, 0.5316925048828125, 0.9965301156044006, 0.007054085843265057 ] ] }, { "q_id": "9205_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06802823394536972, 0.0512201152741909, 0.014470180496573448, 0.030629074200987816, 0.0461890883743763, 0.02853686548769474 ], [ 0.16475018858909607, 0.005620425567030907, 0.05180652439594269, 0.0023056406062096357, 0.09088031947612762, 0.08965405076742172, 0.013622129335999489 ], [ 0.3103158473968506, 0.06740378588438034, 0.0305546373128891, 0.03410026431083679, 0.02185749262571335 ], [ 0.2922736406326294, 0.1389053761959076, 0.2718868851661682, 0.04370449110865593, 0.021512363106012344 ], [ 0.2922750413417816, 0.07443410158157349, 0.03098374791443348, 0.020694678649306297 ], [ 0.14533141255378723, 0.10661662369966507, 0.04629110172390938, 0.05666986480355263, 0.043662697076797485, 0.02028186433017254 ], [ 0.2327088862657547, 0.1565300077199936, 0.030530693009495735, 0.021144112572073936 ], [ 0.13397863507270813, 0.05138721689581871, 0.045705609023571014, 0.02601333148777485 ], [ 0.1957513839006424, 0.09822595864534378, 0.045239269733428955, 0.021751200780272484 ], [ 0.16889254748821259, 0.22015172243118286, 0.0843869224190712, 0.032739587128162384, 0.025993995368480682 ], [ 0.24177765846252441, 0.153882697224617, 0.03687965124845505, 0.02448168210685253 ], [ 0.1250637173652649, 0.37166208028793335, 0.04059799388051033, 0.01995854452252388 ], [ 0.06802835315465927, 0.07195675373077393, 0.041703470051288605, 0.049068138003349304, 0.019639618694782257 ], [ 0.37913161516189575, 0.1584426760673523, 0.09529625624418259, 0.10578498244285583, 0.031202368438243866 ], [ 0.28770095109939575, 0.05679885298013687, 0.11413034796714783, 0.4269860088825226, 0.11416220664978027, 0.027033798396587372 ], [ 0.18008708953857422, 0.1424541473388672, 0.05446653813123703, 0.029756471514701843 ] ] }, { "q_id": "9260_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.18957816064357758, 0.0745769664645195, 0.20440921187400818, 0.1269838958978653, 0.04787124693393707, 0.09173664450645447, 0.23285400867462158, 0.06455890834331512, 0.12224674224853516, 0.05364902690052986, 0.6157600283622742, 0.019432084634900093 ], [ 0.3221575915813446, 0.10571571439504623, 0.03687064349651337, 0.11570725589990616, 0.3295574188232422, 0.04912707209587097, 0.25015899538993835, 0.49084872007369995, 0.010091210715472698 ], [ 0.18989786505699158, 0.1304590106010437, 0.2881421744823456, 0.6028233170509338, 0.01128771249204874 ], [ 0.3058142364025116, 0.1202397346496582, 0.15421421825885773, 0.17147058248519897, 0.3821351230144501, 0.021403906866908073 ], [ 0.4204055368900299, 0.03747662156820297, 0.04175151512026787, 0.019370857626199722, 0.11427229642868042, 0.08624953776597977, 0.20056387782096863, 0.08903875946998596, 0.47318601608276367, 0.010767919942736626 ], [ 0.3140871226787567, 0.10109105706214905, 0.15698540210723877, 0.46546128392219543, 0.01280958391726017 ], [ 0.18957851827144623, 0.1251174658536911, 0.05731986463069916, 0.1147252544760704, 0.04517791420221329, 0.29635924100875854, 0.025667285546660423, 0.2290465533733368, 0.14798958599567413, 0.010388177819550037 ], [ 0.2598934769630432, 0.08066956698894501, 0.20280815660953522, 0.1752023845911026, 0.6989181637763977, 0.016191672533750534 ], [ 0.1895771324634552, 0.12511815130710602, 0.2613285481929779, 0.1971428543329239, 0.057368915528059006, 0.6007168889045715, 0.01046924851834774 ], [ 0.2847142815589905, 0.11774855852127075, 0.11405805498361588, 0.6048086881637573, 0.01192929595708847 ], [ 0.1696396917104721, 0.09639708697795868, 0.14798538386821747, 0.6333675980567932, 0.015225490555167198 ], [ 0.6851311922073364, 0.06189907342195511, 0.020381515845656395, 0.15039744973182678, 0.049108561128377914, 0.2822556793689728, 0.10609173774719238, 0.15427164733409882, 0.3743146061897278, 0.06103958562016487 ], [ 0.7180362343788147, 0.09465441107749939, 0.05590961128473282, 0.08034379035234451, 0.14416256546974182, 0.10274174064397812, 0.0628013089299202 ], [ 0.09787510335445404, 0.08037275820970535, 0.0359693318605423, 0.10334967821836472, 0.196431964635849, 0.35062459111213684, 0.013426057063043118 ], [ 0.18957750499248505, 0.21733824908733368, 0.11808120459318161, 0.03977680951356888, 0.05831991136074066, 0.31790563464164734, 0.5064660310745239, 0.010980888269841671 ], [ 0.1479025036096573, 0.07762482017278671, 0.1428624987602234, 0.014297643676400185, 0.011470305733382702 ] ] }, { "q_id": "10155_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4805784225463867, 0.02185816504061222, 0.04703058302402496, 0.06836038082838058, 0.030284639447927475, 0.3350215554237366, 0.05919822305440903, 0.9636211395263672, 0.029618989676237106 ], [ 0.4151870012283325, 0.05318034067749977, 0.10932421684265137, 0.1011127233505249, 0.022336551919579506, 0.08278260380029678, 0.09891016036272049, 0.035589441657066345, 0.06265890598297119, 0.015677662566304207, 0.11045213043689728, 0.05823896452784538, 0.290576696395874, 0.15093445777893066, 0.8838714361190796, 0.2609340250492096, 0.12329963594675064 ], [ 0.463655561208725, 0.0942462831735611, 0.1134665310382843, 0.3816855847835541, 0.9449778199195862, 0.9544996619224548, 0.07630692422389984 ], [ 0.6114422678947449, 0.018264422193169594, 0.03961682692170143, 0.06683391332626343, 0.3066575229167938, 0.02238699421286583, 0.9658783674240112, 0.037272967398166656 ], [ 0.3534832298755646, 0.19048957526683807, 0.08626595884561539, 0.06282912194728851, 0.42409393191337585, 0.9451041221618652, 0.3605547845363617 ], [ 0.4636572003364563, 0.08705460280179977, 0.08919355273246765, 0.9653905034065247, 0.45034050941467285, 0.04871918261051178 ], [ 0.4727573096752167, 0.11058839410543442, 0.07880371063947678, 0.2900583744049072, 0.9345453381538391, 0.986572265625, 0.03028641827404499 ], [ 0.9110402464866638, 0.29890042543411255, 0.02549363486468792 ], [ 0.3965257406234741, 0.1482444405555725, 0.1600082814693451, 0.3715696632862091, 0.6809735298156738, 0.05118629336357117 ], [ 0.5653117299079895, 0.09670446068048477, 0.10157665610313416, 0.08843351900577545, 0.9241947531700134, 0.2107636034488678, 0.10071594268083572 ], [ 0.3345906138420105, 0.15681439638137817, 0.12218276411294937, 0.07594941556453705, 0.3004285991191864, 0.8888382911682129, 0.03922928497195244 ], [ 0.15692900121212006, 0.08578044921159744, 0.05367259308695793, 0.17846235632896423, 0.029009196907281876, 0.061877258121967316, 0.017930498346686363, 0.1383068710565567, 0.13610513508319855, 0.3536454737186432, 0.16231057047843933, 0.3181554973125458, 0.08327590674161911, 0.8733575344085693, 0.20815597474575043, 0.022133581340312958 ], [ 0.561779797077179, 0.1360495239496231, 0.10713692009449005, 0.9582173228263855, 0.034831658005714417 ], [ 0.4045010209083557, 0.07382785528898239, 0.08053672313690186, 0.23116958141326904, 0.02770894393324852, 0.9381383657455444, 0.8620238304138184, 0.12347350269556046 ], [ 0.5444135069847107, 0.07987742125988007, 0.06605292856693268, 0.1953410804271698, 0.9653670191764832, 0.9018006920814514, 0.05324876308441162 ], [ 0.48058053851127625, 0.08850681781768799, 0.06447496265172958, 0.2653188705444336, 0.8894215822219849, 0.4910935163497925, 0.04265701770782471 ] ] }, { "q_id": "9503_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9949265718460083, 0.9994743466377258, 0.9988774657249451 ], [ 0.9954031705856323, 0.9993496537208557, 0.9986944794654846 ], [ 0.9953010082244873, 0.9993923902511597, 0.9987102746963501 ], [ 0.9944559931755066, 0.9991395473480225, 0.9981878399848938 ], [ 0.9954031705856323, 0.9995009899139404, 0.9986380934715271 ], [ 0.9949265718460083, 0.9993033409118652, 0.9987521171569824 ], [ 0.9954030513763428, 0.9991975426673889, 0.998515784740448 ], [ 0.9954031705856323, 0.9993036985397339, 0.9987117052078247 ], [ 0.9926705360412598, 0.8703414797782898, 0.7264041900634766, 0.9995038509368896, 0.9992185831069946 ], [ 0.9954030513763428, 0.9992098808288574, 0.9985515475273132 ], [ 0.9944559931755066, 0.9989936947822571, 0.9982832670211792 ], [ 0.9944559931755066, 0.9994698166847229, 0.9986554384231567 ], [ 0.9954031705856323, 0.999505877494812, 0.998647153377533 ], [ 0.9954030513763428, 0.9990875720977783, 0.9977905750274658 ], [ 0.9949471354484558, 0.9988879561424255, 0.9975340366363525 ], [ 0.9944561123847961, 0.999014139175415, 0.9979343414306641 ] ] }, { "q_id": "9252_mmlu_physics", "cot_ids": [ 0, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14 ], "rewards": [ [ 0.10153671354055405, 0.004002113826572895, 0.10268644988536835, 0.009008126333355904, 0.08287827670574188, 0.006558328401297331, 0.0201531033962965, 0.08526524901390076, 0.011311034671962261, 0.004089986439794302, 0.027383357286453247, 0.14595632255077362, 0.08103115111589432, 0.01593763753771782, 0.03538583591580391, 0.04620455205440521, 0.017322728410363197, 0.04916403815150261, 0.14668703079223633, 0.24715514481067657 ], [ 0.04963601380586624, 0.030547533184289932, 0.04861614480614662, 0.060902729630470276, 0.20096778869628906, 0.5610718131065369, 0.5531287789344788, 0.011122148483991623 ], [ 0.10153671354055405, 0.028157370164990425, 0.1261555552482605, 0.024822641164064407, 0.11005714535713196, 0.13099150359630585, 0.1360132098197937, 0.2953282296657562, 0.028864223510026932, 0.07100749015808105, 0.03518891707062721, 0.03707313910126686, 0.0036334500182420015 ], [ 0.034455880522727966, 0.08845051378011703, 0.2542692720890045, 0.14343146979808807, 0.24822448194026947, 0.8625745177268982, 0.008420203812420368 ], [ 0.10153748840093613, 0.008298545144498348, 0.03898017480969429, 0.04869794845581055, 0.058089181780815125, 0.061652831733226776, 0.006047017406672239, 0.034424327313899994, 0.028006963431835175, 0.034609630703926086, 0.00018493332026991993, 0.3954484462738037, 0.03991806507110596, 0.14257046580314636, 0.1448470503091812, 0.009598617441952229 ], [ 0.10153666883707047, 0.012771050445735455, 0.04684010520577431, 0.057097986340522766, 0.041042037308216095, 0.03171074762940407, 0.027745503932237625, 0.030654259026050568, 0.1096346378326416, 0.0865580290555954, 0.04977548494935036, 0.04257994890213013, 0.07559692114591599, 0.07507681101560593, 0.18538083136081696, 0.2781767249107361, 0.010465988889336586, 0.07680657505989075, 0.18390101194381714, 0.03766179457306862, 0.13331127166748047, 0.18191580474376678, 0.02815905399620533 ], [ 0.07738171517848969, 0.0775078684091568, 0.0627853274345398, 0.010186980478465557, 0.03496561944484711, 0.05517340451478958, 0.025014853104948997, 0.037392329424619675, 0.4584091901779175, 0.32833895087242126, 0.046991657465696335, 0.10089124739170074, 0.04799959808588028, 0.10570791363716125, 0.04894005134701729, 0.004171454813331366 ], [ 0.03571656718850136, 0.05532694607973099, 0.043274398893117905, 0.03888314217329025, 0.160846546292305, 0.21530184149742126, 0.02696392498910427, 0.09893544763326645, 0.05207695811986923, 0.005938974674791098, 0.021064458414912224, 0.004467124585062265 ], [ 0.09212761372327805, 0.06865387409925461, 0.09792593121528625, 0.0003629559651017189, 0.09605934470891953, 0.0066581363789737225, 0.04996266961097717, 0.02128242515027523, 0.050668563693761826, 0.12221693247556686, 0.02486511878669262, 0.07157859206199646, 0.049527864903211594, 0.003714632475748658 ], [ 0.0955701619386673, 0.0734105259180069, 0.06548719108104706, 0.06978369504213333, 0.030535858124494553, 0.058154862374067307, 0.1612977236509323, 0.30445271730422974, 0.3720152676105499, 0.037573736160993576, 0.09987495839595795, 0.09682904183864594, 0.32443729043006897, 0.07036664336919785, 0.09288622438907623, 0.07724598795175552, 0.030124681070446968, 0.04990021139383316, 0.07872737944126129, 0.038254834711551666, 0.014274430461227894 ], [ 0.0773814395070076, 0.05708328261971474, 0.05210031196475029, 0.00022736874234396964, 0.35465171933174133, 0.0022091895807534456, 0.03437574952840805, 0.04617367312312126, 0.010827703401446342, 0.03609152510762215, 0.28228437900543213, 0.04420975223183632, 0.0709763914346695, 0.2588217258453369, 0.011255912482738495, 0.01348932646214962, 0.00533899525180459 ] ] }, { "q_id": "10319_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.765081524848938, 0.0619555227458477, 0.08445005118846893, 0.04945256561040878, 0.6043758988380432, 0.002718052128329873, 0.035908300429582596, 0.07471758127212524, 0.10564545542001724, 0.011400392279028893, 0.12637461721897125, 0.023315247148275375, 0.053609080612659454, 0.9777241349220276, 0.9834389090538025 ], [ 0.9122637510299683, 0.3576674461364746, 0.902664065361023, 0.004061337094753981, 0.2911440134048462, 0.009973226115107536, 0.15129150450229645, 0.9812009930610657, 0.991592526435852 ], [ 0.6677946448326111, 0.5404757857322693, 0.7059068083763123, 0.004806546960026026, 0.13872496783733368, 0.04788852855563164, 0.15029694139957428, 0.3139776289463043, 0.8493118286132812, 0.9694368839263916 ], [ 0.6482800245285034, 0.38216373324394226, 0.0008742786594666541, 0.15635079145431519, 0.001417572028003633, 0.27518221735954285, 0.3607320189476013, 0.059373609721660614, 0.9385358691215515, 0.9649848937988281 ], [ 0.725209653377533, 0.4754454791545868, 0.6060741543769836, 0.003522854298353195, 0.1530749797821045, 0.05438445508480072, 0.14216198027133942, 0.326201856136322, 0.8855653405189514, 0.9799407124519348 ], [ 0.6482805609703064, 0.4703265130519867, 0.18465809524059296, 0.00040513055864721537, 0.2883058190345764, 0.18808168172836304, 0.25369176268577576, 0.21156013011932373, 0.11358415335416794, 0.10163994878530502, 0.08358350396156311, 0.039843592792749405, 0.12427873909473419, 0.9889267683029175 ], [ 0.7180508971214294, 0.4164751470088959, 0.0005727730458602309, 0.1861279308795929, 0.0015220621135085821, 0.1450168341398239, 0.05393340066075325, 0.09718034416437149, 0.1068929061293602, 0.046906977891922, 0.08918921649456024, 0.9820666313171387 ], [ 0.9148733019828796, 0.13707704842090607, 0.18041260540485382, 0.00031041569309309125, 0.23214341700077057, 0.0006580476765520871, 0.37630602717399597, 0.06999800354242325, 0.23064616322517395, 0.010663622990250587, 0.9292429685592651, 0.9554940462112427 ], [ 0.6900144815444946, 0.35368016362190247, 0.0006398261757567525, 0.14063651859760284, 0.0018776942742988467, 0.35637786984443665, 0.37424182891845703, 0.05266151577234268, 0.11333420872688293, 0.09286441653966904, 0.9835862517356873 ], [ 0.6903370022773743, 0.4429616928100586, 0.13747479021549225, 0.0007083481177687645, 0.3509666919708252, 0.16687101125717163, 0.27827364206314087, 0.023667646571993828, 0.9190076589584351, 0.95609450340271 ], [ 0.6894046068191528, 0.015327103435993195, 0.053628671914339066, 0.03221165016293526, 0.0002316329482709989, 0.11003061383962631, 0.0004242408904246986, 0.17740453779697418, 0.07460989058017731, 0.08255017548799515, 0.00634426437318325, 0.03920305147767067, 0.04544933885335922, 0.08891372382640839, 0.046654682606458664, 0.9856212735176086 ], [ 0.6686007380485535, 0.4368104040622711, 0.1520904004573822, 0.000725043355487287, 0.2951270341873169, 0.19607138633728027, 0.2545838952064514, 0.07374951243400574, 0.11435586959123611, 0.07689564675092697, 0.9874693155288696 ], [ 0.8438220620155334, 0.47270652651786804, 0.7132061719894409, 0.0022520979400724173, 0.14171910285949707, 0.03312817960977554, 0.03923548758029938, 0.07249017804861069, 0.06716161221265793, 0.9889441728591919, 0.9915567636489868 ], [ 0.9093113541603088, 0.13064797222614288, 0.29832983016967773, 0.0005255371797829866, 0.19646988809108734, 0.0004342337779235095, 0.288041353225708, 0.12900936603546143, 0.22913657128810883, 0.8933395147323608, 0.0009959917515516281 ], [ 0.718051016330719, 0.250521719455719, 0.000448789622168988, 0.1300380527973175, 0.0012273231986910105, 0.27004873752593994, 0.3498592674732208, 0.9424603581428528, 0.9405283331871033 ], [ 0.7252103686332703, 0.39817309379577637, 0.0009328385931439698, 0.13487191498279572, 0.0005983265582472086, 0.3562547266483307, 0.2544577419757843, 0.2811746597290039, 0.027695804834365845, 0.0624496154487133, 0.07164477556943893, 0.06696178764104843, 0.9867092370986938 ] ] }, { "q_id": "9763_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.7079681158065796, 0.9941838383674622, 0.9992119073867798 ], [ 0.9455569982528687, 0.9756566286087036, 0.9978493452072144 ], [ 0.9455569982528687, 0.9756566286087036, 0.9978493452072144 ], [ 0.5345710515975952, 0.9943568110466003, 0.9987473487854004 ], [ 0.8933470845222473, 0.9818368554115295, 0.9977262616157532 ], [ 0.9455540180206299, 0.9665318131446838, 0.9969710111618042 ], [ 0.9455525875091553, 0.9756572246551514, 0.9978494644165039 ], [ 0.9455536603927612, 0.9756563305854797, 0.9978494644165039 ], [ 0.9455536603927612, 0.9756563305854797, 0.9978494644165039 ], [ 0.9964732527732849, 0.998979389667511 ], [ 0.9360678791999817, 0.9929754734039307, 0.999153733253479 ], [ 0.9455550312995911, 0.9756566286087036, 0.9978494644165039 ], [ 0.9455550312995911, 0.9756566286087036, 0.9978494644165039 ], [ 0.7273880243301392, 0.9888024926185608, 0.9986515641212463 ], [ 0.9360694885253906, 0.9946073889732361, 0.9992284774780273 ], [ 0.7273974418640137, 0.9864417314529419, 0.9983841180801392 ] ] }, { "q_id": "9452_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9964975714683533, 0.9993796348571777, 0.9999338388442993 ], [ 0.0916009321808815, 0.0750325471162796, 0.10663075745105743, 0.31489911675453186, 0.9988914132118225, 0.9999350309371948 ], [ 0.9958977103233337, 0.9993908405303955, 0.9999275207519531 ], [ 0.9971627593040466, 0.18248513340950012, 0.3882249593734741, 0.22754502296447754, 0.999232292175293, 0.9999674558639526 ], [ 0.09037648141384125, 0.07283945381641388, 0.10736008733510971, 0.31476160883903503, 0.9988918900489807, 0.9999357461929321 ], [ 0.9956414699554443, 0.999460756778717, 0.9999336004257202 ], [ 0.9913479685783386, 0.9993813037872314, 0.9999282360076904 ], [ 0.9978747367858887, 0.9995285272598267, 0.9999431371688843 ], [ 0.9913479685783386, 0.9993634819984436, 0.9999313354492188 ], [ 0.9956187605857849, 0.9994033575057983, 0.9999263286590576 ], [ 0.9913480877876282, 0.9993340373039246, 0.9999302625656128 ], [ 0.9968656897544861, 0.9994421601295471, 0.9999350309371948 ], [ 0.9829249382019043, 0.08020772784948349, 0.23103545606136322, 0.31356191635131836, 0.19963182508945465, 0.999441921710968, 0.9999793767929077 ], [ 0.9996851682662964, 0.9999246597290039 ], [ 0.9970013499259949, 0.9994452595710754, 0.9999399185180664 ], [ 0.9956186413764954, 0.9994033575057983, 0.9999263286590576 ] ] }, { "q_id": "9500_mmlu_physics", "cot_ids": [ 3, 5, 9, 11, 12, 13, 15 ], "rewards": [ [ 0.21177375316619873, 0.13546885550022125, 0.0003681090602185577, 0.0432543084025383, 0.24078018963336945, 0.329721063375473, 0.092167429625988, 0.055145617574453354, 0.013943654485046864, 0.06770700216293335, 0.018934885039925575, 0.08788308501243591, 0.023356327787041664, 0.0056773298420012, 0.07628805190324783, 0.36976146697998047, 0.00474856561049819, 0.009677479043602943 ], [ 0.38705122470855713, 0.10920941084623337, 0.2721565067768097, 0.0254520270973444, 0.04343391954898834, 0.09028029441833496, 0.05824712663888931, 0.13357380032539368, 0.006595420651137829, 0.04627981781959534, 0.2976256310939789, 0.01656871661543846 ], [ 0.26881682872772217, 0.06433164328336716, 0.12150449305772781, 0.021693795919418335, 0.05353270471096039, 0.09989271312952042, 0.4906667470932007, 0.07437502592802048, 0.0008960544364526868 ], [ 0.38704970479011536, 0.10625722259283066, 0.1569596529006958, 0.01623232290148735, 0.03225471451878548 ], [ 0.5179605484008789, 0.257967472076416, 0.028862418606877327, 0.16228926181793213, 0.07601682096719742, 0.05049559846520424, 0.0544893853366375, 0.5853245258331299, 0.004030306823551655 ], [ 0.26892662048339844, 0.1805952787399292, 0.015295994468033314, 0.07358398288488388, 0.04025464877486229, 0.035450227558612823, 0.016745880246162415, 0.48901987075805664, 0.008293060585856438, 0.026037145406007767, 0.0199790820479393, 0.050136007368564606, 0.08211572468280792, 0.05304703116416931, 0.02424180880188942, 0.13230425119400024, 0.049922797828912735 ], [ 0.06665080040693283, 0.011698613874614239, 0.02104095183312893, 0.006086665205657482, 0.031808361411094666, 0.008668357506394386, 7.200204709079117e-05, 0.031340163201093674, 0.005313266534358263, 0.034733109176158905, 0.06048734858632088, 0.0008584775496274233, 0.0002893365453928709, 0.02778557315468788, 0.008410844951868057, 0.01734147034585476, 0.012878955341875553, 0.002023907145485282, 0.32500889897346497, 0.8366593718528748, 0.0007962836534716189 ] ] }, { "q_id": "9799_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.24130025506019592, 0.0002015545906033367, 0.12987738847732544, 0.05811052769422531, 0.06723274290561676, 0.05051179230213165, 0.0072221094742417336, 0.016076477244496346, 0.04531671106815338, 0.04071592912077904, 0.18977655470371246, 0.1018311008810997, 0.013824938796460629, 0.6545275449752808, 0.028352264314889908, 0.7106847763061523, 0.980455219745636 ], [ 0.24130165576934814, 0.02071036770939827, 0.1884959191083908, 0.023570897057652473, 0.7801970839500427, 0.9289523363113403, 0.05451813340187073 ], [ 0.2413007766008377, 0.028687115758657455, 0.05821710452437401, 0.008471646346151829, 0.8575054407119751, 0.9832035303115845 ], [ 0.2413007766008377, 0.0003334945940878242, 0.09583765268325806, 0.060856301337480545, 0.48275822401046753, 0.08159390091896057, 0.7532253861427307, 0.9803304076194763 ], [ 0.24129919707775116, 0.0003334980574436486, 0.10307758301496506, 0.05977458879351616, 0.009923339821398258, 0.02142542041838169, 0.36552536487579346, 0.02657114714384079, 0.6891406774520874, 0.7659060955047607, 0.9841256141662598 ], [ 0.24130244553089142, 0.0003334961656946689, 0.09686953574419022, 0.0639520138502121, 0.48066699504852295, 0.03354505077004433, 0.751637876033783, 0.9829890131950378 ], [ 0.24130234122276306, 0.00020155248057562858, 0.136908158659935, 0.051621999591588974, 0.06357904523611069, 0.0333140604197979, 0.004398394376039505, 0.014393161982297897, 0.02729783020913601, 0.036704469472169876, 0.2041349560022354, 0.08217285573482513, 0.02582809142768383, 0.3747149407863617, 0.07655264437198639, 0.5658758282661438, 0.9878443479537964 ], [ 0.29641950130462646, 0.10488776117563248, 0.21752947568893433, 0.8643158674240112, 0.15013368427753448, 0.9933406710624695 ], [ 0.24130025506019592, 0.0042225755751132965, 0.07080346345901489, 0.05712494999170303, 0.026115447282791138, 0.14155416190624237, 0.02041677199304104, 0.0411725789308548, 0.050776660442352295, 0.08205510675907135, 0.0029912712052464485, 0.6286453008651733, 0.9595491290092468 ], [ 0.24130025506019592, 0.0042225997895002365, 0.0665854886174202, 0.053149595856666565, 0.01919940672814846, 0.0005899384268559515, 0.07921894639730453, 0.061776965856552124, 0.008406898006796837, 0.06997785717248917, 0.047333672642707825, 0.3193800449371338, 0.08590464293956757, 0.0036779320798814297, 0.5266784429550171, 0.9705203175544739 ], [ 0.22392764687538147, 0.07587128132581711, 0.10481252521276474, 0.13824044167995453, 0.140779510140419, 0.05566015839576721, 0.6181748509407043, 0.9827387928962708 ], [ 0.24130244553089142, 0.02716255560517311, 0.11707931011915207, 0.43892374634742737, 0.013711114414036274, 0.5861296057701111, 0.9767821431159973 ], [ 0.24130000174045563, 0.004222540184855461, 0.050237543880939484, 0.04904084652662277, 0.038265813142061234, 0.025041965767741203, 0.0005848779110237956, 0.15614359080791473, 0.007848679088056087, 0.03132600337266922, 0.03205960616469383, 0.17935341596603394, 0.04421831667423248, 0.017063254490494728, 0.02288617193698883, 0.3563748896121979, 0.9775561690330505 ], [ 0.24130043387413025, 0.020710231736302376, 0.1270243525505066, 0.008708897978067398, 0.3055081069469452, 0.3934100568294525, 0.9798693656921387 ], [ 0.2413000762462616, 0.0003334987268317491, 0.09687111526727676, 0.06348508596420288, 0.45514893531799316, 0.03533877804875374, 0.8015264272689819, 0.9843944907188416 ] ] }, { "q_id": "9201_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5766149163246155, 0.3515167236328125, 0.8643082976341248, 0.6116708517074585 ], [ 0.8126940727233887, 0.5097823739051819, 0.6032587289810181, 0.7434485554695129, 0.5059844851493835 ], [ 0.7564582824707031, 0.4341393709182739, 0.4912033975124359, 0.8596701622009277, 0.25206783413887024 ], [ 0.7372027635574341, 0.34487026929855347, 0.8351837992668152, 0.15654884278774261 ], [ 0.5766130685806274, 0.24602599442005157, 0.7916097044944763, 0.05503913387656212, 0.34468746185302734 ], [ 0.7389775514602661, 0.5749853253364563, 0.8372920751571655, 0.3298243582248688 ], [ 0.5766151547431946, 0.41616925597190857, 0.8006722331047058, 0.0075981030240654945, 0.9306313991546631 ], [ 0.565737247467041, 0.34670135378837585, 0.4226509928703308, 0.8377881050109863, 0.29348477721214294 ], [ 0.7913485765457153, 0.40335315465927124, 0.9042519330978394, 0.2595440149307251 ], [ 0.824775755405426, 0.4441615343093872, 0.8279749751091003, 0.2116580456495285 ], [ 0.737201988697052, 0.41030025482177734, 0.5612776279449463, 0.833267331123352, 0.45649105310440063 ], [ 0.791350781917572, 0.13538618385791779, 0.10918138921260834, 0.9389162063598633, 0.8797773718833923 ], [ 0.7913554310798645, 0.39644792675971985, 0.42329832911491394, 0.8817419409751892, 0.7870311737060547, 0.004120687488466501 ], [ 0.7913534045219421, 0.35642194747924805, 0.49521005153656006, 0.8168222308158875, 0.48559704422950745 ], [ 0.5201065540313721, 0.10452400147914886, 0.5063040256500244, 0.8052877187728882, 0.07746472209692001 ], [ 0.8265851736068726, 0.3039568364620209, 0.5912852883338928, 0.8091903924942017, 0.45927128195762634 ] ] }, { "q_id": "9156_mmlu_physics", "cot_ids": [ 0, 4, 6, 7, 11, 13, 14 ], "rewards": [ [ 0.15052206814289093, 0.03174423426389694, 0.035318657755851746, 0.012628011405467987, 0.0452042892575264, 0.056144651025533676, 0.04938811436295509, 0.28119176626205444, 0.05803695321083069 ], [ 0.3974666893482208, 0.01604493521153927, 0.024579912424087524, 0.0006851647631265223, 0.034638673067092896, 0.000404506572522223, 0.07610772550106049, 0.03125379979610443, 0.031877730041742325, 0.030798327177762985, 0.020528316497802734, 0.013630314730107784 ], [ 0.2396671324968338, 0.0007862719357945025, 0.010879730805754662, 0.0018705754773691297, 0.006676883436739445, 0.019927311688661575, 0.03868864104151726, 0.004774648696184158, 0.03213545307517052, 0.008723610080778599, 0.026543397456407547, 0.0005224122432991862, 0.0427301749587059, 0.0020593334920704365, 0.07912810891866684, 0.013496315106749535 ], [ 0.23966504633426666, 0.0007862576167099178, 0.017393097281455994, 0.05663509666919708, 0.004228211473673582, 0.014219478704035282, 0.0326654352247715, 0.05895264819264412, 0.00687775295227766, 0.07219967246055603, 0.01674909144639969, 0.00624976446852088 ], [ 0.23966488242149353, 0.0007862508646212518, 0.08918464928865433, 0.0029486094135791063, 0.01297748927026987, 0.030789606273174286, 0.0003801261482294649, 0.04791662469506264, 0.0017422131495550275, 0.041121870279312134, 0.042073387652635574, 0.06407389044761658 ], [ 0.23966678977012634, 0.0007862658821977675, 0.04564957320690155, 0.0024617433082312346, 0.015628492459654808, 0.024474328383803368, 0.0003279130323790014, 0.03736794367432594, 0.0035983624402433634, 0.01636461168527603, 0.052316367626190186, 0.03797728195786476, 0.05756636708974838, 0.00117410346865654 ], [ 0.23966488242149353, 0.0034213608596473932, 0.11276638507843018, 0.007079779636114836, 0.01584053598344326, 0.02222246117889881, 0.03643104434013367, 0.0048902928829193115, 0.025318387895822525, 0.0071367016062140465, 0.005199816543608904, 0.01891530491411686, 0.01701703481376171 ] ] }, { "q_id": "9359_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 ], "rewards": [ [ 0.9864948987960815, 0.7120535969734192, 0.30682775378227234, 0.997546374797821, 0.9990584254264832 ], [ 0.6359878182411194, 0.09975787252187729, 0.4378211796283722, 0.9990478157997131, 0.9990044236183167 ], [ 0.9752520322799683, 0.8626887202262878, 0.9961705803871155, 0.9987454414367676 ], [ 0.7704685926437378, 0.07079756259918213, 0.08323881775140762, 0.2521358132362366, 0.9979402422904968, 0.9989138841629028 ], [ 0.7148328423500061, 0.04119882360100746, 0.02215384878218174, 0.9969984292984009, 0.9993312358856201 ], [ 0.9897602200508118, 0.6152746677398682, 0.6762990355491638, 0.007357919123023748 ], [ 0.9804501533508301, 0.7859779000282288, 0.7104904055595398, 0.9951216578483582, 0.9984720349311829 ], [ 0.9812712073326111, 0.3222423195838928, 0.7491419911384583, 0.007632664870470762 ], [ 0.795746386051178, 0.0852632001042366, 0.4011775851249695, 0.9982296824455261, 0.9987181425094604 ], [ 0.7148340940475464, 0.03945760801434517, 0.20043186843395233, 0.3621578812599182, 0.9759027361869812, 0.9993809461593628, 0.998976469039917 ], [ 0.9752521514892578, 0.2966011166572571, 0.1514047384262085, 0.39387598633766174, 0.9981016516685486, 0.9974976181983948 ], [ 0.9786802530288696, 0.3271464407444, 0.8180004954338074, 0.9934394955635071, 0.9980069994926453 ], [ 0.7148340940475464, 0.09819656610488892, 0.25210145115852356, 0.5404874682426453, 0.9983707070350647, 0.9993290901184082 ], [ 0.7148328423500061, 0.05908465385437012, 0.10153723508119583, 0.5282865166664124, 0.9898713231086731, 0.9988391995429993 ], [ 0.9865111112594604, 0.2506604790687561, 0.46581271290779114, 0.9979481101036072, 0.998040497303009 ] ] }, { "q_id": "9120_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.6496042013168335, 0.6010767817497253, 0.9676074385643005, 0.1628303974866867 ], [ 0.8638589978218079, 0.17455066740512848, 0.8161977529525757, 0.7278477549552917, 0.09113974124193192 ], [ 0.456704705953598, 0.09636663645505905, 0.18841254711151123, 0.9544849991798401, 0.9773707389831543, 0.07922740280628204 ], [ 0.008055058307945728, 0.04645473510026932, 0.1602635234594345, 0.7074715495109558, 0.12382319569587708 ], [ 0.6930515766143799, 0.1189660131931305, 0.9295694828033447, 0.951779305934906, 0.06475330889225006 ], [ 0.8915008306503296, 0.10916256159543991, 0.9406481385231018, 0.9878347516059875, 0.21856796741485596 ], [ 0.9161087274551392, 0.7738900184631348, 0.7156463265419006, 0.04067736119031906 ], [ 0.6447697281837463, 0.9325597286224365, 0.7379218339920044, 0.019853288307785988 ], [ 0.697983980178833, 0.9765967726707458, 0.9875617027282715, 0.7671858072280884 ], [ 0.8751364350318909, 0.12331757694482803, 0.8426725268363953, 0.9574859142303467, 0.1019800528883934 ], [ 0.5838910937309265, 0.9564023613929749, 0.9901080131530762, 0.7084288001060486 ], [ 0.5868887305259705, 0.16216430068016052, 0.957865297794342, 0.9927123785018921, 0.8229008913040161 ], [ 0.31250882148742676, 0.5882487297058105, 0.4756796658039093, 0.03896942362189293 ], [ 0.35291025042533875, 0.4228469729423523, 0.18668484687805176, 0.015980852767825127 ], [ 0.5699318647384644, 0.09679754823446274, 0.7369092702865601, 0.028604522347450256 ], [ 0.5502994060516357, 0.18621888756752014, 0.9666573405265808, 0.32163140177726746 ] ] }, { "q_id": "9828_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.42162880301475525, 0.5998672246932983, 0.3328028917312622, 0.007282504346221685 ], [ 0.946115255355835, 0.44915512204170227, 0.00605301046743989 ], [ 0.7345133423805237, 0.5064947605133057, 0.9941885471343994, 0.9979956150054932 ], [ 0.9689599275588989, 0.9574366211891174, 0.9976831674575806, 0.9989829659461975 ], [ 0.5829658508300781, 0.7466166615486145, 0.9960858821868896, 0.9985369443893433 ], [ 0.8456982970237732, 0.8495354652404785, 0.6397742033004761, 0.9970306158065796, 0.9979543685913086 ], [ 0.8751859068870544, 0.22560857236385345, 0.9053632616996765, 0.574325442314148, 0.006718468852341175 ], [ 0.8677380681037903, 0.23442180454730988, 0.9827719330787659, 0.7118473649024963, 0.006250772159546614 ], [ 0.9154240489006042, 0.18558037281036377, 0.6521109342575073, 0.6767658591270447, 0.007479508873075247 ], [ 0.9762900471687317, 0.14571331441402435, 0.8943931460380554, 0.006326580420136452 ], [ 0.961189329624176, 0.9709259271621704, 0.3332937955856323, 0.00534975528717041 ], [ 0.947299063205719, 0.8595905900001526, 0.48515114188194275, 0.006867621093988419 ], [ 0.8506784439086914, 0.9473385214805603, 0.7951383590698242, 0.007315336260944605 ], [ 0.8051834106445312, 0.7061266899108887, 0.9935048818588257, 0.9986791014671326 ], [ 0.9809187054634094, 0.018378041684627533, 0.004834601189941168 ], [ 0.553723156452179, 0.438793420791626, 0.9196950197219849, 0.08900083601474762, 0.005588348489254713 ] ] }, { "q_id": "9643_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15 ], "rewards": [ [ 0.12874993681907654, 0.06652060896158218, 0.07299117743968964, 0.05390501767396927, 0.0007371745887212455 ], [ 0.045749228447675705, 0.0251578651368618, 0.07068594545125961, 0.09034837782382965, 0.07308052480220795, 0.03111470676958561, 0.019099177792668343, 0.030735833570361137, 0.03692120313644409, 0.027634289115667343, 0.07755926996469498, 0.04174094647169113, 0.06583008915185928, 0.19703389704227448, 0.037746362388134, 0.19046862423419952, 0.1661003828048706, 0.08597753196954727, 0.046544816344976425, 0.0011321867350488901 ], [ 0.3125912845134735, 0.19614000618457794, 0.12177705764770508, 0.04947994276881218, 0.13290274143218994, 0.0535694845020771, 0.12466932088136673, 0.02991304360330105, 0.05865572765469551, 0.11371941864490509, 0.08463317155838013, 0.9938620328903198, 0.9997510313987732 ], [ 0.0563945509493351, 0.02607976645231247, 0.06591697782278061, 0.071319080889225, 0.07547085732221603, 0.0963023379445076, 0.32084986567497253, 0.09023549407720566, 0.05528023838996887, 0.038394298404455185, 0.02816377766430378, 0.023310936987400055, 0.13280342519283295, 0.029475534334778786, 0.9942511320114136, 0.9997146725654602 ], [ 0.13319501280784607, 0.057778242975473404, 0.04459702968597412, 0.04285159707069397, 0.07367276400327682, 0.18701201677322388, 0.2878943681716919, 0.09973090142011642, 0.043720658868551254, 0.0007722575101070106 ], [ 0.1389862298965454, 0.06667907536029816, 0.087483711540699, 0.08006273955106735, 0.03275756165385246, 0.02901657111942768, 0.08410483598709106, 0.042827706784009933, 0.03235749900341034, 0.0022124317474663258 ], [ 0.04046998918056488, 0.034402985125780106, 0.09071747213602066, 0.0907476469874382, 0.17206068336963654, 0.06701275706291199, 0.10084471851587296, 0.010371175594627857, 0.02329140156507492, 0.03543107956647873, 0.12110600620508194, 0.12745587527751923, 0.9949766397476196, 0.9993206262588501 ], [ 0.08676137775182724, 0.11170907318592072, 0.12025138735771179, 0.11736377328634262, 0.02419208362698555, 0.082469642162323, 0.014104951173067093, 0.00990070030093193, 0.0007316138362511992 ], [ 0.045891471207141876, 0.03167571499943733, 0.09128665179014206, 0.14131346344947815, 0.09978069365024567, 0.05849545821547508, 0.19469596445560455, 0.13292637467384338, 0.0727829858660698, 0.0234540943056345, 0.03810989111661911, 0.04637711122632027, 0.10709036141633987, 0.05596349388360977, 0.9930196404457092, 0.9994285702705383 ], [ 0.07247579097747803, 0.03427959606051445, 0.09153135865926743, 0.07709912210702896, 0.20711790025234222, 0.06890858709812164, 0.08969679474830627, 0.004495455417782068, 0.02283623442053795, 0.03524233028292656, 0.026676032692193985, 0.12657953798770905, 0.0737265795469284, 0.0023618482518941164, 0.0008176114060916007 ], [ 0.10986776649951935, 0.09320806711912155, 0.10203897953033447, 0.15900520980358124, 0.1050422266125679, 0.04904624819755554, 0.1373242884874344, 0.06292915344238281, 0.9940390586853027, 0.9995993971824646 ], [ 0.21115507185459137, 0.10546451807022095, 0.15813639760017395, 0.06886903941631317, 0.10261337459087372, 0.9961078763008118, 0.9994137287139893 ], [ 0.12874917685985565, 0.06849637627601624, 0.05660761520266533, 0.053855132311582565, 0.15699215233325958, 0.07075272500514984, 0.07855943590402603, 0.04555796459317207, 0.056104034185409546, 0.040348559617996216, 0.045013442635536194, 0.0006885037291795015 ], [ 0.15722541511058807, 0.05867213010787964, 0.03054996393620968, 0.010276619344949722, 0.022127017378807068, 0.021802417933940887, 0.036088086664676666, 0.03251923620700836, 0.2821230888366699, 0.039643581956624985, 0.12303631752729416, 0.07813221216201782, 0.036789420992136, 0.002549864584580064 ] ] }, { "q_id": "10206_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06305177509784698, 0.9779874086380005, 0.002151763066649437 ], [ 0.06305312365293503, 0.946922242641449, 0.001662857597693801 ], [ 0.06906033307313919, 0.0013574394397437572 ], [ 0.33536475896835327, 0.8899399042129517, 0.8259708881378174, 0.0021905205212533474 ], [ 0.0428982675075531, 0.8853784203529358, 0.0019117520423606038 ], [ 0.08302874118089676, 0.5405629277229309, 0.0019138121278956532 ], [ 0.17306877672672272, 0.9622721076011658, 0.001814276329241693 ], [ 0.023960083723068237, 0.0016344378236681223 ], [ 0.19889558851718903, 0.9114275574684143, 0.0024591507390141487 ], [ 0.7072743773460388, 0.5895871520042419, 0.0026156676467508078 ], [ 0.06175265461206436, 0.9748772382736206, 0.0023767261300235987 ], [ 0.08302965015172958, 0.9851381778717041, 0.002306648064404726 ], [ 0.7238157391548157, 0.9817380309104919, 0.0016712984070181847 ], [ 0.9527665376663208, 0.7247526049613953, 0.002446755301207304 ], [ 0.06305108964443207, 0.36545512080192566, 0.001917650573886931 ], [ 0.06175094097852707, 0.7880324721336365, 0.0023318855091929436 ] ] }, { "q_id": "9108_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.25577056407928467, 0.11445660144090652, 0.08494910597801208, 0.04620770364999771, 0.021590784192085266 ], [ 0.28644663095474243, 0.07941751182079315, 0.056994952261447906, 0.19838672876358032, 0.34755444526672363, 0.0772177204489708, 0.07818573713302612, 0.05430973321199417 ], [ 0.14821909368038177, 0.23000237345695496, 0.15081486105918884, 0.13414649665355682, 0.11691044270992279, 0.02480718120932579, 0.07929594814777374, 0.12865465879440308, 0.16695204377174377, 0.41886988282203674, 0.10381896793842316, 0.01602601632475853, 0.05644356459379196, 0.07520034164190292, 0.228389173746109, 0.555838942527771, 0.0028386979829519987 ], [ 0.18588881194591522, 0.31341615319252014, 0.05955596640706062, 0.13115045428276062, 0.11164605617523193, 0.08226989209651947, 0.07526781409978867, 0.09836720675230026, 0.12202011793851852, 0.076795794069767, 0.2382122129201889, 0.037419456988573074, 0.003857966745272279 ], [ 0.24948188662528992, 0.10685107856988907, 0.09791351109743118, 0.07331220805644989, 0.025714406743645668, 0.012498453259468079, 0.2919555604457855, 0.03148742392659187, 0.03414107859134674, 0.02703288197517395, 0.028323141857981682 ], [ 0.13917353749275208, 0.17321498692035675, 0.10294266790151596, 0.05679035186767578, 0.08686284720897675, 0.0996171087026596, 0.0227728933095932, 0.029717866331338882 ], [ 0.14472177624702454, 0.11037218570709229, 0.053861577063798904, 0.11596512049436569, 0.002194443717598915 ], [ 0.14821916818618774, 0.23000295460224152, 0.1320498138666153, 0.04705171659588814, 0.06590071320533752, 0.043290313333272934, 0.08343617618083954, 0.03336787968873978 ], [ 0.10893009603023529, 0.07392389327287674, 0.035704564303159714, 0.08212262392044067, 0.04168066009879112, 0.14617405831813812, 0.20761410892009735, 0.0028384309262037277 ], [ 0.12746396660804749, 0.07892917096614838, 0.09613576531410217, 0.10641849786043167, 0.05862142890691757, 0.10737653076648712, 0.04899005964398384, 0.09536810219287872, 0.017607243731617928, 0.09913669526576996, 0.056668154895305634, 0.14454692602157593, 0.12327494472265244, 0.0016957379411906004 ], [ 0.14821922779083252, 0.1768302172422409, 0.03022920712828636, 0.20574849843978882, 0.07403990626335144, 0.13597500324249268, 0.011035131290555, 0.09841326624155045, 0.04094903543591499, 0.019432635977864265 ], [ 0.33672910928726196, 0.18031364679336548, 0.15576429665088654, 0.06176981329917908, 0.025645697489380836 ], [ 0.3210020065307617, 0.08240330964326859, 0.055292196571826935, 0.04618724063038826, 0.09460117667913437, 0.04329179599881172, 0.031041361391544342 ], [ 0.325065940618515, 0.09929543733596802, 0.07992275059223175, 0.0664224699139595, 0.07710640877485275, 0.0420340895652771, 0.014160633087158203 ], [ 0.2431681603193283, 0.04636542871594429, 0.13169841468334198, 0.05421437695622444, 0.07209819555282593, 0.007202856242656708, 0.10496918112039566, 0.039084527641534805, 0.09374891221523285, 0.04316675662994385, 0.038951270282268524, 0.025197504088282585, 0.05394977703690529, 0.025011425837874413, 0.03311796858906746, 0.003615009831264615 ], [ 0.2610286772251129, 0.09112457185983658, 0.060714613646268845, 0.06215708330273628, 0.03432799130678177, 0.028406761586666107, 0.006753754802048206, 0.00227099796757102 ] ] }, { "q_id": "10298_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9957897067070007, 0.9399864077568054, 0.9995176792144775, 0.9999642372131348 ], [ 0.9988104104995728, 0.9479456543922424, 0.9999634027481079 ], [ 0.9995751976966858, 0.9999474287033081 ], [ 0.9991558790206909, 0.9993364214897156, 0.9999591112136841 ], [ 0.9989626407623291, 0.9887187480926514, 0.9996209144592285, 0.9999666213989258 ], [ 0.9988104104995728, 0.999021053314209, 0.9999632835388184 ], [ 0.9989626407623291, 0.884392499923706, 0.9999614953994751 ], [ 0.9988104104995728, 0.9693263173103333, 0.9999532699584961 ], [ 0.9990369081497192, 0.25287866592407227, 0.9939882755279541, 0.9999641180038452 ], [ 0.9988104104995728, 0.709514856338501, 0.9999583959579468 ], [ 0.9989626407623291, 0.20365610718727112, 0.9971792697906494, 0.999957799911499 ], [ 0.9989867806434631, 0.9448685050010681, 0.9999642372131348 ], [ 0.9989626407623291, 0.953967809677124, 0.9999608993530273 ], [ 0.9987260699272156, 0.23360995948314667, 0.9977268576622009, 0.9999654293060303 ], [ 0.9989010095596313, 0.9142375588417053, 0.9928659200668335, 0.9999678134918213 ], [ 0.9989626407623291, 0.17055264115333557, 0.9970805048942566, 0.9999631643295288 ] ] }, { "q_id": "9355_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9994543194770813, 0.9964855909347534, 0.9999446868896484 ], [ 0.9999150037765503, 0.9999492168426514 ], [ 0.9996379613876343, 0.9994431138038635, 0.9999597072601318 ], [ 0.9998809099197388, 0.9999462366104126 ], [ 0.9998855590820312, 0.9999430179595947 ], [ 0.9999051094055176, 0.9999407529830933 ], [ 0.9997542500495911, 0.999942421913147 ], [ 0.9994989633560181, 0.9995535016059875, 0.9999573230743408 ], [ 0.9999058246612549, 0.9999477863311768 ], [ 0.9998760223388672, 0.9999401569366455 ], [ 0.9997542500495911, 0.9989377856254578, 0.9999542236328125 ], [ 0.999885082244873, 0.999942421913147 ], [ 0.9999053478240967, 0.999945878982544 ], [ 0.9998956918716431, 0.9999463558197021 ], [ 0.9999058246612549, 0.9999475479125977 ], [ 0.9995549321174622, 0.9999374151229858 ] ] }, { "q_id": "9464_mmlu_physics", "cot_ids": [ 0, 1, 2, 4, 5, 8, 10, 11, 14 ], "rewards": [ [ 0.19772712886333466, 0.004903702065348625, 0.059354860335588455, 0.0006979129975661635, 0.024877039715647697, 0.0016330534126609564, 0.03660529479384422, 0.0018492373637855053, 0.0039161439053714275, 0.03955870494246483, 0.016668735072016716, 0.6650791764259338 ], [ 0.19772833585739136, 0.004903688561171293, 0.008022072724997997, 0.048995837569236755, 0.003248482244089246, 0.00019962670921813697, 0.032207269221544266, 0.001936619053594768, 0.013944835402071476, 0.007392929866909981, 0.0009219209896400571, 0.03900130093097687, 0.0007752170786261559, 0.028118591755628586, 0.03583283722400665, 0.15450914204120636, 0.38066595792770386 ], [ 0.15882058441638947, 0.0038364308420568705, 0.04360444098711014, 0.0005183973698876798, 0.016120009124279022, 0.018195951357483864, 0.0018288497813045979, 0.029026716947555542, 0.06540472060441971, 0.0003842801961582154, 4.649661059374921e-05, 0.13103020191192627, 0.0746949315071106, 0.0007044774247333407, 0.604164183139801, 0.5336335301399231 ], [ 0.19772887229919434, 0.0049036648124456406, 0.05975540727376938, 0.0006478194845840335, 0.02428743988275528, 0.0016454848228022456, 0.004635272081941366, 0.01585053838789463, 0.028663037344813347, 0.035540442913770676, 0.0014369622804224491, 0.22763629257678986, 0.43527644872665405 ], [ 0.19773007929325104, 0.004903679247945547, 0.013121400959789753, 0.008979186415672302, 0.05989659205079079, 0.0017112062778323889, 0.00877557322382927, 0.18625964224338531, 0.002243442228063941, 0.010939329862594604, 0.039927609264850616, 0.11626991629600525, 0.07433807104825974, 0.728350043296814 ], [ 0.19772841036319733, 0.0049036601558327675, 0.06268059462308884, 0.005825480446219444, 0.006657931488007307, 0.01658460684120655, 0.2359580397605896, 0.0009995534783229232, 0.008028625510632992, 0.0844421237707138, 0.16841158270835876 ], [ 0.18607723712921143, 0.004394687246531248, 0.05195954814553261, 0.0010849268874153495, 0.009370862506330013, 0.004087457899004221, 0.02038191817700863, 0.009993203915655613, 0.040688708424568176, 0.014790792018175125, 0.04572487622499466, 0.11622750014066696, 0.09456368535757065, 0.0033263869117945433, 0.009694943204522133, 0.0051125045865774155 ], [ 0.1699991524219513, 0.006060327403247356, 0.013020158745348454, 0.022273825481534004, 0.0743439793586731, 0.01441565714776516, 0.002194181317463517, 0.01612923853099346, 0.04471622034907341, 0.007689324207603931, 0.03161495923995972, 0.0014396109618246555, 0.006896486040204763, 0.037070684134960175, 0.03824281692504883, 0.167726531624794, 0.08099351078271866, 0.0014942140551283956 ], [ 0.19772803783416748, 0.004034584853798151, 0.24117527902126312, 0.004659540019929409, 0.05928400158882141, 0.000660426972899586, 0.02857370674610138, 0.0348285436630249, 0.07402930408716202 ] ] }, { "q_id": "10339_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.22760267555713654, 0.02434738166630268, 0.05637727305293083, 0.5758891701698303, 0.036366138607263565, 0.04481376335024834, 0.14484606683254242, 0.013098271563649178, 0.009267334826290607 ], [ 0.18197785317897797, 0.114164337515831, 0.03312242776155472, 0.09657221287488937, 0.5763998031616211, 0.01509008090943098, 0.03796312212944031, 0.10587576776742935, 0.09076303243637085, 0.016129739582538605, 0.016693303361535072 ], [ 0.19507521390914917, 0.26012948155403137, 0.44496268033981323, 0.018848847597837448, 0.05429692938923836, 0.052207332104444504, 0.020046070218086243, 0.009441167116165161 ], [ 0.7801245450973511, 0.2599168121814728, 0.4859640598297119, 0.17073674499988556, 0.036273807287216187, 0.14082534611225128, 0.012523391284048557, 0.0009635225869715214 ], [ 0.1311585009098053, 0.08188620209693909, 0.3978038430213928, 0.02674679458141327, 0.052676010876894, 0.005831625312566757 ], [ 0.22760383784770966, 0.0006316581275314093, 0.021459879353642464, 0.8646060824394226, 0.0018201555358245969, 0.02811226062476635, 0.025255020707845688, 0.005540739744901657, 0.02370436303317547, 0.011924996972084045, 0.0010869244579225779 ], [ 0.2803094983100891, 0.1427820771932602, 0.01259033102542162, 0.009203232824802399 ], [ 0.023392390459775925, 0.03345918655395508, 0.050070106983184814, 0.21363581717014313, 0.3969556391239166, 0.9858513474464417 ], [ 0.2687847912311554, 0.10277392715215683, 0.21729551255702972, 0.10066162794828415, 0.46143513917922974, 0.028269488364458084, 0.1696338653564453, 0.0051674614660441875, 0.022998308762907982, 0.01960647664964199 ], [ 0.8510308861732483, 0.17927657067775726, 0.05629640817642212, 0.07055584341287613, 0.41338545083999634, 0.030785148963332176, 0.0818452462553978, 0.0063132308423519135, 0.13093028962612152, 0.012639032676815987, 0.007466878741979599 ], [ 0.26921460032463074, 0.05493396893143654, 0.3797345757484436, 0.04648425057530403, 0.08036775887012482, 0.15879642963409424, 0.5646834969520569, 0.04413910210132599, 0.5609166622161865, 0.9870748519897461 ], [ 0.16061916947364807, 0.3780900537967682, 0.038510821759700775, 0.12818840146064758, 0.059512075036764145, 0.023092694580554962, 0.012035367079079151, 0.007652707397937775 ], [ 0.7843067646026611, 0.2747434079647064, 0.030225779861211777, 0.09923962503671646, 0.047070737928152084, 0.0029147907625883818 ], [ 0.2658352553844452, 0.17489781975746155, 0.45320773124694824, 0.02232799306511879, 0.047025345265865326, 0.1515982747077942, 0.013801606371998787, 0.11918279528617859, 0.019508615136146545, 0.012640776112675667 ], [ 0.5056846141815186, 0.2333095818758011, 0.3183717429637909, 0.0055000935681164265, 0.004622726701200008 ] ] }, { "q_id": "10016_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8683924674987793, 0.29644158482551575, 0.14691612124443054, 0.05277875065803528, 0.38338741660118103, 0.1262241154909134, 0.6816830039024353, 0.17928360402584076, 0.27665314078330994, 0.9981914162635803, 0.9992989301681519 ], [ 0.8683925867080688, 0.03395305201411247, 0.20689718425273895, 0.00035402519279159606, 0.32494425773620605, 0.020757488906383514, 0.33998051285743713, 0.0012311391765251756, 0.29802969098091125, 0.05647686868906021, 0.9989907145500183, 0.9996693134307861 ], [ 0.9528666138648987, 0.1621331423521042, 0.3218865692615509, 0.0827346071600914, 0.5024781227111816, 0.7215898633003235, 0.04598856717348099, 0.1581450253725052, 0.04380149021744728, 0.9985207915306091, 0.9998069405555725 ], [ 0.8287384510040283, 0.05198206007480621, 0.1457088738679886, 0.04553696885704994, 0.09560082107782364, 0.03122216835618019, 0.9985591769218445, 0.9996343851089478 ], [ 0.9280834197998047, 0.1885920614004135, 0.5851401686668396, 0.26717454195022583, 0.9994010925292969, 0.9998254179954529 ], [ 0.8683929443359375, 0.03395330160856247, 0.13524067401885986, 0.16854244470596313, 0.03658226132392883, 0.2827346920967102, 0.6312235593795776, 0.043417852371931076, 0.250533789396286, 0.07644638419151306, 0.9984556436538696, 0.9997974038124084 ], [ 0.4171741008758545, 0.24661102890968323, 0.05131736770272255, 0.473486989736557, 0.36501604318618774, 0.10481400787830353, 0.9989141225814819, 0.999796450138092 ], [ 0.9050611257553101, 0.0999126061797142, 0.21010428667068481, 0.05950441211462021, 0.5526514649391174, 0.7920084595680237, 0.05441894382238388, 0.1142120361328125, 0.0332222580909729, 0.9983763694763184, 0.9998557567596436 ], [ 0.6164889931678772, 0.10395467281341553, 0.8478341102600098, 0.9996383190155029, 0.9999047517776489 ], [ 0.9615193009376526, 0.10394689440727234, 0.1686479151248932, 0.0006721193203702569, 0.13932569324970245, 0.26902326941490173, 0.04788241535425186, 0.2527952790260315, 0.009162550792098045, 0.10643373429775238, 0.6648861169815063, 0.05726950988173485, 0.22336234152317047, 0.07613147795200348, 0.9977309107780457, 0.999687671661377 ], [ 0.4578551948070526, 0.20008797943592072, 0.32062050700187683, 0.33136460185050964, 0.23161593079566956, 0.9971216320991516, 0.9988732933998108 ], [ 0.407596230506897, 0.9006158709526062, 0.9993742108345032, 0.9998370409011841 ], [ 0.5937822461128235, 0.3845207095146179, 0.2573058307170868, 0.9988922476768494, 0.9998502731323242 ], [ 0.5475019812583923, 0.06861559301614761, 0.05634361878037453, 0.15120261907577515, 0.11124610900878906, 0.06152615696191788, 0.12446703761816025, 0.016277842223644257, 0.09879330545663834, 0.07827609032392502, 0.322604775428772, 0.1159210354089737, 0.07073303312063217, 0.022417519241571426, 0.996119499206543, 0.9995424747467041 ], [ 0.8008739352226257, 0.04172716289758682, 0.07620475441217422, 0.40710189938545227, 0.9994841814041138, 0.999883770942688 ], [ 0.7924699187278748, 0.611423134803772, 0.5819913744926453, 0.9983127117156982, 0.9995303153991699 ] ] }, { "q_id": "9199_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.6517167091369629, 0.6416232585906982, 0.10096229612827301, 0.12672404944896698, 0.06044907495379448, 0.3253224790096283, 0.9836154580116272, 0.9931890964508057 ], [ 0.6780956983566284, 0.5058640837669373, 0.4794762134552002, 0.08398362249135971, 0.016065122559666634, 0.1930369883775711, 0.25148826837539673, 0.9864115118980408, 0.9840195178985596 ], [ 0.4071071147918701, 0.5368747115135193, 0.49307137727737427, 0.26588186621665955, 0.8602713942527771, 0.16050417721271515, 0.5125565528869629, 0.2073938399553299, 0.9960726499557495, 0.9666029810905457 ], [ 0.9677048921585083, 0.049436334520578384, 0.6635160446166992, 0.02669581212103367, 0.3789987862110138, 0.9731160998344421, 0.9770647287368774 ], [ 0.17564229667186737, 0.10462556779384613, 0.0010613457998260856, 0.04108163341879845, 0.027216611430048943, 0.2118668109178543, 0.362183541059494, 0.004544057883322239, 0.4605295956134796, 0.11556827276945114, 0.04966728761792183, 0.017165925353765488, 0.6065964102745056, 0.086289182305336, 0.9764318466186523, 0.9905651807785034 ], [ 0.6517108082771301, 0.49619776010513306, 0.3608171045780182, 0.06145992502570152, 0.1304740011692047, 0.003175878431648016, 0.11229271441698074, 0.29393115639686584, 0.43538030982017517, 0.3676086366176605, 0.688643753528595, 0.18044434487819672, 0.9898528456687927, 0.9935135245323181 ], [ 0.6172193288803101, 0.5583994388580322, 0.6028972864151001, 0.09465882182121277, 0.1876974254846573, 0.0913764014840126, 0.015986306592822075, 0.6452232003211975, 0.087648905813694, 0.9899908304214478, 0.989897608757019 ], [ 0.3140997588634491, 0.0008202579920180142, 0.24533317983150482, 0.005513748619705439, 0.2976559102535248, 0.029294194653630257, 0.9747506976127625, 0.9851102828979492 ], [ 0.6517121195793152, 0.5640480518341064, 0.37489083409309387, 0.03902357071638107, 0.13210541009902954, 0.07171829044818878, 0.2306806892156601, 0.6585304141044617, 0.08395938575267792, 0.23810820281505585, 0.984288215637207, 0.9918899536132812 ], [ 0.5054926872253418, 0.4572853446006775, 0.42193731665611267, 0.051782142370939255, 0.12573044002056122, 0.10945336520671844, 0.6883823871612549, 0.07018012553453445, 0.9872179627418518, 0.9916402101516724 ], [ 0.6517121195793152, 0.45843109488487244, 0.5232288837432861, 0.039081260561943054, 0.09360179305076599, 0.16222107410430908, 0.4790121912956238, 0.09650653600692749, 0.9906103014945984, 0.9917681217193604 ], [ 0.037329114973545074, 0.06656841933727264, 0.0071946801617741585, 0.7618273496627808, 0.045519646257162094, 0.2616278827190399, 0.017114466056227684, 0.9785528182983398, 0.9290273785591125 ], [ 0.48911696672439575, 0.3362191617488861, 0.11919966340065002, 0.2827094495296478, 0.38517704606056213, 0.43282198905944824, 0.6341402530670166, 0.18120336532592773, 0.9790331721305847, 0.9860029220581055 ], [ 0.3049883246421814, 0.5136066675186157, 0.035825248807668686, 0.12283385545015335, 0.165299654006958, 0.24929220974445343, 0.6634793281555176, 0.08484027534723282, 0.21673338115215302, 0.9795326590538025, 0.9813334345817566 ], [ 0.608256459236145, 0.5713973641395569, 0.6341221332550049, 0.06312412768602371, 0.11278577148914337, 0.16108116507530212, 0.2331981211900711, 0.6621500253677368, 0.05086373910307884, 0.1651720106601715, 0.9786849021911621, 0.98775315284729 ], [ 0.6172159314155579, 0.5631489753723145, 0.06610586494207382, 0.12449140846729279, 0.1840672343969345, 0.11785075068473816, 0.5654809474945068, 0.06577522307634354, 0.9835289716720581, 0.9911971092224121 ] ] }, { "q_id": "9142_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.14312051236629486, 0.2086297571659088, 0.1908581703901291, 0.014457877725362778, 0.024884596467018127, 0.36863869428634644, 0.06607319414615631, 0.001145073096267879 ], [ 0.05263145640492439, 0.12724973261356354, 0.05679796263575554, 0.001025144592858851 ], [ 0.17109377682209015, 0.04575936496257782, 0.0809825137257576, 0.01411539874970913, 0.0391111746430397, 0.05970219150185585, 0.09580352902412415, 0.009665116667747498, 0.21492744982242584, 0.8013898134231567, 0.0004957046476192772 ], [ 0.054980408400297165, 0.08022123575210571, 0.030384786427021027, 0.029601741582155228, 0.03458680585026741, 0.014837858267128468, 0.03877650573849678, 0.05056947469711304, 0.003698942484334111, 0.04562944918870926, 0.0687088668346405, 0.0012220855569466949 ], [ 0.0720604956150055, 0.05745274946093559, 0.1588643491268158, 0.041361141949892044, 0.020472785457968712, 0.03427779674530029, 0.000161275384016335, 0.051284898072481155, 0.025800440460443497, 0.1381095051765442, 0.23071660101413727, 0.0008311154670082033 ], [ 0.25455012917518616, 0.10413803160190582, 0.24787059426307678, 0.010506496764719486, 0.01597900129854679, 0.0003637626941781491, 0.07520916312932968, 0.017892960458993912, 0.011142779141664505 ], [ 0.15280045568943024, 0.04878462105989456, 0.33466941118240356, 0.013554809615015984, 0.024991512298583984, 0.05772240087389946, 0.007192572578787804, 0.05984687805175781, 0.10667391866445541, 0.014267107471823692, 0.2198326140642166, 0.0032760482281446457, 0.14811594784259796, 0.006746845785528421, 0.08400379866361618, 0.025681229308247566, 0.019794797524809837 ], [ 0.06600555032491684, 0.08493665605783463, 0.07557227462530136, 0.01295335404574871, 0.026599034667015076, 0.0001989913871511817, 0.038349587470293045, 0.010769367218017578, 0.08497212827205658, 0.0009578376193530858, 0.44633564352989197, 0.731137216091156, 0.0005484733264893293 ], [ 0.19901609420776367, 0.20646801590919495, 0.11426067352294922, 0.01717088185250759, 0.031157860532402992, 0.00023112910275813192, 0.20979724824428558, 0.4678366184234619, 0.0007492793956771493 ], [ 0.06474357098340988, 0.035056572407484055, 0.02893456071615219, 0.14411821961402893, 0.02522166818380356, 0.03134525567293167, 0.0001453078439226374, 0.14261570572853088, 0.00520715955644846, 0.03119313158094883, 0.0022162029054015875, 0.0418868325650692, 0.4000599682331085, 0.8253408670425415, 0.00046337349340319633 ], [ 0.07043560594320297, 0.0917317122220993, 0.1609303206205368, 0.739070475101471, 0.00046585453674197197 ], [ 0.12248916923999786, 0.019250255078077316, 0.028705911710858345, 0.000336677476298064, 0.06830771267414093, 0.018169324845075607, 0.05487740784883499, 0.0004824570787604898, 0.48073577880859375, 0.00669134221971035, 0.132578045129776, 0.8655300140380859, 0.21893857419490814, 0.0004814362619072199 ], [ 0.053467944264411926, 0.00791575014591217, 0.026248767971992493, 0.07510452717542648, 0.03890256583690643, 0.04800441116094589, 0.09634421765804291, 0.014275874011218548, 0.11698988080024719, 0.2195112258195877, 0.8029360175132751, 0.00043508547241799533 ], [ 0.07206173986196518, 0.019041821360588074, 0.027356285601854324, 0.00023625495668966323, 0.012361831031739712, 0.011571437120437622, 0.012268547900021076, 0.02822485938668251, 0.0838852971792221, 0.023655494675040245, 0.07520511746406555, 0.00040638577775098383, 0.03613695129752159, 0.5088658928871155, 0.9245010018348694, 0.31507956981658936, 0.00040211263694800436 ], [ 0.05346784368157387, 0.03462422639131546, 0.12669287621974945, 0.026212569326162338, 0.00019135119509883225, 0.06688183546066284, 0.10617636889219284, 0.00254809414036572, 0.43772128224372864, 0.15721771121025085, 0.9129235744476318, 0.00042953158845193684 ], [ 0.042672209441661835, 0.14164529740810394, 0.01224899385124445, 0.03525400534272194, 0.08480563014745712, 0.07622016221284866, 0.030631083995103836, 0.03494991362094879, 0.2408384084701538, 0.7403827905654907, 0.15631236135959625, 0.0004901656066067517 ] ] }, { "q_id": "9654_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4722817838191986, 0.03397750481963158, 0.10789036005735397, 0.16872575879096985, 0.02723737247288227, 0.037383850663900375, 0.03751301392912865, 0.0007415952277369797 ], [ 0.4991934299468994, 0.01635028049349785, 0.16194811463356018, 0.13316914439201355, 0.9810047745704651, 0.2961912453174591, 0.1754290610551834, 0.16166464984416962, 0.02719873934984207, 0.1184135153889656, 0.3819025754928589, 0.09564338624477386, 0.05464600771665573, 0.9991014003753662 ], [ 0.4991934299468994, 0.03585025668144226, 0.55721515417099, 0.9957697987556458, 0.42138347029685974, 0.06960088759660721, 0.03720976412296295, 0.12621822953224182, 0.24791443347930908, 0.021460801362991333, 0.9794750213623047 ], [ 0.4991914927959442, 0.015034507028758526, 0.1409052312374115, 0.07140355557203293, 0.04050527513027191, 0.005408063996583223, 0.17389585077762604, 0.20865361392498016, 0.13528890907764435, 0.05933777242898941, 0.020252268761396408, 0.09477993100881577, 0.19967642426490784, 0.07839766144752502, 0.052282124757766724, 0.010931778699159622, 0.0010254576336592436, 0.0018294373294338584 ], [ 0.49919557571411133, 0.017422562465071678, 0.0347525030374527, 0.03299413621425629, 0.0009285971755161881 ], [ 0.428034245967865, 0.023521695286035538, 0.022110402584075928, 0.0793803483247757, 0.9376631379127502, 0.012916059233248234, 0.2172330617904663, 0.1110682561993599, 0.011988358572125435, 0.10172434896230698, 0.23702678084373474, 0.9811628460884094 ], [ 0.4424009919166565, 0.01415480300784111, 0.08580188453197479, 0.7986924052238464, 0.009349824860692024, 0.06936756521463394, 0.0389380045235157, 0.005872833076864481, 0.036619894206523895, 0.15992262959480286, 0.023131119087338448, 0.9724960327148438 ], [ 0.48304256796836853, 0.015410669147968292, 0.16855962574481964, 0.9741199016571045, 0.3395683467388153, 0.2336920201778412, 0.02974565513432026, 0.09936604648828506, 0.10182618349790573, 0.1336970180273056, 0.9992805123329163 ], [ 0.4607163071632385, 0.011906513944268227, 0.03422044962644577, 0.43158790469169617, 0.013520327396690845, 0.07353107631206512, 0.02934589609503746, 0.006352662108838558, 0.10745613276958466, 0.05132152512669563, 0.002369226887822151 ], [ 0.4379357099533081, 0.012503593228757381, 0.06634226441383362, 0.005830721464008093, 0.004338468890637159, 0.01905382238328457, 0.01087179034948349, 0.005609376356005669, 0.0438179075717926, 0.010803491808474064, 0.002126393374055624 ], [ 0.499190092086792, 0.038959551602602005, 0.026621785014867783, 0.0819912701845169, 0.001863825018517673, 0.0019307384500280023 ], [ 0.25029024481773376, 0.013283060863614082, 0.9720813632011414, 0.37059569358825684, 0.024826670065522194, 0.076447032392025, 0.333693265914917, 0.9992606043815613 ], [ 0.4830470681190491, 0.02264462411403656, 0.14796699583530426, 0.9874479174613953, 0.026840096339583397, 0.15748389065265656, 0.02398197539150715, 0.011393073946237564, 0.0835510790348053, 0.1128646656870842, 0.9990724325180054 ], [ 0.4830513596534729, 0.0233463104814291, 0.21893206238746643, 0.13117669522762299, 0.9891911745071411, 0.333121120929718, 0.410672128200531, 0.1210482269525528, 0.03126225993037224, 0.14725111424922943, 0.5001894235610962, 0.13068686425685883, 0.19832423329353333, 0.9992305040359497 ], [ 0.499194860458374, 0.020810026675462723, 0.15523123741149902, 0.9781196117401123, 0.25943702459335327, 0.19190114736557007, 0.0175634752959013, 0.1291327178478241, 0.0791223794221878, 0.14480231702327728, 0.9993365406990051 ], [ 0.499194860458374, 0.020810026675462723, 0.4085721969604492, 0.10997726768255234, 0.9804995656013489, 0.3892027735710144, 0.5870022177696228, 0.14925900101661682, 0.027364974841475487, 0.17000077664852142, 0.5605376362800598, 0.3704744875431061, 0.6318877339363098, 0.9995622038841248 ] ] }, { "q_id": "9455_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.47345077991485596, 0.37433549761772156, 0.8241167664527893, 0.0004893185687251389, 0.0002729539410211146 ], [ 0.6719913482666016, 0.033404070883989334, 0.08180558681488037, 0.37873727083206177, 0.04303024336695671, 0.05406545102596283, 0.09701697528362274, 0.12134688347578049, 0.07382834702730179, 0.2524294853210449, 0.2269601970911026, 0.0003663870447780937 ], [ 0.6326479315757751, 0.3819774091243744, 0.4554058909416199, 0.05764663964509964, 0.9640236496925354, 0.000282953871646896 ], [ 0.6326451897621155, 0.9360925555229187, 0.2246047407388687, 0.527821958065033, 0.03607054799795151, 0.9178140163421631, 0.000286949536530301 ], [ 0.7126671671867371, 0.43751299381256104, 0.9137297868728638, 0.44486257433891296, 0.0012226863764226437, 0.00031479939934797585 ], [ 0.8112941384315491, 0.09503092616796494, 0.385579913854599, 0.0628717839717865, 0.12850916385650635, 0.9992974996566772, 0.9999397993087769 ], [ 0.8992980122566223, 0.3446004390716553, 0.0545666478574276, 0.9938883185386658, 0.9999045133590698 ], [ 0.6326459646224976, 0.8712613582611084, 0.1526353508234024, 0.5728586316108704, 0.00105424749199301, 0.0002747316611930728 ], [ 0.8112941384315491, 0.08690714091062546, 0.397163063287735, 0.07058536261320114, 0.8152542114257812, 0.0002877124643418938 ], [ 0.6719905138015747, 0.7974510192871094, 0.9777494072914124, 0.066465824842453, 0.0006286402349360287, 0.00026682057068683207 ], [ 0.8112941384315491, 0.09503092616796494, 0.36600953340530396, 0.051430609077215195, 0.15420353412628174, 0.004373541101813316, 0.00029152067145332694 ], [ 0.9487378001213074, 0.4184775948524475, 0.033935900777578354, 0.9940819144248962, 0.9999117851257324 ], [ 0.8112941384315491, 0.176422119140625, 0.06118160858750343, 0.27292338013648987, 0.004148642998188734, 0.0002901210682466626 ], [ 0.671990692615509, 0.3679566979408264, 0.9032555222511292, 0.4216298460960388, 0.0010566964047029614, 0.00028656431823037565 ], [ 0.9111613631248474, 0.24381022155284882, 0.04176279157400131, 0.9992802739143372, 0.999941349029541 ] ] }, { "q_id": "9630_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.45036810636520386, 0.17990002036094666, 0.8939410448074341, 0.17209532856941223, 0.12896110117435455 ], [ 0.4521941840648651, 0.9579010009765625, 0.9696913361549377, 0.18584264814853668 ], [ 0.5021359324455261, 0.6833733320236206, 0.000961169833317399 ], [ 0.49580416083335876, 0.3878237307071686, 0.41870737075805664, 0.11398246139287949 ], [ 0.5021336078643799, 0.9870527386665344, 0.0010257409885525703 ], [ 0.47030124068260193, 0.18204045295715332, 0.7187171578407288, 0.0011872194008901715 ], [ 0.5640146732330322, 0.15161697566509247, 0.0875592976808548 ], [ 0.5137277841567993, 0.9569807648658752, 0.16480661928653717, 0.11756075918674469 ], [ 0.49732735753059387, 0.21632501482963562, 0.739177942276001, 0.08562945574522018 ], [ 0.7341379523277283, 0.6821811199188232, 0.09467606246471405 ], [ 0.5021355152130127, 0.24220030009746552, 0.9126875400543213, 0.0010387977818027139 ], [ 0.4118771553039551, 0.8335709571838379, 0.18308107554912567, 0.04907980188727379, 0.08805260062217712 ], [ 0.5137263536453247, 0.9536328911781311, 0.4359559118747711, 0.14060397446155548 ], [ 0.5137262344360352, 0.46625351905822754, 0.0010247871978208423 ], [ 0.5137253999710083, 0.30569368600845337, 0.0009932818356901407 ], [ 0.5021367073059082, 0.2973476052284241, 0.9871279001235962, 0.0009540970786474645 ] ] }, { "q_id": "9240_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.08189689368009567, 0.07197901606559753, 0.13115045428276062, 0.019653644412755966, 0.0038632277864962816 ], [ 0.03515516594052315, 0.031851284205913544, 0.029083985835313797, 0.06569170951843262, 0.06077811121940613, 0.019378121942281723, 0.00236162799410522 ], [ 0.09857843816280365, 0.029207846149802208, 0.06455004215240479, 0.1445271074771881, 0.058283284306526184, 0.027759941294789314, 0.0021502424497157335 ], [ 0.06754110753536224, 0.07697370648384094, 0.11010750383138657, 0.12098865956068039, 0.010598433203995228, 0.0022597291972488165 ], [ 0.06582983583211899, 0.022869305685162544, 0.04351803660392761, 0.0051201870664954185, 0.047067735344171524, 0.009377911686897278, 0.00905658956617117 ], [ 0.05704859271645546, 0.08103761076927185, 0.09861955791711807, 0.12980104982852936, 0.021604344248771667, 0.003468697192147374 ], [ 0.033967163413763046, 0.040831729769706726, 0.022088564932346344, 0.0014232845278456807 ], [ 0.1069042906165123, 0.03287621587514877, 0.047841865569353104, 0.0018288298742845654 ], [ 0.036389805376529694, 0.1553717851638794, 0.5980536341667175, 0.0035529194865375757 ], [ 0.01994926482439041, 0.018974343314766884, 0.02908680960536003, 0.11225911974906921, 0.01734386757016182, 0.016492992639541626, 0.008429741486907005, 0.016326867043972015, 0.01654760353267193, 0.003467230824753642 ], [ 0.031270582228899, 0.024822214618325233, 0.001406002906151116 ], [ 0.027007322758436203, 0.03170742094516754, 0.024279067292809486, 0.001380939851514995 ], [ 0.1054535061120987, 0.04349484294652939, 0.06389475613832474, 0.05408621206879616, 0.04193590581417084, 0.8644850850105286 ], [ 0.05167476087808609, 0.08457531034946442, 0.10007692873477936, 0.06058375909924507, 0.13065652549266815, 0.033188000321388245, 0.015897652134299278, 0.004787847399711609 ], [ 0.05026064068078995, 0.0759170725941658, 0.13031530380249023, 0.13162536919116974, 0.024333449080586433, 0.0030251590069383383 ] ] }, { "q_id": "9805_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.3379468619823456, 0.21163003146648407, 0.22400695085525513, 0.0956781879067421, 0.18868176639080048, 0.16149857640266418, 0.2002861052751541, 0.11314570903778076 ], [ 0.7604385018348694, 0.16077427566051483, 0.18609541654586792, 0.002905183471739292, 0.21754392981529236, 0.1442394256591797, 0.22352392971515656, 0.016794564202427864 ], [ 0.20030252635478973, 0.06902441382408142, 0.05915968120098114, 0.25844019651412964, 0.1585405468940735, 0.21888884902000427, 0.16023819148540497, 0.2244858294725418, 0.06279321759939194, 0.041995927691459656, 0.056022100150585175, 0.19681519269943237, 0.010538269765675068 ], [ 0.7049862146377563, 0.1131305918097496, 0.0775989219546318, 0.0593145452439785, 0.11411748081445694, 0.18636605143547058, 0.21195439994335175, 0.1789444088935852, 0.12198099493980408, 0.0756855383515358, 0.14878739416599274, 0.18542790412902832, 0.5631698966026306 ], [ 0.37520697712898254, 0.17725150287151337, 0.09213384240865707, 0.0007657700916752219, 0.11152850091457367, 0.13738134503364563, 0.08282635360956192, 0.005494162440299988, 0.15561366081237793, 0.2913229465484619, 0.23300939798355103, 0.17103752493858337, 0.11007045954465866, 0.12158334255218506, 0.19688983261585236, 0.1268409788608551, 0.25614044070243835, 0.009647693485021591 ], [ 0.2640284597873688, 0.19747769832611084, 0.008394738659262657, 0.05017051473259926, 0.028834348544478416, 0.06575841456651688, 0.02296414226293564, 0.29130837321281433, 0.08145198971033096, 0.23183000087738037, 0.1818533092737198, 0.2550436854362488, 0.0017183764139190316 ], [ 0.38838285207748413, 0.3065362572669983, 0.06651433557271957, 0.07919950783252716, 0.09792589396238327, 0.25765088200569153, 0.08612290024757385, 0.17565293610095978, 0.26654985547065735, 0.0013310645008459687 ], [ 0.7779186367988586, 0.1439231038093567, 0.17376984655857086, 0.19725094735622406, 0.1053752601146698, 0.06060207262635231, 0.03527965396642685, 0.17800600826740265, 0.19095566868782043, 0.32422181963920593 ], [ 0.15711064636707306, 0.22370083630084991, 0.3491910994052887, 0.13076819479465485, 0.18234197795391083, 0.13450729846954346, 0.20488311350345612, 0.00396185414865613 ], [ 0.4070405960083008, 0.1520126312971115, 0.07195834070444107, 0.09251505881547928, 0.11027403920888901, 0.3111390173435211, 0.17540644109249115, 0.12344527989625931, 0.1272168904542923, 0.1383637636899948, 0.16461165249347687, 0.011997218243777752 ], [ 0.3308047652244568, 0.08408257365226746, 0.3526821434497833, 0.2508409023284912, 0.24749456346035004, 0.14984595775604248, 0.07331881672143936, 0.05948757752776146, 0.0018348476151004434 ], [ 0.28307560086250305, 0.1244049072265625, 0.08461843430995941, 0.15926508605480194, 0.14292745292186737, 0.2698870003223419, 0.17178311944007874, 0.10516925156116486, 0.1737225353717804, 0.07185807079076767, 0.17839579284191132, 0.2802169919013977, 0.040821608155965805 ], [ 0.388388067483902, 0.1633348912000656, 0.07515598088502884, 0.11779969930648804, 0.18786506354808807, 0.06245936080813408, 0.23586563766002655, 0.36385172605514526, 0.2572362720966339, 0.26250308752059937, 0.0940554291009903, 0.03283516690135002, 0.14090071618556976, 0.04865197837352753, 0.13189949095249176, 0.013280096463859081 ], [ 0.7049868106842041, 0.139052152633667, 0.3664260804653168, 0.19740048050880432, 0.4425395727157593, 0.43692442774772644 ], [ 0.3200753629207611, 0.10047503560781479, 0.085438571870327, 0.29985684156417847, 0.13317063450813293, 0.2530316114425659, 0.21673274040222168, 0.1499844342470169, 0.03811441361904144, 0.22533968091011047, 0.0014817984774708748 ] ] }, { "q_id": "10285_mmlu_physics", "cot_ids": [ 1, 2, 5, 6, 7, 9, 13, 15 ], "rewards": [ [ 0.2534758150577545, 0.005579388700425625, 0.006293387617915869, 0.02898556925356388, 0.035837963223457336, 0.002255320083349943, 0.5276470184326172, 0.03831550478935242, 0.02584032155573368, 0.01443271990865469, 0.007554162759333849, 0.011978822760283947, 0.013410269282758236, 0.01564762182533741, 0.036511290818452835, 0.021675141528248787, 0.007463381160050631, 0.039922650903463364, 0.02759532257914543, 0.007852407172322273, 0.02676435187458992, 0.030748194083571434, 0.040417686104774475, 0.025202307850122452, 0.08427056670188904, 0.022152144461870193, 0.08068210631608963, 0.0027478127740323544 ], [ 0.25347453355789185, 0.01784674823284149, 0.011510971002280712, 0.016775913536548615, 0.001397584448568523, 0.01946570910513401, 0.0027033155784010887, 0.028262680396437645, 0.007796292658895254, 0.08422043174505234, 0.04415912181138992, 0.023843538016080856, 0.015941033139824867, 0.023729747161269188, 0.02026134356856346, 0.02491201087832451, 0.008445574901998043, 0.020640898495912552, 0.012688339687883854, 0.028024649247527122, 0.0532149039208889, 0.3563389182090759, 0.01904902793467045, 0.009056530892848969, 0.004851039499044418, 0.03741404414176941, 0.06556713581085205, 0.023258406668901443, 0.005911997053772211, 0.10331203043460846, 0.002560393651947379 ], [ 0.2534729838371277, 0.005579287651926279, 0.006293437443673611, 0.03697047010064125, 0.9169631600379944, 0.016629142686724663, 0.00995995756238699, 0.015820760279893875, 0.0236179381608963, 0.049711380153894424, 0.10106609016656876, 0.029693789780139923, 0.01218033954501152, 0.02700098231434822, 0.021999873220920563, 0.19772084057331085, 0.9952298402786255 ], [ 0.2534758150577545, 0.00636623939499259, 0.005039696581661701, 0.020753435790538788, 0.023965101689100266, 0.003525558626279235, 0.04133138433098793, 0.009633033536374569, 0.8377156257629395, 0.024577762931585312, 0.014863795600831509, 0.015250654891133308, 0.00956251472234726, 0.01557504665106535, 0.008935291320085526, 0.017445703968405724, 0.034575704485177994, 0.032332032918930054, 0.028907187283039093, 0.053560953587293625, 0.01448164414614439, 0.04639367014169693, 0.03055616281926632, 0.014509552158415318, 0.030570445582270622, 0.03997054696083069, 0.00863940641283989, 0.034771014004945755, 0.011234618723392487, 0.039555568248033524, 0.9861927628517151 ], [ 0.25347769260406494, 0.0076681096106767654, 0.004124908242374659, 0.015392288565635681, 0.027821354568004608, 0.0037654638290405273, 0.03945370391011238, 0.009550472721457481, 0.04450240731239319, 0.015147898346185684, 0.02331649698317051, 0.01625766046345234, 0.029415054246783257, 0.02732730470597744, 0.025045666843652725, 0.03465045616030693, 0.02947639301419258, 0.3088441491127014, 0.027028242126107216, 0.0452190525829792, 0.026792623102664948, 0.04681471362709999, 0.06636574864387512, 0.03983939439058304, 0.11261934041976929, 0.2065129578113556, 0.0035284494515508413 ], [ 0.25169727206230164, 0.004321071784943342, 0.9191889762878418, 0.009099725633859634, 0.05887888744473457, 0.005996025167405605, 0.03691926971077919, 0.0670725479722023, 0.9919857978820801 ], [ 0.2534763514995575, 0.00324392132461071, 0.01681763492524624, 0.006915300153195858, 0.052051328122615814, 0.011625216342508793, 0.025987429544329643, 0.002647148445248604 ], [ 0.2534765303134918, 0.01252036727964878, 0.006284983363002539, 0.017202140763401985, 0.0838921070098877, 0.004294185433536768, 0.15300284326076508, 0.01656491681933403, 0.027421090751886368, 0.016311557963490486, 0.0147971510887146, 0.016723008826375008, 0.010644548572599888, 0.032191842794418335, 0.017812330275774002, 0.028531448915600777, 0.020958809182047844, 0.051870014518499374, 0.034921810030937195, 0.0656888410449028, 0.018063420429825783, 0.03043186292052269, 0.059281181544065475, 0.0213923342525959, 0.0375889353454113, 0.059477388858795166, 0.06694959849119186 ] ] }, { "q_id": "9217_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.003997812978923321, 0.0004769926017615944 ], [ 0.0059906961396336555, 0.0005333037697710097 ], [ 0.0038293860852718353, 0.0004824731731787324 ], [ 0.006201430223882198, 0.0005221274914219975 ], [ 0.0034582368098199368, 0.0006191632128320634 ], [ 0.993232011795044, 0.7963109612464905, 0.9986086487770081 ], [ 0.0037560793571174145, 0.00047597018419764936 ], [ 0.995191216468811, 0.9889428615570068, 0.9993849992752075 ], [ 0.003649333259090781, 0.0004731041844934225 ], [ 0.007274214178323746, 0.9954734444618225 ], [ 0.006317043211311102, 0.01228373683989048, 0.000645133201032877 ], [ 0.0035091014578938484, 0.03555808216333389, 0.0021308071445673704, 0.0005702499765902758 ], [ 0.2685951888561249, 0.994009256362915, 0.9994770884513855 ], [ 0.003992936573922634, 0.0004951511509716511 ], [ 0.8424416184425354, 0.9975897073745728, 0.999405026435852 ], [ 0.49052590131759644, 0.9968892931938171, 0.9993096590042114 ] ] }, { "q_id": "9456_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.23807188868522644, 0.9992361068725586, 0.9999594688415527 ], [ 0.9918145537376404, 0.9997289776802063, 0.9999758005142212 ], [ 0.8458587527275085, 0.30976584553718567, 0.99944669008255, 0.999956488609314 ], [ 0.9728776216506958, 0.9996858835220337, 0.9999598264694214 ], [ 0.018665779381990433, 0.9995790123939514, 0.9999639987945557 ], [ 0.23808398842811584, 0.9995018243789673, 0.9999654293060303 ], [ 0.745934784412384, 0.3746671676635742, 0.933501124382019, 0.4727424383163452, 0.9996153116226196, 0.9999741315841675 ], [ 0.9728782773017883, 0.9996744394302368, 0.9999668598175049 ], [ 0.9840590953826904, 0.8838820457458496, 0.9995917677879333, 0.9999723434448242 ], [ 0.9416142702102661, 0.9997014403343201, 0.9999675750732422 ], [ 0.2380640059709549, 0.23793186247348785, 0.18096835911273956, 0.9985718727111816, 0.9999446868896484 ], [ 0.9810196757316589, 0.9989011287689209, 0.9999526739120483 ], [ 0.23804178833961487, 0.9996455907821655, 0.9999572038650513 ], [ 0.9798638820648193, 0.9048210978507996, 0.9043692350387573, 0.030818387866020203, 0.9993311166763306, 0.9999675750732422 ], [ 0.9922268390655518, 0.3250669836997986, 0.9997531771659851, 0.999981164932251 ], [ 0.23805943131446838, 0.9996215105056763, 0.9999604225158691 ] ] }, { "q_id": "10335_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.6806904077529907, 0.5234200954437256, 0.9983691573143005, 0.9999563694000244 ], [ 0.6581258773803711, 0.9996685981750488, 0.9999586343765259 ], [ 0.998791515827179, 0.9999366998672485 ], [ 0.9998125433921814, 0.9999665021896362 ], [ 0.9998158812522888, 0.9999675750732422 ], [ 0.9998158812522888, 0.9989458918571472, 0.9999679327011108 ], [ 0.9998008608818054, 0.9999682903289795 ], [ 0.9987508058547974, 0.9999063014984131 ], [ 0.999810516834259, 0.9999581575393677 ], [ 0.9998158812522888, 0.9989458918571472, 0.9999679327011108 ], [ 0.9997860789299011, 0.9988890290260315, 0.999968409538269, 0.9999243021011353 ], [ 0.040172383189201355, 0.9989292025566101, 0.9999251365661621 ], [ 0.9997740387916565, 0.9999638795852661 ], [ 0.9997473359107971, 0.9999598264694214 ], [ 0.01526004821062088, 0.9982373714447021, 0.9999377727508545 ], [ 0.9997809529304504, 0.9999603033065796 ] ] }, { "q_id": "9532_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.038266636431217194, 0.021453682333230972, 0.020935602486133575, 0.02216147445142269, 0.13326413929462433, 0.981304407119751, 0.9972622394561768 ], [ 0.33608561754226685, 0.1724817156791687, 0.2985551655292511, 0.4027702510356903, 0.4324311912059784, 0.9939633011817932 ], [ 0.0382663793861866, 0.06537045538425446, 0.0018919989233836532, 0.03844427689909935, 0.9919222593307495 ], [ 0.03826651722192764, 0.017704136669635773, 0.014136902056634426, 0.027897600084543228, 0.08116379380226135, 0.43837612867355347, 0.9932796359062195 ], [ 0.03826667368412018, 0.016403356567025185, 0.013630974106490612, 0.027532758191227913, 0.2705259621143341, 0.9881592988967896, 0.9975391626358032 ], [ 0.03826649859547615, 0.018519850447773933, 0.015004400163888931, 0.014290690422058105, 0.4236461818218231, 0.9935433864593506 ], [ 0.038266900926828384, 0.02182995155453682, 0.019123336300253868, 0.023260390385985374, 0.5995070934295654, 0.9949309229850769 ], [ 0.18035832047462463, 0.11734115332365036, 0.18155537545681, 0.14153175055980682, 0.0781392827630043, 0.07455229014158249, 0.17821717262268066, 0.04344656318426132, 0.9893504977226257 ], [ 0.038266707211732864, 0.034809909760951996, 0.17226675152778625, 0.9798984527587891, 0.997032880783081 ], [ 0.03826654702425003, 0.31197836995124817, 0.00256168469786644, 0.02583596482872963, 0.9900655746459961 ], [ 0.37904903292655945, 0.04052630811929703, 0.9761715531349182, 0.9969122409820557 ], [ 0.038266900926828384, 0.01351992692798376, 0.01608433946967125, 0.02115081436932087, 0.2234872430562973, 0.0016284402227029204, 0.07968746870756149, 0.9912772178649902 ], [ 0.34346890449523926, 0.22316032648086548, 0.24444541335105896, 0.840350329875946, 0.9958842396736145, 0.99544358253479 ], [ 0.07810597866773605, 0.35925084352493286, 0.0022358957212418318, 0.019904082641005516, 0.0618177205324173, 0.9945148229598999 ], [ 0.3403250575065613, 0.1331283152103424, 0.2546660602092743, 0.3970652222633362, 0.7887381315231323, 0.9969229102134705 ], [ 0.038266636431217194, 0.019233088940382004, 0.03830064460635185, 0.039107974618673325, 0.7383530735969543, 0.9941348433494568 ] ] }, { "q_id": "9884_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 ], "rewards": [ [ 0.6404462456703186, 0.021351492032408714, 0.039331600069999695, 0.017506243661046028, 0.02598891407251358, 0.03747322037816048, 0.0032685056794434786, 0.03817092254757881, 0.025991244241595268, 0.9834845662117004, 0.00044668669579550624 ], [ 0.6181913018226624, 0.0053688520565629005, 0.01947648823261261, 0.029421959072351456, 0.031990982592105865, 0.02598092518746853, 0.002108881715685129, 0.003226183820515871, 0.02380930446088314, 0.06989898532629013, 0.0004191321786493063, 0.09643014520406723, 0.010901848785579205, 0.4622615873813629, 0.0003484397893771529 ], [ 0.6810785531997681, 0.006472498178482056, 0.0001475441240472719, 0.03138728439807892, 0.009397124871611595, 0.028284115716814995, 0.059591684490442276, 0.0008670749375596642, 0.02464619278907776, 0.03430662676692009, 0.035960983484983444, 0.0004511749430093914 ], [ 0.1467367559671402, 0.028456103056669235, 0.03684639930725098, 0.015010600909590721, 0.1269254982471466, 0.016844313591718674, 0.07944860309362411, 0.022198664024472237, 0.024775778874754906, 0.03677152469754219, 0.05624505132436752, 0.025144008919596672, 0.01090418454259634, 0.0005751911667175591 ], [ 0.9561578631401062, 0.009683258831501007, 0.03326740488409996, 0.011617816053330898, 0.05985751003026962, 0.03872481733560562, 0.04935186356306076, 0.0370984710752964, 0.05843159183859825, 0.03400907292962074, 0.0004982864484190941 ], [ 0.6810756325721741, 0.008724319748580456, 0.03784876689314842, 0.013790084980428219, 0.01672082208096981, 0.023609207943081856, 0.023842940106987953, 0.03348103165626526, 0.02409467101097107, 0.01534696388989687, 0.08185265958309174, 0.0005802296800538898 ], [ 0.6404491662979126, 0.01377364993095398, 0.05868026241660118, 0.018233131617307663, 0.015865815803408623, 0.02956085279583931, 0.01753009296953678, 0.03057658113539219, 0.005668348632752895, 0.11310809850692749, 0.9975205063819885, 0.9999030828475952 ], [ 0.16795043647289276, 0.028529437258839607, 0.010816504247486591, 0.01759031042456627, 0.015227549709379673, 0.018484987318515778, 0.0022899832110852003, 0.12066301703453064, 0.04265136271715164, 0.0005628681392408907 ], [ 0.6810756325721741, 0.012800277210772038, 0.0002905611472669989, 0.050416357815265656, 0.0056576356291770935, 0.029328230768442154, 0.03749064356088638, 0.018976422026753426, 0.021964166313409805, 0.0017055526841431856, 0.03515821695327759, 0.0423663966357708, 0.0005197381833568215 ], [ 0.6404514908790588, 0.009648991748690605, 0.00022420997265726328, 0.019478965550661087, 0.031083887442946434, 0.036151040345430374, 0.027682505548000336, 0.06696268171072006, 0.009282490238547325, 0.030547676607966423, 0.04258175939321518, 0.07834245264530182, 0.05245093256235123, 0.04489253833889961, 0.0019712508656084538, 0.0005116206011734903 ], [ 0.018010109663009644, 0.009221517480909824, 0.017854005098342896, 0.030138641595840454, 0.02789289504289627, 0.09333242475986481, 0.14009681344032288, 0.016493719071149826, 0.016908887773752213, 0.030553283169865608, 0.01912306435406208, 0.10342611372470856, 0.0005674744606949389 ], [ 0.8557537198066711, 0.015796884894371033, 0.0349508672952652, 0.023748688399791718, 0.060484956949949265, 0.041676584631204605, 0.056619055569171906, 0.04198012501001358, 0.068763867020607, 0.9963891506195068, 0.9998409748077393 ], [ 0.014333939179778099, 0.00048275766312144697, 0.04843592643737793, 0.006672444753348827, 0.022557826712727547, 0.016210634261369705, 0.027206450700759888, 0.0010579046793282032, 0.034995391964912415, 0.0031733736395835876, 0.000671865011099726 ], [ 0.6404464244842529, 0.010948491282761097, 0.04103734716773033, 0.017095796763896942, 0.03780735656619072, 0.039110999554395676, 0.025891972705721855, 0.056098222732543945, 0.11641070991754532, 0.08147925138473511, 0.03887590393424034, 0.029531607404351234, 0.03387543559074402, 0.3222229778766632, 0.0005240341415628791 ], [ 0.31524425745010376, 0.010579823516309261, 0.02450532093644142, 0.06988993287086487, 0.03346266224980354, 0.06668558716773987, 0.030145680531859398, 0.007482096552848816, 0.022894959896802902, 0.041071005165576935, 0.02190723828971386, 0.0005287136882543564 ] ] }, { "q_id": "9133_mmlu_physics", "cot_ids": [ 0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4995594024658203, 0.15746591985225677, 0.6872987747192383, 0.4491821527481079, 0.5175946950912476, 0.03159276023507118, 0.1725090593099594, 0.057897038757801056, 0.6384536623954773, 0.015810510143637657, 0.44619184732437134, 0.978679895401001, 0.9974955916404724 ], [ 0.4409218728542328, 0.025244714692234993, 0.13178034126758575, 0.6333480477333069, 0.04739156737923622, 0.6567492485046387, 0.033065665513277054, 0.4088701605796814, 0.9836843013763428, 0.9976775050163269 ], [ 0.45564505457878113, 0.23722612857818604, 0.751773476600647, 0.8279255032539368, 0.9883920550346375, 0.9970439076423645 ], [ 0.13569504022598267, 0.08061441034078598, 0.11590148508548737, 0.27244967222213745, 0.013511771336197853, 0.5162423849105835, 0.807334840297699, 0.9902018904685974, 0.9972447156906128 ], [ 0.33474108576774597, 0.011573411524295807, 0.020997464656829834, 0.13008369505405426, 0.5016646385192871, 0.34131401777267456, 0.096058689057827, 0.646724283695221, 0.9924166202545166 ], [ 0.3347434103488922, 0.0019820895977318287, 0.2222263664007187, 0.0004207775054965168, 0.3213237524032593, 0.0008069421164691448, 0.019749734550714493, 0.15258915722370148, 0.93880295753479, 0.9930216670036316 ], [ 0.6050676107406616, 0.20379401743412018, 0.5388622879981995, 0.04367785155773163, 0.6815130114555359, 0.797573983669281, 0.9919004440307617, 0.997867226600647 ], [ 0.5833649039268494, 0.21897438168525696, 0.07740426063537598, 0.6719065308570862, 0.012482473626732826, 0.17681105434894562, 0.06190721318125725, 0.6233618855476379, 0.9774336218833923, 0.9971798658370972 ], [ 0.1233195811510086, 0.11186103522777557, 0.000335779128363356, 0.7669891119003296, 0.029452815651893616, 0.6913867592811584, 0.0010655533988028765, 0.704056441783905, 0.9691534042358398, 0.003968443721532822 ], [ 0.5833600759506226, 0.23122695088386536, 0.7733957767486572, 0.034219469875097275, 0.7278308868408203, 0.026384443044662476, 0.4706665277481079, 0.9821010231971741, 0.9970333576202393 ], [ 0.1904345154762268, 0.13963647186756134, 0.1675843894481659, 0.507326066493988, 0.03574883192777634, 0.8567528128623962, 0.1650201678276062, 0.44270941615104675, 0.9826937317848206, 0.9979169964790344 ], [ 0.3347395658493042, 0.017371585592627525, 0.0909322202205658, 0.1174653172492981, 0.38244256377220154, 0.028105901554226875, 0.10764873027801514, 0.05314325913786888, 0.42958080768585205, 0.21109932661056519, 0.3686436116695404, 0.9851967096328735, 0.9981805086135864 ], [ 0.23791301250457764, 0.09801805019378662, 0.0033170587848871946, 0.019426830112934113, 0.07959617674350739, 0.20114487409591675, 0.004560237284749746, 0.45402082800865173, 0.058732252568006516, 0.8366380929946899, 0.9890009164810181, 0.9975830316543579 ], [ 0.17794468998908997, 0.17167899012565613, 0.10236090421676636, 0.0981992706656456, 0.2610495388507843, 0.027844423428177834, 0.06724009662866592, 0.4775995910167694, 0.8416973352432251, 0.10824399441480637, 0.3963501453399658, 0.983407199382782, 0.9970613121986389 ] ] }, { "q_id": "10289_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.17358152568340302, 0.05177406966686249, 0.10221011936664581, 0.0390692837536335, 0.7942772507667542, 0.9885134100914001 ], [ 0.1006912887096405, 0.04777379706501961, 0.06824207305908203, 0.05921990051865578, 0.010642515495419502, 0.038610875606536865, 0.017254674807190895, 0.0679965615272522, 0.10589738935232162, 0.05214361473917961, 0.04928751662373543, 0.014379720203578472, 0.0010205396683886647 ], [ 0.24206914007663727, 0.11093852669000626, 0.13534164428710938, 0.9879314303398132, 0.9950165152549744 ], [ 0.1601688414812088, 0.0271003395318985, 0.08971314132213593, 0.7409069538116455, 0.18018977344036102, 0.9847041368484497, 0.9979857206344604 ], [ 0.1601685732603073, 0.020730337128043175, 0.02486308664083481, 0.04938375577330589, 0.6058854460716248, 0.15974703431129456, 0.001875360612757504, 0.010883652605116367, 0.05708245560526848, 0.8219355940818787, 0.990113377571106 ], [ 0.16016831994056702, 0.02073081210255623, 0.029751695692539215, 0.5705886483192444, 0.09927493333816528, 0.28548264503479004, 0.9929064512252808, 0.9983237385749817 ], [ 0.1601693332195282, 0.02073068358004093, 0.05055198818445206, 0.6736586689949036, 0.09342927485704422, 0.1844853311777115, 0.9790254235267639, 0.9971887469291687 ], [ 0.1601690798997879, 0.020730607211589813, 0.20500928163528442, 0.01771155372262001, 0.9813450574874878, 0.994820237159729 ], [ 0.1601690798997879, 0.01583302952349186, 0.02624961920082569, 0.018489252775907516, 0.20167560875415802, 0.01701373979449272, 0.08038922399282455, 0.990523636341095, 0.9952437281608582 ], [ 0.09881466627120972, 0.06102177873253822, 0.9251344799995422, 0.9829130172729492 ], [ 0.1309734731912613, 0.20767420530319214, 0.9725701212882996, 0.9945969581604004 ], [ 0.16016927361488342, 0.02073049172759056, 0.03921934589743614, 0.3788878917694092, 0.08926493674516678, 0.14472432434558868, 0.9802019000053406, 0.9970232844352722 ], [ 0.16016831994056702, 0.02073081210255623, 0.040621720254421234, 0.3704720437526703, 0.08278940618038177, 0.14754840731620789, 0.989589512348175, 0.9973495006561279 ], [ 0.16016991436481476, 0.020730741322040558, 0.03748568892478943, 0.04220135509967804, 0.241427481174469, 0.09123038500547409, 0.14473551511764526, 0.9769914746284485, 0.9970335960388184 ], [ 0.09494263678789139, 0.12678247690200806, 0.04913441836833954, 0.21643376350402832, 0.0403561107814312, 0.9124568104743958, 0.989009439945221 ], [ 0.1456536054611206, 0.12490163743495941, 0.9749564528465271, 0.9914073348045349 ] ] }, { "q_id": "9443_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8311291933059692, 0.6291078329086304, 0.06852111965417862, 0.09160882234573364, 0.1301100254058838, 0.027750495821237564, 0.16458778083324432, 0.3173343241214752, 0.12088130414485931, 0.9920808672904968, 0.9994478821754456 ], [ 0.8077772855758667, 0.7048125267028809, 0.057549815624952316, 0.08792637288570404, 0.02702030912041664, 0.27055418491363525, 0.9958195686340332, 0.9995469450950623 ], [ 0.7528917193412781, 0.8115717172622681, 0.5208438038825989, 0.9980415105819702, 0.9995686411857605 ], [ 0.09819123893976212, 0.07620301097631454, 0.3657269775867462, 0.9111442565917969, 0.035700473934412, 0.17964337766170502, 0.0017688518855720758, 0.36026614904403687, 0.13961559534072876, 0.9951804876327515, 0.9992951154708862 ], [ 0.6179433465003967, 0.8149924278259277, 0.030262911692261696, 0.024225810542702675, 0.18123576045036316, 0.032601308077573776, 0.09517521411180496, 0.008524640463292599, 0.18970058858394623, 0.9943617582321167, 0.9994555115699768 ], [ 0.8691078424453735, 0.7684305310249329, 0.06808977574110031, 0.018717126920819283, 0.03491753712296486, 0.11984488368034363, 0.040991637855768204, 0.2151901125907898, 0.9882319569587708, 0.9992339611053467 ], [ 0.8686231374740601, 0.5572212934494019, 0.07317862659692764, 0.10337641835212708, 0.9900858402252197, 0.9992126226425171 ], [ 0.13128194212913513, 0.045895375311374664, 0.000446642457973212, 0.048690441995859146, 0.16448462009429932, 0.8358949422836304, 0.17392230033874512, 0.027312355116009712, 0.20200687646865845, 0.18754532933235168, 0.3130398392677307, 0.17278246581554413, 0.9900646805763245, 0.9990513920783997 ], [ 0.10168109834194183, 0.08286374807357788, 0.09700034558773041, 0.014364764094352722, 0.09420782327651978, 0.28622671961784363, 0.020172419026494026, 0.022617517039179802, 0.08600279688835144, 0.27930325269699097, 0.08720262348651886, 0.9872105121612549, 0.0009422639850527048 ], [ 0.11433703452348709, 0.04487113282084465, 0.00013863334606867284, 0.11937074363231659, 0.9081541299819946, 0.058160215616226196, 0.44478341937065125, 0.032539643347263336, 0.19866257905960083, 0.00494455685839057, 0.08621672540903091, 0.010075408034026623, 0.9612163305282593, 0.0009504840709269047 ], [ 0.08556205034255981, 0.06609658896923065, 0.08406700938940048, 0.05593457818031311, 0.26572880148887634, 0.026981281116604805, 0.6366785764694214, 0.10994687676429749, 0.9954700469970703, 0.9993813037872314 ], [ 0.6678923964500427, 0.8649778366088867, 0.051063649356365204, 0.026837404817342758, 0.0002781741786748171, 0.21710903942584991, 0.039691150188446045, 0.17338153719902039, 0.04238737374544144, 0.1634720414876938, 0.9894223809242249, 0.9994138479232788 ], [ 0.19344428181648254, 0.0974721685051918, 0.32608041167259216, 0.8178033232688904, 0.03256377577781677, 0.11801005899906158, 0.028585685417056084, 0.1436799317598343, 0.9924848675727844, 0.9990667700767517 ], [ 0.5209975838661194, 0.8076609373092651, 0.2673887312412262, 0.12936696410179138, 0.9903061389923096, 0.9987456798553467 ], [ 0.9377963542938232, 0.04149884358048439, 0.021096890792250633, 0.028199704363942146, 0.00019770293147303164, 0.15307040512561798, 0.03856884315609932, 0.11277874559164047, 0.07762622833251953, 0.0013056054012849927 ], [ 0.9219434857368469, 0.693867564201355, 0.06350980699062347, 0.5729568004608154, 0.04016853868961334, 0.31566181778907776, 0.9963567852973938, 0.99936443567276 ] ] }, { "q_id": "10153_mmlu_physics", "cot_ids": [ 0, 2, 3, 5, 6, 7, 8, 9, 13, 14, 15 ], "rewards": [ [ 0.21706819534301758, 0.05354314297437668, 0.09543035924434662, 0.07115931063890457, 0.028795292600989342, 0.008453206159174442 ], [ 0.21706850826740265, 0.05189337581396103, 0.11356920748949051, 0.06695052236318588, 0.1859017312526703, 0.38694462180137634, 0.24849151074886322, 0.07700329273939133, 0.0014280363684520125 ], [ 0.21706882119178772, 0.03745357692241669, 0.04663127660751343, 0.14565306901931763, 0.08783234655857086, 0.01759970560669899, 0.007647299207746983 ], [ 0.21706777811050415, 0.07192367315292358, 0.02982887625694275, 0.18644921481609344, 0.17430870234966278, 0.15400493144989014, 0.03830724582076073, 0.0020048334263265133 ], [ 0.21707038581371307, 0.044634509831666946, 0.016073912382125854, 0.11790075898170471, 0.08062055706977844, 0.18608812987804413, 0.1453382670879364, 0.011502119712531567 ], [ 0.21706858277320862, 0.06320496648550034, 0.007454629056155682, 0.10912033170461655, 0.053399961441755295, 0.05768716707825661, 0.06779370456933975, 0.005138833541423082, 0.057271283119916916, 0.00720568373799324, 0.036906249821186066, 0.02943047136068344, 0.007667757570743561, 0.016533875837922096 ], [ 0.21707069873809814, 0.08736483007669449, 0.016620386391878128, 0.18806521594524384, 0.04413554072380066, 0.421821266412735, 0.4022860527038574, 0.001491767936386168 ], [ 0.21706965565681458, 0.03056042641401291, 0.08697236329317093, 0.0018812634516507387, 0.03360864147543907, 0.2640230059623718, 0.004504059441387653, 0.07514458149671555, 0.004786777310073376, 0.09074646234512329, 0.06952234357595444, 0.012908359058201313 ], [ 0.21707038581371307, 0.08957581222057343, 0.09325172752141953, 0.028147313743829727, 0.04136083275079727, 0.029405120760202408, 0.009817592799663544, 0.014213189482688904, 0.0011297615710645914 ], [ 0.13546720147132874, 0.0515676811337471, 0.05343148857355118, 0.0576263889670372, 0.12130215018987656, 0.19174805283546448, 0.04100620374083519, 0.15079830586910248, 0.0013288796180859208 ], [ 0.21706795692443848, 0.09608941525220871, 0.11536378413438797, 0.07464933395385742, 0.3346732258796692, 0.050917886197566986, 0.012434695847332478, 0.007436369080096483 ] ] }, { "q_id": "9649_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 7, 11 ], "rewards": [ [ 0.46174007654190063, 0.0001860200718510896, 4.312070814194158e-05, 5.08823104610201e-05, 0.0015571363037452102, 0.0009418749832548201, 0.0002800178772304207 ], [ 0.4324856996536255, 0.1006561890244484, 0.04332245513796806, 0.04282221570611, 0.017371365800499916, 0.03132186830043793, 0.08142220228910446, 0.1463446319103241, 0.07172363251447678, 0.2505472004413605, 0.9054040312767029, 0.000600457948166877 ], [ 0.3594389259815216, 0.010347207076847553, 0.0024372695479542017, 0.0028668560553342104, 0.002310618292540312, 0.006652072072029114, 0.006788980681449175, 0.002437046729028225 ], [ 0.4617408215999603, 0.018952742218971252, 0.011383739300072193, 0.011981572024524212, 0.013787704519927502, 0.01759248599410057, 0.16153757274150848, 0.018576819449663162, 0.04084635153412819, 0.27271178364753723, 0.017804814502596855, 0.10229261964559555, 0.03127535805106163, 0.038898859173059464, 0.015193922445178032, 0.0268243458122015, 0.008490057662129402 ], [ 0.3594362735748291, 0.10073058307170868, 0.09242181479930878, 0.13189014792442322, 0.09352876245975494, 0.015889285132288933, 0.3251335024833679, 0.34599629044532776, 0.7331160306930542, 0.0005755805177614093 ], [ 0.359436959028244, 0.024508537724614143, 0.022529710084199905, 0.022041328251361847, 0.03247779607772827, 0.029892761260271072, 0.06556547433137894, 0.047999486327171326, 0.0141677837818861, 0.3716120719909668, 0.3240490257740021, 0.20435553789138794, 0.000664851104374975 ] ] }, { "q_id": "9863_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 ], "rewards": [ [ 0.06915727257728577, 0.041107118129730225, 0.00039748300332576036, 0.040822144597768784, 0.010882857255637646, 0.09967076033353806, 0.00045741902431473136, 0.17803174257278442, 0.26335400342941284, 0.24382269382476807 ], [ 0.04613642394542694, 0.02505510114133358, 0.03847727179527283, 0.04076153039932251, 0.042620208114385605, 0.012508299201726913, 0.1284540742635727, 0.2281142771244049, 0.2122151255607605 ], [ 0.11495977640151978, 0.11400312930345535, 0.08725235611200333, 0.03806144744157791, 0.04515272006392479, 0.03143726661801338, 0.13543210923671722, 0.16007226705551147, 0.150766983628273, 0.0076913293451070786 ], [ 0.08417508751153946, 0.004889380186796188, 0.0038052585441619158, 0.01697251945734024, 0.0002075820229947567, 0.06049484759569168, 0.0019807901699095964, 0.03624702990055084, 0.014401381835341454, 0.5934450030326843, 0.8217083215713501 ], [ 0.09587881714105606, 0.006244403775781393, 0.03106166608631611, 0.0004422844504006207, 0.048431530594825745, 0.03717648237943649, 0.0044614216312766075, 0.17289242148399353, 0.6332242488861084 ], [ 0.020159337669610977, 0.028810713440179825, 0.0003127669624518603, 0.0322287380695343, 0.03975222632288933, 0.0654207170009613, 0.038545072078704834, 0.0960264801979065, 0.0003726415743585676, 0.18901747465133667, 0.05506336688995361, 0.020016714930534363 ], [ 0.1425468623638153, 0.009724613279104233, 0.03470546007156372, 0.0020729009993374348, 0.03471274673938751, 0.05549544095993042, 0.047134511172771454, 0.0006541103357449174, 0.0321374237537384, 0.05267448350787163, 0.20499832928180695, 0.10682355612516403, 0.025700312107801437 ], [ 0.11008919030427933, 0.008155650459229946, 0.03791365772485733, 0.0003841572906821966, 0.034245312213897705, 0.05683606117963791, 0.053227681666612625, 0.17443713545799255, 0.021814651787281036 ], [ 0.10482563823461533, 0.047465741634368896, 0.043691642582416534, 0.038442619144916534, 0.08475049585103989, 0.10258593410253525, 0.033269066363573074, 0.07515239715576172, 0.16191983222961426, 0.18310661613941193 ], [ 0.08350611478090286, 0.008237527683377266, 0.04400302469730377, 0.00033711412106640637, 0.04798833280801773, 0.05989254266023636, 0.040644507855176926, 0.032264746725559235, 0.03197365254163742, 0.024889133870601654, 0.015627605840563774, 0.020928647369146347, 0.013508444651961327, 0.0050459145568311214 ], [ 0.1100868508219719, 0.009564950130879879, 0.03423149511218071, 0.03749588876962662, 0.0806303471326828, 0.21029451489448547, 0.23820719122886658 ], [ 0.08417446166276932, 0.0069325752556324005, 0.025405528023838997, 0.00415610009804368, 0.00012070234515704215, 0.09353891015052795, 0.012815729714930058, 0.014616617932915688, 0.1832304149866104, 0.012741613201797009, 0.002644176594913006, 0.022493237629532814, 0.02529466338455677, 0.028459912165999413, 0.05953574925661087, 0.08182023465633392, 0.10310743004083633, 0.027903497219085693 ], [ 0.11008859425783157, 0.00815572403371334, 0.030365360900759697, 0.06330379843711853, 0.019502311944961548, 0.01840871386229992, 0.050266083329916, 0.05768115445971489, 0.023884838446974754 ], [ 0.11008773744106293, 0.008155816234648228, 0.09849796444177628, 0.0639946237206459, 0.07795098423957825, 0.0044773356057703495, 0.0246058888733387, 0.007241691928356886, 0.036281462758779526, 0.05953873693943024, 0.02808896265923977, 0.023978231474757195 ], [ 0.04906703159213066, 0.028093701228499413, 0.046040378510951996, 0.03322860226035118, 0.00937085784971714, 0.05336272716522217, 0.061680253595113754, 0.024741478264331818 ] ] }, { "q_id": "9420_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.040068369358778, 0.2572377026081085, 0.5782686471939087, 0.9145081639289856 ], [ 0.06828924268484116, 0.1388425976037979, 0.6274494528770447, 0.8243188261985779 ], [ 0.02300434187054634, 0.0013110034633427858, 0.005913070403039455, 0.013739463873207569, 0.8802742958068848, 0.5252407789230347 ], [ 0.06373980641365051, 0.32829543948173523, 0.5703050494194031, 0.8376919031143188 ], [ 0.5739925503730774, 0.14478757977485657, 0.26927390694618225, 0.9791472554206848, 0.8822979927062988 ], [ 0.21965070068836212, 0.9137391448020935, 0.803434431552887, 0.7694200277328491 ], [ 0.06828965246677399, 0.2196616679430008, 0.7328593134880066, 0.7971086502075195 ], [ 0.06828935444355011, 0.1316235214471817, 0.3515830934047699, 0.018835000693798065 ], [ 0.0334363728761673, 0.246747225522995, 0.2510010600090027, 0.8025003671646118 ], [ 0.06828932464122772, 0.08475367724895477, 0.241615891456604, 0.8694125413894653 ], [ 0.05173597112298012, 0.27314475178718567, 0.2208438515663147, 0.8576880693435669 ], [ 0.023004543036222458, 0.0013507065596058965, 0.024290671572089195, 0.9404939413070679, 0.932808518409729 ], [ 0.046532656997442245, 0.13897693157196045, 0.07338150590658188, 0.3683186173439026, 0.8773599863052368 ], [ 0.04825414717197418, 0.16536423563957214, 0.0871298536658287, 0.878271758556366 ], [ 0.05152024328708649, 0.1874563992023468, 0.779218852519989, 0.9777076244354248, 0.9046636819839478 ], [ 0.07079815864562988, 0.13642588257789612, 0.2166646271944046, 0.9040273427963257 ] ] }, { "q_id": "9527_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.09354125708341599, 0.05986014008522034, 0.7071489095687866, 0.0031650415621697903 ], [ 0.22732490301132202, 0.010407621040940285, 0.007516935933381319, 0.001111102756112814, 0.030463609844446182, 0.01589220017194748, 0.04070580005645752, 0.0031402241438627243, 0.07047474384307861, 0.1205955371260643, 0.0014593856176361442 ], [ 0.17158104479312897, 0.01754400134086609, 0.07877197116613388, 0.029704809188842773, 0.0860956460237503, 0.02691660262644291, 0.8449921607971191, 0.11809084564447403, 0.9382534623146057, 0.09403003752231598 ], [ 0.3333054780960083, 0.029640650376677513, 0.1273731142282486, 0.7688199281692505, 0.9563271403312683, 0.15781937539577484 ], [ 0.20929816365242004, 0.013620706275105476, 0.01585366204380989, 0.03356782719492912, 0.029761428013443947, 0.10160211473703384, 0.04628889262676239, 0.07079605758190155, 0.11889582127332687, 0.6252837181091309, 0.37600088119506836, 0.11037907004356384, 0.9134556651115417, 0.03318460285663605 ], [ 0.08078842610120773, 0.11030589789152145, 0.013780958950519562, 0.06992462277412415, 0.18181371688842773, 0.17572325468063354, 0.010357941500842571, 0.07056434452533722, 0.011059042997658253, 0.06453968584537506, 0.0020064448472112417 ], [ 0.0565207414329052, 0.05423087999224663, 0.057160042226314545, 0.22197923064231873, 0.02340475656092167, 0.03642228990793228, 0.04585624113678932, 0.06265440583229065, 0.0311787948012352, 0.5731887221336365, 0.04889928176999092, 0.9607818126678467, 0.024711720645427704 ], [ 0.051066651940345764, 0.04966834932565689, 0.05527558550238609, 0.02763984724879265, 0.06943698227405548, 0.11883289366960526, 0.02116762287914753, 0.03183126077055931, 0.1269916146993637, 0.02354022115468979, 0.3463748097419739, 0.33095818758010864, 0.08799656480550766, 0.9641128182411194, 0.0626339316368103 ], [ 0.20929855108261108, 0.013620712794363499, 0.017091043293476105, 0.000404719467042014, 0.03248153254389763, 0.013782946392893791, 0.08320719748735428, 0.06835027039051056, 0.13172699511051178, 0.027631442993879318, 0.09178898483514786, 0.47272413969039917, 0.39229363203048706, 0.9684261679649353, 0.13521647453308105 ], [ 0.20929570496082306, 0.016016293317079544, 0.016671644523739815, 0.03274514526128769, 0.008406611159443855, 0.23058070242404938, 0.050746649503707886, 0.07015886902809143, 0.22073113918304443, 0.0262648593634367, 0.5451990365982056, 0.3431977927684784, 0.8648664951324463, 0.06195070594549179 ], [ 0.05106600746512413, 0.049796707928180695, 0.05810588598251343, 0.008912227116525173, 0.09813480824232101, 0.08298075944185257, 0.3093009293079376, 0.0159907229244709, 0.03591201826930046, 0.44846612215042114, 0.08862918615341187, 0.08904077112674713, 0.943743884563446, 0.02334236539900303 ], [ 0.07877225428819656, 0.06610047817230225, 0.020953506231307983, 0.06936918944120407, 0.058575812727212906, 0.0622628778219223, 0.04912266135215759, 0.012021024711430073, 0.0027706350665539503 ], [ 0.05106709152460098, 0.04966861382126808, 0.05527560040354729, 0.014904985204339027, 0.049690473824739456, 0.005835757125169039, 0.07190369069576263, 0.08707912266254425, 0.0022756746038794518 ], [ 0.3333032727241516, 0.029588062316179276, 0.010184596292674541, 0.1270487904548645, 0.15930531919002533, 0.04215167835354805, 0.11335880309343338, 0.018089216202497482, 0.6556671261787415, 0.26843342185020447, 0.057853102684020996, 0.9683370590209961, 0.40273550152778625 ], [ 0.2092970460653305, 0.031392402946949005, 0.02218637987971306, 0.00026438303757458925, 0.024638675153255463, 0.08048970997333527, 0.3004762828350067, 0.10332342982292175, 0.14862428605556488, 0.02797571010887623, 0.06293579190969467, 0.6212126016616821, 0.4150769114494324, 0.12267826497554779, 0.9253258109092712, 0.027399543672800064 ], [ 0.2092956304550171, 0.05179907754063606, 0.047742851078510284, 0.10635770112276077, 0.13214443624019623, 0.8833868503570557, 0.031379736959934235 ] ] }, { "q_id": "9186_mmlu_physics", "cot_ids": [ 3, 4, 5, 6, 7, 8, 10, 12, 13 ], "rewards": [ [ 0.16414092481136322, 0.007886072620749474, 0.0004543202230706811, 0.055617187172174454, 0.00399354100227356, 0.12543290853500366, 0.0008523587021045387, 0.043342046439647675, 0.009446640498936176, 0.02352743409574032, 0.03732829540967941, 0.19752614200115204, 0.0032668563071638346 ], [ 0.2569405734539032, 0.06882251054048538, 0.08919785171747208, 0.21001844108104706, 0.08357781171798706, 0.1466556340456009, 0.06645343452692032, 0.08890596777200699, 0.15061289072036743, 0.028968367725610733 ], [ 0.15660034120082855, 0.08126921951770782, 0.28459832072257996, 0.22698688507080078, 0.12872491776943207, 0.05141402781009674 ], [ 0.1641433984041214, 0.02224625088274479, 0.06081418693065643, 0.16201911866664886, 0.19735121726989746, 0.06783591210842133, 0.8182971477508545, 0.002952110255137086, 0.005609831307083368 ], [ 0.08340518921613693, 0.11421739310026169, 0.09501854330301285, 0.04502112418413162, 0.15981169044971466, 0.12263916432857513, 0.23893533647060394, 0.10899148136377335, 0.1296238899230957, 0.0681537389755249 ], [ 0.16414158046245575, 0.03555554896593094, 0.07411996275186539, 0.00014690440730191767, 0.11358406394720078, 0.00673306779935956, 0.981968343257904, 0.6953519582748413, 0.027739394456148148, 0.10036196559667587, 0.010229233652353287, 0.11059149354696274, 0.28491920232772827, 0.10554228723049164, 0.2579037547111511, 0.08512173593044281, 0.06851640343666077 ], [ 0.16414327919483185, 0.04681428521871567, 0.10156260430812836, 0.09435193240642548, 0.25460541248321533, 0.07441065460443497, 0.08295707404613495, 0.10835570842027664, 0.1175299882888794, 0.4842913746833801, 0.0034055192954838276 ], [ 0.14725440740585327, 0.00409027561545372, 0.008488505147397518, 0.014740693382918835, 0.03709578141570091, 0.19041113555431366, 0.79756760597229, 0.0030669488478451967 ], [ 0.164140984416008, 0.04546032473444939, 0.0500357560813427, 0.07723959535360336, 0.20287901163101196, 0.025261815637350082, 0.023534828796982765, 0.2701616585254669, 0.010115394368767738, 0.20298859477043152, 0.36112159490585327, 0.5418182015419006, 0.0808480829000473 ] ] }, { "q_id": "9507_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.3626149296760559, 0.2603762447834015, 0.05248391255736351, 0.015211576595902443 ], [ 0.49429991841316223, 0.15459921956062317, 0.026237057521939278 ], [ 0.3626144826412201, 0.051731549203395844, 0.07436569780111313, 0.18450520932674408, 0.03251904249191284, 0.05929640308022499, 0.2770521640777588 ], [ 0.5039756894111633, 0.29236045479774475, 0.27037277817726135, 0.03858568146824837, 0.005797956604510546, 0.008594602346420288 ], [ 0.5609025359153748, 0.07958335429430008, 0.03181185573339462, 0.10193502902984619 ], [ 0.3950658142566681, 0.2740277945995331, 0.1417265683412552, 0.00969274714589119 ], [ 0.3626169264316559, 0.23454906046390533, 0.41268062591552734, 0.0458642914891243, 0.018000828102231026 ], [ 0.3660285472869873, 0.02397938258945942, 0.0751495212316513, 0.215541273355484, 0.15132053196430206, 0.4724206030368805, 0.061642732471227646, 0.08945801109075546, 0.062385208904743195, 0.3015385568141937, 0.15217196941375732, 0.0822272077202797, 0.22809015214443207, 0.052741602063179016, 0.09576338529586792 ], [ 0.36261722445487976, 0.21731318533420563, 0.4648666977882385, 0.16245076060295105, 0.08268649131059647, 0.16215789318084717 ], [ 0.36261382699012756, 0.1774710863828659, 0.023347388952970505, 0.11209651082754135, 0.15310515463352203, 0.04150070250034332, 0.026994530111551285, 0.019141457974910736, 0.0235053151845932, 0.018317990005016327 ], [ 0.3626164495944977, 0.24230797588825226, 0.48213517665863037, 0.14330726861953735, 0.005928505212068558 ], [ 0.3626149296760559, 0.5883960127830505, 0.052027784287929535, 0.028324689716100693, 0.08890193700790405, 0.13760244846343994, 0.0021762880496680737 ], [ 0.3660285472869873, 0.0701347067952156, 0.2054450660943985, 0.5533289909362793, 0.1669176071882248, 0.06421830505132675, 0.00489613926038146 ], [ 0.36261656880378723, 0.26511427760124207, 0.49368807673454285, 0.04729389026761055, 0.014863740652799606 ], [ 0.36225461959838867, 0.13638246059417725, 0.2596541941165924, 0.07699162513017654, 0.10904507339000702, 0.08934970945119858, 0.05686341971158981, 0.031533993780612946 ], [ 0.4601653218269348, 0.24020028114318848, 0.08371758460998535, 0.01611078530550003 ] ] }, { "q_id": "9878_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9947640895843506, 0.9998028874397278, 0.9999483823776245 ], [ 0.9947640895843506, 0.9998037219047546, 0.9999457597732544 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9947640895843506, 0.9998037219047546, 0.9999457597732544 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9947640895843506, 0.9998037219047546, 0.9999457597732544 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9963240623474121, 0.9998086094856262, 0.99994957447052 ], [ 0.9947640895843506, 0.9998037219047546, 0.9999457597732544 ], [ 0.9963240623474121, 0.9998099207878113, 0.9999517202377319 ], [ 0.9963240623474121, 0.9998099207878113, 0.9999517202377319 ] ] }, { "q_id": "10078_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.1272052377462387, 0.10659351944923401, 0.0006285017589107156, 0.08418656140565872, 0.010039123706519604, 0.10847669094800949, 0.039764080196619034, 0.001978851156309247 ], [ 0.14087983965873718, 0.07519365102052689, 0.13433386385440826, 0.009653821587562561, 0.0032396672759205103, 0.00296076200902462 ], [ 0.422063410282135, 0.028998130932450294, 0.12680190801620483, 0.10020889341831207, 0.007782991509884596, 0.018309537321329117, 0.0027408781461417675 ], [ 0.14077742397785187, 0.07287994027137756, 0.12436174601316452, 0.005111407954245806, 0.0030616961885243654, 0.0025074006989598274 ], [ 0.4003830552101135, 0.020336540415883064, 0.1053108274936676, 0.1784978061914444, 0.010631128214299679, 0.021242305636405945, 0.0038043279200792313 ], [ 0.3662463426589966, 0.032556548714637756, 0.0516294501721859, 0.052735935896635056, 0.04545993357896805, 0.02114505134522915, 0.03609704598784447, 0.05004971846938133, 0.07485787570476532, 0.029823727905750275, 0.015318527817726135, 0.002867553848773241 ], [ 0.14193859696388245, 0.11759094148874283, 0.05786612629890442, 0.005351998843252659, 0.003378255758434534, 0.0028193024918437004 ], [ 0.2267725020647049, 0.13058486580848694, 0.23589804768562317, 0.033801496028900146, 0.004114852286875248, 0.0032659899443387985 ], [ 0.2901434004306793, 0.039624735713005066, 0.0899212658405304, 0.08088001608848572, 0.2340005785226822, 0.12267868965864182, 0.03273409232497215, 0.006063148844987154 ], [ 0.2359621375799179, 0.08829612284898758, 0.14433826506137848, 0.017849858850240707, 0.0031812270171940327, 0.002842370653524995 ], [ 0.1548573076725006, 0.09689502418041229, 0.10926751047372818, 0.14722572267055511, 0.0448809452354908, 0.03447619453072548, 0.0039552138186991215 ], [ 0.1270572394132614, 0.05162786319851875, 0.07229015231132507, 0.015987087041139603, 0.017643315717577934, 0.002722816774621606 ], [ 0.23564672470092773, 0.044931747019290924, 0.08408419042825699, 0.18261705338954926, 0.031281400471925735, 0.04350974038243294, 0.003961268812417984 ], [ 0.1272047758102417, 0.10691999644041061, 0.26720720529556274, 0.03134842962026596, 0.15493088960647583, 0.022944359108805656, 0.0033256409224122763 ], [ 0.1407785713672638, 0.11133524030447006, 0.1689617782831192, 0.07170370221138, 0.053797680884599686, 0.004547859542071819 ], [ 0.1389487385749817, 0.08541658520698547, 0.15581877529621124, 0.01181943528354168, 0.014686367474496365, 0.0026984482537955046 ] ] }, { "q_id": "10193_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.4764884114265442, 0.07262524217367172, 0.13029557466506958, 0.1182737797498703, 0.01909717544913292, 0.034764982759952545, 0.0541713573038578, 0.362916499376297, 0.0036655229050666094 ], [ 0.1318349689245224, 0.02299444191157818, 0.031860873103141785, 0.03776202350854874, 0.031062612310051918, 0.01847808249294758, 0.029775366187095642, 0.05731452256441116, 0.04716015234589577, 0.01765875145792961, 0.0804130956530571, 0.004304412752389908 ], [ 0.1318364292383194, 0.0009405225864611566, 0.07486554235219955, 0.013873548246920109, 0.020283807069063187, 0.039002925157547, 0.08069824427366257, 0.15002615749835968, 0.014395840466022491, 0.023726897314190865, 0.012470546178519726, 0.05402885377407074, 0.12656472623348236, 0.01118047721683979, 0.04878448694944382, 0.08704657107591629, 0.009974143467843533, 0.18178023397922516, 0.021972691640257835, 0.4056593179702759, 0.002180185867473483, 0.006041898857802153, 0.01018854882568121, 0.004453789442777634 ], [ 0.13183589279651642, 0.00016134628094732761, 0.04211345687508583, 0.02417588047683239, 0.032385069876909256, 0.07224862277507782, 0.04167923331260681, 0.13748450577259064, 0.035923607647418976, 0.03407170996069908, 0.01163387019187212, 0.030450895428657532, 0.06440737843513489, 0.029853282496333122, 0.04265432432293892, 0.05261571705341339, 0.006752005312591791, 0.1025824174284935, 0.6796994805335999, 0.005376032553613186, 0.004408783745020628 ], [ 0.1318361759185791, 0.0005921716219745576, 0.0740867331624031, 0.016315627843141556, 0.021891048178076744, 0.03492628037929535, 0.00041754019912332296, 0.1550222635269165, 0.11692855507135391, 0.027083611115813255, 0.24558065831661224, 0.005664279218763113, 0.025183452293276787, 0.6953052878379822, 0.05449177324771881, 0.030448824167251587, 0.9095571041107178, 0.9983307719230652 ], [ 0.1318361759185791, 0.00016717847029212862, 0.05995461344718933, 0.022881384938955307, 0.023617498576641083, 0.007731648627668619, 0.03791651129722595, 0.023300886154174805, 0.6297815442085266, 0.00492657907307148 ], [ 0.1318361759185791, 0.00018742836255114526, 0.06285686045885086, 0.013316298834979534, 0.021479053422808647, 0.08998402953147888, 0.02086700312793255, 0.08414904028177261, 0.012546292506158352, 0.03317582234740257, 0.015543853864073753, 0.054110750555992126, 0.04447781667113304, 0.05771542713046074, 0.046185705810785294, 0.00393451564013958, 0.10905609279870987, 0.0007704624440521002, 0.025775283575057983, 0.004054243676364422 ], [ 0.13183611631393433, 0.0005309164989739656, 0.18129943311214447, 0.00037305994192138314, 0.08641694486141205, 0.009732592850923538, 0.026426881551742554, 0.004106360953301191, 0.04436396807432175, 0.004754694178700447, 0.12579360604286194, 0.005802806932479143 ], [ 0.13183638453483582, 0.002433952409774065, 0.16440658271312714, 0.019424352794885635, 0.021115293726325035, 0.03270801156759262, 0.00029209154308773577, 0.10217515379190445, 0.04161722585558891, 0.11827616393566132, 0.03074648790061474, 0.03419722616672516, 0.01776301860809326, 0.04277683421969414, 0.03144066408276558, 0.04410380870103836, 0.06632586568593979, 0.01023445837199688, 0.05912446230649948, 0.11465423554182053, 0.003772489493712783 ], [ 0.1318361759185791, 0.0002487307065166533, 0.04105132818222046, 0.02599668875336647, 0.030203215777873993, 0.05058488994836807, 0.017399312928318977, 0.04120979085564613, 0.03099772147834301, 0.014881186187267303, 0.03445390239357948, 0.03848820924758911, 0.024400707334280014, 0.04953780770301819, 0.0755947157740593, 0.0007801641477271914, 0.040823232382535934, 0.11079084128141403, 0.01413891464471817, 0.0588504895567894, 0.0050755636766552925 ], [ 0.1318369209766388, 0.0003756687801796943, 0.03978371247649193, 0.025515465065836906, 0.07505836337804794, 0.13896915316581726, 0.03671974688768387, 0.01633651927113533, 0.04508601874113083, 0.05243153125047684, 0.058608029037714005, 0.16732759773731232, 0.006057938560843468 ], [ 0.13183507323265076, 0.00010556427150731906, 0.06018178537487984, 0.02665681205689907, 0.049614716321229935, 0.1301572024822235, 0.034115269780159, 0.015290099196135998, 0.02911604568362236, 0.03371097519993782, 0.05168181657791138, 0.06330189853906631, 0.017668548971414566, 0.18127480149269104, 0.004854961298406124 ], [ 0.13183802366256714, 0.00010556285997154191, 0.06497645378112793, 0.018716026097536087, 0.0383039154112339, 0.07156892120838165, 0.027288194745779037, 0.5305683612823486, 0.019620541483163834, 0.95649254322052, 0.9979137778282166 ], [ 0.1318361759185791, 0.01972472481429577, 0.02624598704278469, 0.02266671136021614, 6.064452099963091e-05, 0.10682955384254456, 0.051468633115291595, 0.040718574076890945, 0.08971548825502396, 0.023334050551056862, 0.038648705929517746, 0.012450293637812138, 0.049625374376773834, 0.056342657655477524, 0.05401241034269333, 0.013317087665200233, 0.13421940803527832, 0.7413042783737183, 0.003341207280755043, 0.004551442340016365, 0.004439139738678932 ], [ 0.13183605670928955, 0.00013991209561936557, 0.06230927258729935, 0.01260847132652998, 0.015539622865617275, 0.062365297228097916, 0.015780841931700706, 0.07368572801351547, 0.01317423116415739, 0.03387496992945671, 0.01690814271569252, 0.04632159695029259, 0.05089786276221275, 0.05234524980187416, 0.04456771910190582, 0.0007337948773056269, 0.031398143619298935, 0.08162850886583328, 0.004516127053648233 ] ] }, { "q_id": "10256_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.015338498167693615, 0.04067782312631607, 0.003054732223972678, 0.0015050839865580201 ], [ 0.015338476747274399, 0.0034053444396704435, 0.001048182137310505 ], [ 0.03974713012576103, 0.008473381400108337, 0.00137275829911232 ], [ 0.29461583495140076, 0.020488861948251724, 0.0034849473740905523, 0.00157705950550735 ], [ 0.07024194300174713, 0.009316506795585155, 0.001130404300056398 ], [ 0.019436951726675034, 0.008983646519482136, 0.0011073910864070058 ], [ 0.024370849132537842, 0.0055471546947956085, 0.0011932272464036942 ], [ 0.021683750674128532, 0.020174821838736534, 0.005263103637844324, 0.001436206977814436 ], [ 0.023455306887626648, 0.00950100738555193, 0.0018853400833904743 ], [ 0.027637427672743797, 0.005324278026819229, 0.0012127842055633664 ], [ 0.13513173162937164, 0.043404411524534225, 0.013835280202329159, 0.0014779472257941961 ], [ 0.8452432155609131, 0.023086607456207275, 0.989600419998169, 0.9993256330490112 ], [ 0.11549588292837143, 0.01035422645509243, 0.6169147491455078 ], [ 0.02933279052376747, 0.009446123614907265, 0.7617959380149841 ], [ 0.07721509784460068, 0.00551143242046237, 0.0009726324351504445 ], [ 0.05573215335607529, 0.010241943411529064, 0.0013515932951122522 ] ] }, { "q_id": "10090_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.14759016036987305, 0.20964716374874115, 0.15863440930843353, 0.4948651194572449, 0.0007002602214924991 ], [ 0.11779379844665527, 0.1676120012998581, 0.22825101017951965, 0.1442916989326477, 0.023450588807463646, 0.1906217485666275, 0.012639520689845085, 0.039801545441150665, 0.0040315892547369, 0.17113341391086578, 0.044455528259277344, 0.11019635200500488, 0.006155164912343025 ], [ 0.14759010076522827, 0.23193252086639404, 0.17368420958518982, 0.27623897790908813, 0.04304666444659233, 0.32316604256629944, 0.005041525233536959, 0.0008681679028086364 ], [ 0.2115805596113205, 0.20114509761333466, 0.34825843572616577, 0.1327429711818695, 0.012011888436973095, 0.0057684616185724735, 0.003863730700686574, 0.10266466438770294, 0.0199880450963974, 0.08010014146566391, 0.006386036518961191 ], [ 0.14759062230587006, 0.14851005375385284, 0.10807518661022186, 0.08670099824666977, 0.11297782510519028, 0.00792503822594881, 0.15280984342098236, 0.00631850166246295, 0.020913606509566307, 0.030490577220916748, 0.0013882252387702465, 0.0014996821992099285 ], [ 0.14759062230587006, 0.2319299578666687, 0.1722625195980072, 0.20333914458751678, 0.24575579166412354, 0.022246137261390686, 0.1587407886981964, 0.019895542412996292, 0.024758294224739075, 0.1587117314338684, 0.6987364292144775, 0.001851976616308093 ], [ 0.15225934982299805, 0.1873285323381424, 0.0003150440752506256, 0.045477379113435745, 0.01336728036403656, 0.277264267206192, 0.5664366483688354, 0.029072877019643784, 0.006501755211502314, 0.004097346682101488, 0.16357946395874023, 0.025039473548531532, 0.06312502920627594, 0.005665946751832962 ], [ 0.14759093523025513, 0.19946502149105072, 0.25528183579444885, 0.03405098617076874, 0.011100259609520435, 0.05147466063499451, 0.006482582073658705, 0.007205382455140352, 0.10491176694631577, 0.013127620331943035, 0.0881263017654419, 0.05032776668667793, 0.005742076318711042 ], [ 0.17679809033870697, 0.2146397978067398, 0.156354621052742, 0.2567037045955658, 0.014781429432332516, 0.014684918336570263, 0.0017837340710684657 ], [ 0.1475917100906372, 0.21497856080532074, 0.10016241669654846, 0.06552765518426895, 0.05341063439846039, 0.12847121059894562, 0.008506261743605137, 0.017225412651896477, 0.08358350396156311, 0.10308979451656342, 0.06919623166322708, 0.00593697652220726 ], [ 0.1475895643234253, 0.20964938402175903, 0.1586344689130783, 0.17782635986804962, 0.33851948380470276, 0.021802956238389015, 0.04783320799469948, 0.0699738934636116, 0.0049833618104457855 ], [ 0.14759062230587006, 0.19946379959583282, 0.23602242767810822, 0.19727753102779388, 0.1867167055606842, 0.007908832281827927, 0.008841377682983875, 0.0034932636190205812, 0.06756000220775604, 0.005419672001153231 ], [ 0.14759044349193573, 0.2144082486629486, 0.20934177935123444, 0.361390084028244, 0.03578097000718117, 0.021483302116394043, 0.15995259582996368, 0.5985984206199646, 0.0006836626562289894 ], [ 0.1475898027420044, 0.21498073637485504, 0.17817924916744232, 0.08935747295618057, 0.18338631093502045, 0.013672074303030968, 0.01652560383081436, 0.08927083015441895, 0.0441196970641613, 0.12428954243659973, 0.04647164046764374, 0.006089210510253906 ], [ 0.14758847653865814, 0.2096487432718277, 0.1504647582769394, 0.4481474757194519, 0.05115695670247078, 0.01983013190329075, 0.020926574245095253, 0.07644221186637878, 0.8338309526443481, 0.003961613401770592 ], [ 0.14759129285812378, 0.2144084870815277, 0.18613818287849426, 0.054817840456962585, 0.017012950032949448, 0.0701107308268547, 0.06459880620241165, 0.07033424079418182, 0.0007317909621633589 ] ] }, { "q_id": "9692_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8223956227302551, 0.007117127534002066, 0.005676037631928921, 0.060769371688365936, 0.03221747651696205, 0.011662025935947895, 0.05626970902085304, 0.00036825999268330634, 0.11112265288829803, 0.13031645119190216, 0.007347182370722294, 0.9514814615249634, 0.9908485412597656, 0.9820276498794556 ], [ 0.9126952886581421, 0.5889533162117004, 0.02536747045814991, 0.21216556429862976, 0.1325569897890091, 0.059604160487651825, 0.4630148112773895, 0.045140042901039124, 0.01926000416278839, 0.022758498787879944 ], [ 0.9626469016075134, 0.3702562749385834, 0.6066877841949463, 0.25909021496772766, 0.15275324881076813, 0.4341813027858734, 0.023153865709900856, 0.03745187819004059 ], [ 0.9626466631889343, 0.7908976078033447, 0.2840111553668976, 0.3800935745239258, 0.6293707489967346, 0.012276907451450825, 0.2576674818992615, 0.033709485083818436, 0.06990347802639008, 0.8493578433990479, 0.3823900520801544 ], [ 0.7911803722381592, 0.3704884946346283, 0.48840874433517456, 0.17196261882781982, 0.0013061825884506106, 0.6530560255050659, 0.004050408490002155, 0.3524853587150574, 0.517447292804718, 0.6789471507072449 ], [ 0.9626467823982239, 0.40750446915626526, 0.13456952571868896, 0.8985705375671387, 0.01162722148001194, 0.04599011316895485, 0.16410526633262634, 0.03666284680366516, 0.0586603581905365, 0.06953585147857666 ], [ 0.9552492499351501, 0.2917920649051666, 0.28526967763900757, 0.32884591817855835, 0.7614780068397522, 0.028039170429110527, 0.026455162093043327 ], [ 0.9626462459564209, 0.4460919499397278, 0.8128597736358643, 0.47688180208206177, 0.012341608293354511, 0.6615201234817505, 0.014434740878641605, 0.7454151511192322, 0.7251240611076355 ], [ 0.9626463651657104, 0.17187830805778503, 0.0944155901670456, 0.39841514825820923, 0.6109985709190369, 0.33819133043289185, 0.03120352327823639, 0.8682326078414917, 0.8606102466583252 ], [ 0.9676480889320374, 0.4448118209838867, 0.6136226058006287, 0.13396339118480682, 0.29848718643188477, 0.025931498035788536, 0.16343435645103455, 0.97444087266922, 0.9968559741973877, 0.9911210536956787 ], [ 0.9552492499351501, 0.44054001569747925, 0.5495775938034058, 0.3096082806587219, 0.011257142759859562, 0.010154131799936295 ], [ 0.8895605206489563, 0.4458945095539093, 0.7202597260475159, 0.24496787786483765, 0.27427181601524353, 0.4238247871398926, 0.2029542624950409, 0.02219122275710106, 0.1301066279411316, 0.032404620200395584 ], [ 0.9680561423301697, 0.19641390442848206, 0.3335186839103699, 0.6366627216339111, 0.012563682161271572, 0.1889687180519104, 0.02437734231352806, 0.2927147150039673, 0.022760536521673203, 0.0705401748418808, 0.04065670445561409 ], [ 0.9626464247703552, 0.35695329308509827, 0.14204111695289612, 0.23086947202682495, 0.25032350420951843, 0.0032323787454515696, 0.9959296584129333, 0.9958586096763611 ], [ 0.9626467823982239, 0.36001938581466675, 0.6441417932510376, 0.2708115577697754, 0.3711114525794983, 0.44001591205596924, 0.017583562061190605, 0.3511873781681061, 0.04931337758898735, 0.04309375211596489 ], [ 0.9626469016075134, 0.24420148134231567, 0.5395762920379639, 0.8504651188850403, 0.20363539457321167, 0.09000711143016815, 0.030428364872932434, 0.15523548424243927, 0.21342602372169495, 0.012476479634642601, 0.5540319085121155, 0.002051530173048377, 0.033896852284669876, 0.0291263610124588 ] ] }, { "q_id": "10355_mmlu_physics", "cot_ids": [ 0, 8, 10, 11 ], "rewards": [ [ 0.24423106014728546, 0.03463485836982727, 0.019970986992120743, 0.05998639017343521, 0.38739606738090515, 0.09492854028940201, 0.0074818492867052555, 0.03646763414144516, 0.028608813881874084, 0.0664132684469223, 0.11896923184394836, 0.04468357563018799, 0.022108888253569603, 0.019810838624835014, 0.011107008904218674, 0.035586923360824585, 0.001711929915472865 ], [ 0.24423588812351227, 0.04435496777296066, 0.1531112641096115, 0.17868073284626007, 0.01907467097043991, 0.11524637043476105, 0.015945835039019585, 0.3682134449481964, 0.7551478743553162, 0.9986380934715271 ], [ 0.24423176050186157, 0.04343171790242195, 0.01002816017717123, 0.04684523493051529, 0.0007376201101578772, 0.3747577369213104, 0.05359392985701561, 0.006701868958771229, 0.027447963133454323, 0.014012445695698261, 0.10466524958610535, 0.03389536961913109, 0.027120715007185936, 0.023017385974526405, 0.013394374400377274, 0.11122201383113861, 0.0014570957282558084 ], [ 0.2442321926355362, 0.04206164926290512, 0.017095832154154778, 0.07931739836931229, 0.0007932335720397532, 0.31726470589637756, 0.011908557265996933, 0.006291821599006653, 0.02850431390106678, 0.0004778231668751687, 0.12367050349712372, 0.015967004001140594, 0.04953664168715477, 0.003410060191527009, 0.1483352780342102, 0.020436380058526993, 0.01567879505455494, 0.023648127913475037, 0.004634350538253784, 0.3281776010990143, 0.01693766936659813, 0.018047170713543892, 0.0013713547959923744 ] ] }, { "q_id": "10100_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9437960982322693, 0.19751906394958496, 0.0816715881228447 ], [ 0.9777336716651917, 0.6653633117675781, 0.11711416393518448 ], [ 0.9881945848464966, 0.964201807975769, 0.9750060439109802, 0.3065091073513031 ], [ 0.7685836553573608, 0.534146785736084, 0.052272580564022064 ], [ 0.9881945848464966, 0.9084161520004272, 0.039366912096738815 ], [ 0.9675034284591675, 0.11453259736299515, 0.10718966275453568, 0.0701799988746643 ], [ 0.9881945848464966, 0.9938704967498779, 0.994828999042511, 0.999005138874054 ], [ 0.9665697813034058, 0.9912359714508057, 0.9968120455741882 ], [ 0.9247203469276428, 0.3413150906562805, 0.18561403453350067 ], [ 0.9946187734603882, 0.30214694142341614 ], [ 0.9337266683578491, 0.9626820087432861, 0.8796048164367676 ], [ 0.993763267993927, 0.989997923374176, 0.9792879223823547 ], [ 0.9675024151802063, 0.45360809564590454, 0.9639750123023987, 0.9763196706771851 ], [ 0.9824252724647522, 0.26434510946273804, 0.8980228900909424, 0.24533864855766296 ], [ 0.9881948232650757, 0.8599530458450317, 0.10585902631282806 ], [ 0.9881947040557861, 0.19422009587287903, 0.06642956286668777 ] ] }, { "q_id": "9495_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ], "rewards": [ [ 0.2654455900192261, 0.04844273626804352, 0.09029842168092728, 0.010989964008331299, 0.033874671906232834, 0.09471433609724045, 0.13632404804229736, 0.5826694965362549, 0.008055256679654121 ], [ 0.26544392108917236, 0.2632662057876587, 0.09061360359191895, 0.06248851120471954, 0.07089968025684357, 0.007266203407198191, 0.007038258947432041 ], [ 0.3063249886035919, 0.07614707201719284, 0.14745062589645386, 0.006246901582926512, 0.032821983098983765, 0.06462935358285904, 0.23268631100654602, 0.12463004887104034, 0.09497418999671936, 0.03516709804534912, 0.8657500147819519, 0.013087988831102848 ], [ 0.30632486939430237, 0.07614760100841522, 0.1474488079547882, 0.3804820775985718, 0.033540040254592896, 0.07413161545991898, 0.08714156597852707, 0.08069457113742828, 0.08511222898960114, 0.9621118307113647, 0.018858037889003754 ], [ 0.2391851395368576, 0.3115111291408539, 0.7391500473022461, 0.11647208034992218, 0.2508452832698822, 0.7632535099983215, 0.12892548739910126, 0.15929363667964935, 0.011220586486160755, 0.008934753946959972 ], [ 0.3063279092311859, 0.34509721398353577, 0.0007634669309481978, 0.7659778594970703, 0.0027719871141016483, 0.04386531934142113, 0.00720992824062705, 0.007889177650213242 ], [ 0.1915169060230255, 0.07382048666477203, 0.0038910876028239727, 0.028398236259818077, 0.10596653819084167, 0.02206539362668991, 0.27621448040008545, 0.026582421734929085 ], [ 0.30632486939430237, 0.7464698553085327, 0.7842568159103394, 0.10418961197137833, 0.021295418962836266, 0.011930852197110653 ], [ 0.3063228130340576, 0.34509408473968506, 0.0007634603534825146, 0.4177163243293762, 0.022658877074718475, 0.0647762343287468, 0.015566466376185417, 0.007988516241312027 ], [ 0.298999547958374, 0.314510703086853, 0.8321916460990906, 0.0013504622038453817, 0.0438515841960907, 0.23338593542575836, 0.27035942673683167, 0.8305650949478149, 0.013601685874164104 ], [ 0.26783788204193115, 0.09752209484577179, 0.3054914176464081, 0.17067930102348328, 0.23625902831554413, 0.031921129673719406, 0.09824678301811218, 0.22176411747932434, 0.00725488131865859, 0.21181680262088776, 0.02892603911459446, 0.006851962301880121 ], [ 0.18831224739551544, 0.25686192512512207, 0.0022733958903700113, 0.61562579870224, 0.05722463130950928, 0.013731802813708782, 0.008177701383829117 ], [ 0.3063254952430725, 0.07614719867706299, 0.0019072580616921186, 0.17715661227703094, 0.12881731986999512, 0.035763416439294815, 0.050449736416339874, 0.29662010073661804, 0.009141357615590096 ], [ 0.4092334806919098, 0.0011353164445608854, 0.03438008576631546, 0.06131567806005478, 0.37330159544944763, 0.03524124622344971, 0.18552012741565704, 0.012577224522829056, 0.21728481352329254, 0.017440181225538254 ], [ 0.26784026622772217, 0.09752209484577179, 0.0005839109071530402, 0.1151655837893486, 0.0034124560188502073, 0.06080237030982971, 0.5857145190238953, 0.019870107993483543, 0.12333396822214127, 0.0931149274110794, 0.022459983825683594, 0.3396739065647125, 0.020972883328795433 ] ] }, { "q_id": "9906_mmlu_physics", "cot_ids": [ 0, 2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14 ], "rewards": [ [ 0.5585036277770996, 0.07929174602031708, 0.06156422570347786, 0.10662680864334106, 0.06513195484876633, 0.9884632229804993, 0.9989120960235596 ], [ 0.07925349473953247, 0.016682256013154984, 0.11414804309606552, 0.03004186786711216, 0.06525494158267975, 0.012144001200795174, 0.11469712108373642, 0.06811798363924026, 0.9898760914802551, 0.9990584254264832 ], [ 0.07702986896038055, 0.3383179008960724, 0.19229453802108765, 0.05262760445475578, 0.02646728791296482, 0.04666970297694206, 0.0017594852251932025 ], [ 0.17900213599205017, 0.05493998900055885, 0.11072909086942673, 0.08618802577257156, 0.1505594551563263, 0.014819538220763206 ], [ 0.07925449311733246, 0.02497897855937481, 0.021185465157032013, 0.00041900432552210987, 0.05205575004220009, 0.004274287726730108, 0.0007694538799114525, 0.01359720341861248, 0.025088122114539146, 0.024833839386701584, 0.9973427653312683 ], [ 0.3933591842651367, 0.10396274924278259, 0.2701708674430847, 0.032148540019989014, 0.0007910614367574453 ], [ 0.07925495505332947, 0.027299245819449425, 0.046069156378507614, 0.0986998975276947, 0.07772734016180038, 0.004766673315316439, 0.0030524195171892643, 0.016195544973015785, 0.029611440375447273, 0.019274039193987846, 0.0010126179549843073, 0.011292477138340473, 0.02612648718059063, 0.0018208443652838469, 0.061100125312805176, 0.995445728302002 ], [ 0.5063238143920898, 0.11786496639251709, 0.05098985508084297, 0.0016716786194592714 ], [ 0.0792558565735817, 0.06254225969314575, 0.0139100831001997, 0.019152170047163963, 0.07191982865333557, 0.016426915302872658, 0.06234656646847725, 0.05328159034252167, 0.012219667434692383, 0.06529467552900314, 0.9651989936828613, 0.9966070652008057 ], [ 0.07688766717910767, 0.09633520245552063, 0.04386698082089424, 0.027136055752635002, 0.008181020617485046, 0.1079224944114685, 0.08526867628097534, 0.07850629091262817, 0.06113799661397934, 0.03555459901690483, 0.030392339453101158, 0.0613776259124279, 0.10623155534267426, 0.13349397480487823, 0.04432740435004234, 0.0018363354029133916 ], [ 0.06598091870546341, 0.20601339638233185, 0.02927836962044239, 0.07472513616085052, 0.01564742997288704, 0.12117400020360947, 0.03429838642477989, 0.23660288751125336, 0.9233129024505615, 0.9987107515335083 ], [ 0.07925429195165634, 0.02197623811662197, 0.04258183389902115, 0.06184148043394089, 0.0009523097542114556, 0.01489321980625391, 0.02334989793598652, 0.013117657974362373, 0.007107144221663475, 0.009311503730714321, 0.16243192553520203, 0.997147262096405 ] ] }, { "q_id": "9393_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.41400665044784546, 0.17457222938537598, 0.020674798637628555, 0.05520744249224663, 0.03005879558622837, 0.05400899797677994, 0.02565506473183632, 0.03146553039550781, 0.11600437760353088, 0.05923182889819145, 0.3144056499004364, 0.002109350636601448 ], [ 0.4707963764667511, 0.040512096136808395, 0.12556302547454834, 0.11861760914325714, 0.087616927921772, 0.03583521395921707, 0.0514652319252491, 0.029185980558395386 ], [ 0.40518268942832947, 0.1625441312789917, 0.07858598232269287, 0.011564606800675392, 0.0008956326637417078 ], [ 0.797304630279541, 0.18775539100170135, 0.04618438333272934, 0.02374003455042839 ], [ 0.1930932104587555, 0.02768396958708763, 0.022318491712212563, 0.03341951593756676, 0.09048916399478912, 0.049090977758169174, 0.060191329568624496, 0.016378577798604965 ], [ 0.7539299726486206, 0.21901948750019073, 0.0761222168803215, 0.10449391603469849, 0.020998051390051842, 0.0008205128251574934 ], [ 0.226237490773201, 0.01058910135179758, 0.059107065200805664, 0.017294811084866524, 0.033018115907907486, 0.009661579504609108, 0.015979502350091934, 0.0012620625784620643, 0.014764820225536823, 0.16876395046710968, 0.021644433960318565, 0.22565999627113342, 0.17751938104629517, 0.595705509185791, 0.002345320302993059 ], [ 0.22623734176158905, 0.006906441412866116, 0.008310499601066113, 0.011661256663501263, 0.20010654628276825, 0.11449077725410461, 0.643112301826477, 0.9888020753860474 ], [ 0.22623668611049652, 0.002999291056767106, 0.09716863185167313, 0.00505835423246026, 0.08233526349067688, 0.0018847925821319222, 0.09811358153820038, 0.01717144437134266, 0.013977466151118279, 0.009586978703737259, 0.0018665653187781572, 0.0017137887189164758 ], [ 0.2262372523546219, 0.0034621828235685825, 0.021008899435400963, 0.006884601432830095, 0.007037845905870199, 0.06715691089630127, 0.02067647874355316, 0.03448941931128502, 0.007783658802509308, 0.015273600816726685, 0.05903857573866844, 0.01159061398357153, 0.02239384315907955, 0.028324874117970467, 0.0019007191294804215, 0.001725934911519289 ], [ 0.7420551776885986, 0.20425066351890564, 0.02564680390059948, 0.0017671047244220972 ], [ 0.6874905824661255, 0.16804248094558716, 0.09693533927202225, 0.040384676307439804, 0.042979296296834946, 0.035277143120765686, 0.11242600530385971, 0.04375603795051575, 0.10406830161809921, 0.03763144090771675, 0.05636712536215782, 0.024582676589488983, 0.001274291193112731 ], [ 0.33260035514831543, 0.03661400452256203, 0.02213347516953945, 0.03987937420606613, 0.05493278428912163, 0.07207360863685608, 0.24506418406963348, 0.020393172279000282, 0.3249076306819916, 0.2714652419090271, 0.8216193914413452, 0.9802426695823669 ], [ 0.43366652727127075, 0.02951044775545597, 0.04665808007121086, 0.05103445425629616, 0.12046483159065247, 0.9730693697929382, 0.9906324148178101 ], [ 0.4754854440689087, 0.03514682129025459, 0.12869203090667725, 0.07409065216779709, 0.03854955732822418, 0.018393876031041145, 0.02270645461976528, 0.06214712932705879, 0.11429333686828613, 0.020769236609339714, 0.6667525172233582, 0.9698631167411804, 0.046951401978731155 ], [ 0.7360895872116089, 0.2064843624830246, 0.11010722070932388, 0.019283363595604897, 0.015750641003251076, 0.0007071104482747614 ] ] }, { "q_id": "9821_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9956091046333313, 0.8811712861061096, 0.0005763804074376822, 0.3855099678039551, 0.5810697078704834, 0.053799793124198914, 0.14555923640727997, 0.07411577552556992, 0.9980111122131348, 0.9998393058776855 ], [ 0.9935897588729858, 0.0653693675994873, 0.7557321786880493, 0.8041576743125916, 0.6008810997009277, 0.050102658569812775, 0.16669394075870514, 0.1255163550376892, 0.9982831478118896, 0.9998618364334106 ], [ 0.9956092238426208, 0.7577811479568481, 0.8216477632522583, 0.0006494031986221671, 0.37779325246810913, 0.5190844535827637, 0.05892091616988182, 0.15410903096199036, 0.07679319381713867, 0.14250774681568146, 0.9980789422988892, 0.9998437166213989 ], [ 0.9957885146141052, 0.8740182518959045, 0.5928924083709717, 0.04370010644197464, 0.1290246993303299, 0.0865086168050766, 0.999076247215271, 0.9998761415481567 ], [ 0.9923468828201294, 0.7706934213638306, 0.4239499866962433, 0.20266948640346527, 0.9982956051826477, 0.9998303651809692 ], [ 0.935300350189209, 0.8467403054237366, 0.46676692366600037, 0.13564817607402802, 0.998461127281189, 0.9998979568481445 ], [ 0.9592766761779785, 0.8184565305709839, 0.859153151512146, 0.0015916062984615564, 0.43425440788269043, 0.058030273765325546, 0.2026173174381256, 0.09799668192863464, 0.9983848333358765, 0.9998703002929688 ], [ 0.7672594785690308, 0.0922808051109314, 0.7199073433876038, 0.8515681624412537, 0.0004707254411187023, 0.4343450963497162, 0.7034215331077576, 0.04838106036186218, 0.21724830567836761, 0.087465301156044, 0.16543728113174438, 0.997714638710022, 0.9998406171798706 ], [ 0.9531799554824829, 0.8815485835075378, 0.19437460601329803, 0.9984583854675293, 0.9998728036880493 ], [ 0.9963372945785522, 0.7616472244262695, 0.3992687165737152, 0.05155884101986885, 0.11778522282838821, 0.10634061694145203, 0.998893678188324, 0.999893069267273 ], [ 0.9956092238426208, 0.7446874976158142, 0.8270753026008606, 0.0006815230590291321, 0.265779972076416, 0.5387722253799438, 0.060481905937194824, 0.157972052693367, 0.11518634110689163, 0.15544870495796204, 0.9983627200126648, 0.9998692274093628 ], [ 0.9911949634552002, 0.9078289270401001, 0.8976318836212158, 0.4816257059574127, 0.13666711747646332, 0.997708797454834, 0.9998138546943665 ], [ 0.9956092238426208, 0.062191471457481384, 0.6969873905181885, 0.8053588271141052, 0.52005934715271, 0.2741915285587311, 0.5915865898132324, 0.26903218030929565, 0.9976342916488647, 0.9998062252998352 ], [ 0.9713872671127319, 0.7925780415534973, 0.8353003859519958, 0.0007919518393464386, 0.3150373101234436, 0.5596999526023865, 0.05702722445130348, 0.1603376567363739, 0.10254362225532532, 0.9981595873832703, 0.9998612403869629 ], [ 0.9956092238426208, 0.0621909499168396, 0.6969872713088989, 0.8053585886955261, 0.0013680662959814072, 0.4742147922515869, 0.15825018286705017, 0.1895361840724945, 0.25058096647262573, 0.9982917904853821, 0.999836802482605 ], [ 0.934322714805603, 0.7894583344459534, 0.000525347946677357, 0.8893350958824158, 0.0025227246806025505, 0.43824464082717896, 0.6870501041412354, 0.05695444345474243, 0.22882913053035736, 0.1001005470752716, 0.9980573058128357, 0.9998175501823425 ] ] }, { "q_id": "10122_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9932494163513184, 0.889567494392395, 0.9990265369415283, 0.9994009733200073 ], [ 0.9940164089202881, 0.8742194771766663, 0.9979751706123352, 0.9990108013153076 ], [ 0.9901043772697449, 0.8645221590995789, 0.9994801878929138, 0.9995143413543701 ], [ 0.9914094805717468, 0.9989172220230103, 0.9991773962974548 ], [ 0.9925699830055237, 0.999218225479126, 0.9992914199829102 ], [ 0.9834385514259338, 0.8446581959724426, 0.9994755387306213, 0.9995276927947998 ], [ 0.9927546381950378, 0.9990580677986145, 0.9992996454238892 ], [ 0.9940164089202881, 0.8953585624694824, 0.9981243014335632, 0.9990542531013489 ], [ 0.9834384322166443, 0.9988105297088623, 0.9992220401763916 ], [ 0.9940165281295776, 0.8953580856323242, 0.9991415739059448, 0.9994111061096191 ], [ 0.9940165281295776, 0.8953584432601929, 0.9990319013595581, 0.9994632601737976 ], [ 0.989822506904602, 0.8537757396697998, 0.9991409778594971, 0.9993711113929749 ], [ 0.9914093613624573, 0.998981773853302, 0.9990687966346741 ], [ 0.9940164089202881, 0.9990767240524292, 0.9991360306739807 ], [ 0.9922937154769897, 0.7383278012275696, 0.9990741014480591, 0.9994268417358398 ], [ 0.9940165281295776, 0.8953587412834167, 0.9993392825126648, 0.9994617104530334 ] ] }, { "q_id": "10338_mmlu_physics", "cot_ids": [ 0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.038011059165000916, 0.024180367588996887, 0.03572523966431618, 0.026601366698741913, 0.014347431249916553, 0.012020793743431568, 0.3468857407569885, 0.005618666764348745, 0.03153592720627785, 0.018439924344420433, 0.06202559545636177, 0.008799373172223568 ], [ 0.028054865077137947, 0.013765450567007065, 0.02126460336148739, 0.005862105637788773, 0.002379409037530422, 0.015579835511744022, 0.050115689635276794, 0.02871621400117874, 0.006608345080167055, 0.02868044562637806, 0.04394473135471344, 0.015708236023783684, 0.02456025592982769, 0.012850476428866386 ], [ 0.028055202215909958, 0.013765676878392696, 0.032268352806568146, 0.005677531473338604, 0.022075127810239792, 0.03591908514499664, 0.05184176564216614, 0.003588553983718157, 0.006165481172502041, 0.040949542075395584, 0.0232244823127985, 0.05078371614217758, 0.06856751441955566, 0.028886795043945312 ], [ 0.028055084869265556, 0.013765613548457623, 0.02303146757185459, 0.00530611164867878, 0.0021701036021113396, 0.04662441089749336, 0.018787840381264687, 0.04727380350232124, 0.054328449070453644, 0.04483824223279953 ], [ 0.6477899551391602, 0.009174861945211887, 0.04503834992647171, 0.03845538571476936, 0.06371254473924637, 0.013671264052391052, 0.056740328669548035, 0.046184953302145004, 0.003426601644605398, 0.12991921603679657, 0.02135530114173889, 0.028650930151343346, 0.057916395366191864, 0.00505950627848506 ], [ 0.028054913505911827, 0.013765509240329266, 0.02109338529407978, 0.004580353386700153, 0.045200277119874954, 0.011556564830243587, 0.0005343509837985039, 0.004604881629347801, 0.005127906799316406, 0.009163781069219112, 0.003964512143284082, 0.0004924503155052662, 0.006242451258003712 ], [ 0.5652316212654114, 0.08735229074954987, 0.3886181712150574, 0.035214584320783615, 0.006452488247305155 ], [ 0.038011334836483, 0.12916216254234314, 0.18135812878608704, 0.0028191376477479935, 0.05235934630036354, 0.012039415538311005, 0.07683112472295761, 0.0014172272058203816, 0.027702519670128822, 0.16135992109775543, 0.018460916355252266, 0.13717760145664215, 0.14882665872573853, 0.06716486811637878, 0.16159480810165405, 0.9414902925491333, 0.03656274080276489 ], [ 0.08015947788953781, 0.0105897206813097, 0.057409387081861496, 0.057263001799583435, 0.0018059235299006104, 0.03516077250242233, 0.05351277068257332, 0.026324719190597534, 0.07072538137435913, 0.03744596242904663, 0.03194102644920349 ], [ 0.03801104426383972, 0.11821842938661575, 0.0007682977593503892, 0.18515770137310028, 0.002883140929043293, 0.037833280861377716, 0.042818911373615265, 0.05067170038819313, 0.019203178584575653, 0.07075174152851105, 0.18980425596237183, 0.25605031847953796, 0.043251149356365204 ], [ 0.13908720016479492, 0.0010895368177443743, 0.06735647469758987, 0.02201833575963974, 0.0032039848156273365, 0.06869138777256012, 0.00026107302983291447, 0.14580902457237244, 0.007715510204434395, 0.016011858358979225, 0.017850100994110107, 0.054758548736572266, 0.05920916795730591, 0.010024662129580975 ], [ 0.02805543690919876, 0.001059125759638846, 5.464141577249393e-05, 0.012714223936200142, 0.2141275852918625, 0.01001423317939043, 0.004245380870997906, 0.026013197377324104, 0.0006571314879693091, 0.037302274256944656, 0.003832771209999919, 0.028215453028678894, 0.03021835908293724, 0.014398222789168358 ], [ 0.02805543690919876, 0.0137655483558774, 0.029581859707832336, 0.0026522912085056305, 0.01963653415441513, 0.027554765343666077, 0.05075176805257797, 0.0021513127721846104, 0.005456067621707916, 0.01958012394607067, 0.03792911022901535, 0.039532408118247986, 0.08088958263397217, 0.03202636167407036, 0.024467119947075844, 0.01504523679614067, 0.014900777488946915 ], [ 0.1390872448682785, 0.0010895202867686749, 0.0555059090256691, 0.05716831609606743, 0.026211436837911606, 0.00827824231237173, 0.04990703612565994, 0.07113341242074966, 0.004160303622484207, 0.5914056897163391, 0.0034272545017302036, 0.03452145680785179, 0.018882660195231438, 0.08269000053405762, 0.03519248217344284, 0.029799746349453926, 0.02504693530499935, 0.014970813877880573 ] ] }, { "q_id": "9886_mmlu_physics", "cot_ids": [ 0, 2, 7, 8, 9, 10, 11, 12, 13 ], "rewards": [ [ 0.023713966831564903, 0.0008157740230672061 ], [ 0.06429729610681534, 0.03395427390933037, 0.04916376993060112, 0.06350152939558029, 0.13558310270309448, 0.0820142850279808, 0.038440506905317307, 0.01981920190155506, 0.06559835374355316, 0.06426236033439636, 0.08653868734836578, 0.07503397762775421, 0.08597064763307571, 0.04882751777768135, 0.0010722883744165301 ], [ 0.04720444232225418, 0.008832353167235851, 0.015070164576172829, 0.02472323551774025, 0.050062261521816254, 0.002644410589709878, 0.04866943880915642, 0.08640971779823303, 0.05625631660223007, 0.23000948131084442, 0.19624552130699158, 0.04681232571601868, 0.06350851058959961 ], [ 0.09929927438497543, 0.018485790118575096, 0.1042485460639, 0.08748675882816315, 0.010733957402408123, 0.06830459088087082, 0.058639273047447205, 0.002950754715129733, 0.0328013114631176, 0.09814831614494324, 0.1678759604692459, 0.6957993507385254, 0.0690801739692688 ], [ 0.04720429331064224, 0.0013279698323458433, 0.025312649086117744, 0.07893601059913635, 0.07665382325649261, 0.0077852122485637665, 0.030616026371717453, 0.03937874734401703, 0.019078079611063004, 0.02296048402786255, 0.033593639731407166, 0.02409016340970993, 0.03406774252653122, 0.22639304399490356, 0.08740214258432388, 0.06646914035081863, 0.06599576026201248 ], [ 0.047204457223415375, 0.0013103761011734605, 0.03485256806015968, 0.0022472538985311985, 0.07982990890741348, 0.003279963508248329, 0.1681099534034729, 0.008620909415185452, 0.0321669727563858, 0.036973003298044205, 0.039365991950035095, 0.03587152436375618, 0.050321727991104126, 0.013552519492805004, 0.056256845593452454, 0.06366332620382309 ], [ 0.04720441997051239, 0.0021715322509407997, 0.011869898065924644, 0.0023348070681095123, 0.009163934737443924, 0.04569626972079277, 0.07577258348464966, 0.005693087354302406, 0.01076519675552845, 0.09242641925811768, 0.013978216797113419, 0.02530847117304802, 0.0033455705270171165 ], [ 0.04720465466380119, 0.0021714826580137014, 0.004423877224326134, 0.0032962411642074585, 0.03953850641846657, 0.00044384863576851785, 0.0007228970644064248, 0.028475938364863396, 0.003330943174660206, 0.03578552231192589, 0.015429984778165817, 0.036333899945020676, 0.003583752317354083, 0.04955116659402847, 0.010499206371605396, 0.017506513744592667, 0.03247348219156265, 0.022829299792647362 ], [ 0.047204457223415375, 0.0014019429218024015, 0.0005904303397983313, 0.036805082112550735, 0.011087646707892418, 0.0954902246594429, 0.048353273421525955, 0.5327069163322449, 0.008855369873344898, 0.036584146320819855, 0.021317660808563232, 0.09545456618070602, 0.014773508533835411, 0.0903191864490509, 0.10853200405836105, 0.011406929232180119, 0.05362112820148468, 0.0569305494427681 ] ] }, { "q_id": "10188_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 7, 8, 10, 13, 14, 15 ], "rewards": [ [ 0.33035778999328613, 0.08593898266553879, 0.038258302956819534, 0.07568559795618057, 0.034301526844501495, 0.13688454031944275, 0.02892337553203106, 0.14623507857322693, 0.02505226992070675, 0.01045706495642662, 0.014110688120126724, 0.017731189727783203, 0.04788443446159363, 0.025616949424147606, 0.002342110499739647 ], [ 0.26732420921325684, 0.0010455427691340446, 0.09164319187402725, 0.011534134857356548, 0.02241167612373829, 0.02617909386754036, 0.048520300537347794, 0.03492843732237816, 0.15689562261104584, 0.009153082966804504, 0.00034708346356637776, 0.11317571252584457, 0.030179563909769058, 0.09726087749004364, 0.03516561537981033, 0.0773095041513443, 0.0327286422252655, 0.1367764174938202, 0.17810370028018951, 0.06273911148309708, 0.9915242195129395, 0.9992156028747559 ], [ 0.19889406859874725, 0.23499932885169983, 0.2105211615562439, 0.8743153214454651, 0.9283527135848999, 0.9610475301742554 ], [ 0.1799701750278473, 0.1937968134880066, 0.2389216125011444, 0.2502557933330536, 0.22432447969913483, 0.04832243174314499, 0.09108942747116089, 0.0024752942845225334 ], [ 0.292540043592453, 0.010713256895542145, 0.03264812380075455, 0.03135576844215393, 0.04426317662000656, 0.11865066736936569, 0.0013107986887916923, 0.12020422518253326, 0.028652988374233246, 0.00717403506860137, 0.10544604063034058, 0.04886755347251892, 0.07761892676353455, 0.0721590518951416, 0.060290537774562836, 0.039471741765737534, 0.02080252580344677, 0.9866011738777161, 0.9988306164741516 ], [ 0.2673240303993225, 0.0010455517331138253, 0.10227292776107788, 0.006923390086740255, 0.035412516444921494, 0.013818128034472466, 0.07091554254293442, 0.22550073266029358, 0.0564352422952652, 0.031500399112701416, 0.9904226064682007, 0.9986057877540588 ], [ 0.2673264443874359, 0.13235999643802643, 0.0915486067533493, 0.025233935564756393, 0.138044536113739, 0.031686436384916306, 0.1589968502521515, 0.15213069319725037, 0.16328772902488708, 0.09702929854393005, 0.04650203138589859, 0.06354538351297379, 0.9822824001312256 ], [ 0.26732495427131653, 0.009430279023945332, 0.025447629392147064, 0.048403672873973846, 0.0007550012087449431, 0.1284053921699524, 0.019964801147580147, 0.13883480429649353, 0.016554854810237885, 0.0923428162932396, 0.13640154898166656, 0.02628287859261036, 0.06688966602087021, 0.06994441896677017, 0.03233565017580986, 0.9894373416900635, 0.9986522793769836 ], [ 0.29254260659217834, 0.10972603410482407, 0.052499283105134964, 0.08075617253780365, 0.007895846851170063, 0.011198477819561958, 0.07053104788064957, 0.03666890785098076, 0.17142432928085327, 0.20429369807243347, 0.05429477617144585, 0.13805627822875977, 0.1789194643497467, 0.10949776321649551, 0.09483317285776138, 0.2935520112514496, 0.03638281673192978, 0.9903801679611206, 0.9987794756889343 ], [ 0.2673247456550598, 0.0005743152578361332, 0.13538990914821625, 0.01572805643081665, 0.025150367990136147, 0.02729530818760395, 0.03243778645992279, 0.05405323579907417, 0.1660161316394806, 0.01332872174680233, 0.13320046663284302, 0.03390570729970932, 0.11936021596193314, 0.014841079711914062, 0.13021713495254517, 0.06293877214193344, 0.07663992047309875, 0.03166215494275093, 0.9845722913742065, 0.9988443851470947 ], [ 0.26732540130615234, 0.01112615317106247, 0.12855984270572662, 0.04011661559343338, 0.02143205888569355, 0.0023674413096159697, 0.31139108538627625, 0.020923156291246414, 0.4645298421382904, 0.9173054695129395, 0.9547150731086731 ], [ 0.267324298620224, 0.013310485519468784, 0.050695545971393585, 0.030566729605197906, 0.023529963567852974, 0.0010580159723758698, 0.0901249423623085, 0.04653944447636604, 0.0019110125722363591, 0.19480080902576447, 0.052103277295827866, 0.05180816724896431, 0.03560240939259529, 0.10955961793661118, 0.17594893276691437, 0.09608834236860275, 0.9543774127960205, 0.9649721384048462 ] ] }, { "q_id": "10169_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9875901937484741, 0.9746142029762268, 0.9282174110412598, 0.9998980760574341 ], [ 0.9327879548072815, 0.9998798370361328 ], [ 0.9829164147377014, 0.9644890427589417, 0.9769089818000793, 0.9998992681503296 ], [ 0.9853348731994629, 0.9653092622756958, 0.9994785189628601, 0.9999490976333618 ], [ 0.9363464713096619, 0.9533215165138245, 0.9519540071487427, 0.9999226331710815 ], [ 0.9365596175193787, 0.9651086926460266, 0.9999197721481323 ], [ 0.9912279844284058, 0.9646285772323608, 0.9999221563339233 ], [ 0.9757947325706482, 0.9467905759811401, 0.9999215602874756 ], [ 0.960541844367981, 0.9390114545822144, 0.9999266862869263 ], [ 0.9829742908477783, 0.40319594740867615, 0.9992547631263733, 0.9999444484710693 ], [ 0.9638712406158447, 0.949139416217804, 0.9999006986618042 ], [ 0.9888854026794434, 0.9758296012878418, 0.9999269247055054 ], [ 0.9714880585670471, 0.7301761507987976, 0.9141747355461121, 0.9999196529388428 ], [ 0.9830394387245178, 0.9414445757865906, 0.8888576030731201, 0.9999023675918579 ], [ 0.9872841835021973, 0.9801458716392517, 0.9999302625656128 ], [ 0.9754067063331604, 0.6204607486724854, 0.9981712102890015, 0.9999380111694336 ] ] }, { "q_id": "10233_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9846380352973938, 0.9874194264411926, 0.18516835570335388, 0.356679230928421, 0.9678932428359985, 0.9530218839645386 ], [ 0.986687183380127, 0.9923619031906128, 0.2588708698749542, 0.052560530602931976 ], [ 0.041896555572748184, 0.01603236049413681, 0.012989171780645847, 0.28886133432388306, 0.9900670051574707, 0.17045986652374268, 0.16749794781208038, 0.1365688592195511, 0.05090678483247757, 0.025298602879047394 ], [ 0.49249404668807983, 0.26442858576774597, 0.9744980931282043, 0.12768585979938507, 0.11430905014276505, 0.20292000472545624, 0.07711022347211838 ], [ 0.9856428503990173, 0.9866167306900024, 0.15107733011245728, 0.9865108132362366, 0.0026752976700663567 ], [ 0.010731046088039875, 0.9934919476509094, 0.35347023606300354, 0.18422655761241913, 0.8237976431846619, 0.9209691882133484 ], [ 0.010225883685052395, 0.1812354028224945, 0.9844977259635925, 0.18986433744430542, 0.24318043887615204, 0.9846935272216797, 0.42675524950027466 ], [ 0.9869070053100586, 0.9852210879325867, 0.2898706793785095, 0.23401086032390594, 0.9945515990257263, 0.0017292819684371352 ], [ 0.9966116547584534, 0.22279037535190582, 0.5051270127296448, 0.7113742232322693 ], [ 0.49249717593193054, 0.012993806041777134, 0.014694463461637497, 0.4967110753059387, 0.9866912364959717, 0.12334386259317398, 0.04802008345723152, 0.05748129263520241, 0.012516523711383343, 0.16413772106170654, 0.130653977394104, 0.10956241190433502, 0.03180357441306114, 0.15363049507141113, 0.9912617206573486, 0.9961221814155579 ], [ 0.49249598383903503, 0.011568296700716019, 0.01353350467979908, 0.4292581081390381, 0.9889168739318848, 0.20509307086467743, 0.06049710139632225, 0.06535553187131882, 0.011949348263442516, 0.14764606952667236, 0.12032798677682877, 0.10273471474647522, 0.01667954958975315, 0.11264832317829132, 0.9877261519432068, 0.9942580461502075 ], [ 0.9835635423660278, 0.9831647872924805, 0.14749564230442047, 0.23994316160678864, 0.05133580416440964, 0.03704114630818367 ], [ 0.9773374795913696, 0.9787325263023376, 0.17160631716251373, 0.7177941203117371, 0.048102062195539474 ], [ 0.974884569644928, 0.9750224947929382, 0.09087977558374405, 0.11757878214120865, 0.053353507071733475, 0.26805517077445984, 0.13348723948001862, 0.7210410833358765, 0.7958499789237976 ], [ 0.9786309003829956, 0.972780704498291, 0.08470670878887177, 0.16934187710285187, 0.10226189345121384, 0.25239312648773193, 0.20306815207004547, 0.2174464762210846, 0.02581753581762314, 0.22293119132518768, 0.1858907788991928, 0.9952452778816223, 0.9794802665710449 ], [ 0.9856426119804382, 0.9895985126495361, 0.14080920815467834, 0.17115166783332825, 0.2541119158267975, 0.9335548281669617, 0.8784924745559692 ] ] }, { "q_id": "9508_mmlu_physics", "cot_ids": [ 0, 1, 2, 4, 6, 7, 8, 11, 14 ], "rewards": [ [ 0.16769205033779144, 0.14352676272392273, 0.02072790637612343, 0.06851369142532349, 0.03839652240276337, 0.07210402935743332, 0.052787937223911285, 0.12066226452589035, 0.6509731411933899, 0.0025243377313017845 ], [ 0.11515188962221146, 0.010020914487540722, 0.6202735304832458, 0.04659262299537659, 0.12698474526405334, 0.2281254380941391, 0.40198901295661926, 0.0014907540753483772 ], [ 0.1676919162273407, 0.0035127918235957623, 0.1244535818696022, 0.029797539114952087, 0.1512475460767746, 0.0032291661482304335, 0.05021725222468376, 0.00719981174916029, 0.09220561385154724, 0.005939869675785303, 0.017756447196006775, 0.03469602018594742, 0.0018006792524829507 ], [ 0.42871272563934326, 0.002579630585387349, 0.001652348437346518, 0.00954499002546072, 0.0029041420202702284, 0.023146294057369232, 0.022564219310879707, 0.2972780466079712, 0.015440071001648903, 0.6197989583015442, 0.38635075092315674, 0.7455816268920898, 0.0004605047288350761, 0.7618933320045471, 0.9463016986846924, 0.23665869235992432 ], [ 0.16769051551818848, 0.006960880942642689, 0.1722247153520584, 0.005461846478283405, 0.1663597822189331, 0.13838762044906616, 0.6821591854095459, 0.6665456891059875, 0.75826495885849, 0.6748533248901367, 0.0012844695011153817 ], [ 0.16769199073314667, 0.00355346966534853, 0.009745552204549313, 0.1630801409482956, 0.1451372504234314, 0.0038480530492961407, 0.03557250648736954, 0.0647021159529686, 0.24891215562820435, 0.12461588531732559, 0.016711104661226273, 0.0019712282810360193 ], [ 0.3254185914993286, 0.06797758489847183, 0.017070887610316277, 0.0014972265344113111 ], [ 0.1676919162273407, 0.006960986647754908, 0.3226541578769684, 0.0058348714374005795, 0.06418710947036743, 0.1016823947429657, 0.1765827089548111, 0.40390709042549133, 0.23713891208171844, 0.8977838754653931, 0.8731776475906372, 0.9634130597114563 ], [ 0.1676943302154541, 0.034459035843610764, 0.12327222526073456, 0.49013862013816833, 0.8790086507797241, 0.9454013109207153, 0.8879624605178833 ] ] }, { "q_id": "9422_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.1340193897485733, 0.0459669791162014, 0.0862521231174469, 0.07193876802921295, 0.023223960772156715 ], [ 0.1379658579826355, 0.17479826509952545, 0.1878090649843216, 0.28915369510650635, 0.8294638991355896, 0.9318070411682129 ], [ 0.8415625691413879, 0.5359595417976379, 0.1909499317407608, 0.2869771420955658 ], [ 0.8764761686325073, 0.2535744309425354, 0.46041709184646606, 0.9790610671043396, 0.9809807538986206 ], [ 0.8764737844467163, 0.4171101152896881, 0.0814061164855957, 0.2830336093902588 ], [ 0.8539737462997437, 0.5381425619125366, 0.32860317826271057, 0.9502254128456116, 0.9703177809715271 ], [ 0.09168083220720291, 0.08109881728887558, 0.10815896093845367, 0.03212551772594452, 0.5349665284156799, 0.0582902766764164, 0.2879467010498047 ], [ 0.13796471059322357, 0.10453014820814133, 0.052921418100595474, 0.024537624791264534, 0.03148413822054863, 0.9506367444992065, 0.9058628678321838 ], [ 0.8764755129814148, 0.44221940636634827, 0.04615093022584915, 0.2216119021177292 ], [ 0.8764759302139282, 0.3494746685028076, 0.4595242440700531, 0.96104896068573, 0.973691463470459 ], [ 0.07593750953674316, 0.18474453687667847, 0.1506083756685257, 0.36467742919921875, 0.041525088250637054, 0.1669677495956421 ], [ 0.08953619748353958, 0.004443286918103695, 0.021624470129609108, 0.22214561700820923, 0.004459107294678688, 0.9139714241027832, 0.9043087959289551 ], [ 0.09168035537004471, 0.08967802673578262, 0.06594983488321304, 0.15869289636611938, 0.23113560676574707, 0.09567935764789581, 0.8656559586524963 ], [ 0.8032839894294739, 0.1909344643354416, 0.49057450890541077 ], [ 0.853974461555481, 0.49556198716163635, 0.9533928632736206, 0.9571489095687866 ], [ 0.8152058720588684, 0.5517579317092896, 0.03308752179145813, 0.11943311244249344 ] ] }, { "q_id": "9524_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.13238826394081116, 0.09356377273797989, 0.09487947076559067, 0.033042773604393005, 0.03915437310934067, 0.028668371960520744, 0.0413326732814312, 0.023371223360300064, 0.08422406017780304, 0.10639260709285736, 0.03647179156541824, 0.027107592672109604 ], [ 0.29329803586006165, 0.15231984853744507, 0.11183782666921616, 0.05226157233119011, 0.1227501854300499, 0.00593465706333518, 0.0016491705318912864 ], [ 0.8141626715660095, 0.11579321324825287, 0.0939365029335022, 0.9342642426490784, 0.13707569241523743, 0.0006036024424247444 ], [ 0.8657114505767822, 0.0925421193242073, 0.038494862616062164, 0.03612740710377693, 0.10300306230783463, 0.2985036373138428, 0.8918893337249756, 0.0012465434847399592 ], [ 0.5158324837684631, 0.2593528926372528, 0.037424590438604355, 0.09778507798910141, 0.19003558158874512, 0.02547718584537506, 0.18875804543495178, 0.6383315324783325, 0.000552761775907129 ], [ 0.680095911026001, 0.14105625450611115, 0.7793221473693848, 0.000487669778522104, 0.001351168379187584, 0.018936844542622566, 0.023631500080227852, 0.014192353002727032, 0.022383080795407295, 0.03082495555281639, 0.03141307085752487, 0.0036408649757504463 ], [ 0.42392536997795105, 0.49089425802230835, 0.01806012913584709, 0.35126835107803345, 0.03161446377635002, 0.08794327080249786, 0.9066428542137146, 0.28038734197616577, 0.0011580289574339986 ], [ 0.3032895028591156, 0.08022455126047134, 0.41757842898368835, 0.03687591105699539, 0.09000754356384277, 0.6166938543319702, 0.0012571424013003707 ], [ 0.29871997237205505, 0.03053727187216282, 0.03027956932783127, 0.04629463702440262, 0.06707119941711426, 0.07286470383405685, 0.005661239847540855, 0.03278431296348572, 0.0010299308924004436 ], [ 0.6396381855010986, 0.05947741121053696, 0.03093848004937172, 0.05621921643614769, 0.13412728905677795, 0.017081594094634056, 0.10915101319551468, 0.03600996360182762, 0.0917854756116867, 0.009847614914178848, 0.0012744999257847667 ], [ 0.73713618516922, 0.13869261741638184, 0.12786027789115906, 0.047881416976451874, 0.04825703799724579, 0.04982598125934601, 0.039724621921777725, 0.04769773781299591, 0.0032480652444064617 ], [ 0.5220532417297363, 0.10616999119520187, 0.31334230303764343, 0.22041460871696472, 0.0016900693299248815, 0.00093083520187065 ], [ 0.341521292924881, 0.08263508230447769, 0.3120478689670563, 0.052378129214048386, 0.05705849453806877, 0.016403062269091606, 0.13924428820610046, 0.09825586527585983, 0.9495959281921387, 0.44581735134124756, 0.0004958000499755144 ], [ 0.39385494589805603, 0.107467420399189, 0.0809309259057045, 0.02173437550663948, 0.06845808029174805, 0.30707255005836487, 0.1344374716281891, 0.8696489930152893, 0.0011727074161171913 ], [ 0.8074480295181274, 0.10318576544523239, 0.12844590842723846, 0.41816920042037964, 0.8877449035644531, 0.10782021284103394, 0.05128680169582367, 0.047923412173986435, 0.06826720386743546, 0.018502531573176384, 0.16623246669769287, 0.17534154653549194, 0.7630866765975952, 0.0005640889285132289 ], [ 0.5689597129821777, 0.0864359512925148, 0.06960376352071762, 0.058155179023742676, 0.1060737818479538, 0.03403930366039276, 0.0008000389789231122 ] ] }, { "q_id": "9676_mmlu_physics", "cot_ids": [ 4, 6, 7, 8, 9, 13, 14, 15 ], "rewards": [ [ 0.15096165239810944, 0.01129376981407404, 0.09887026250362396, 0.007375279441475868, 0.2509255111217499, 0.24009709060192108, 0.00451918737962842, 0.005329861305654049, 0.0038139778189361095, 0.01028436329215765, 0.008969591930508614, 0.008158420212566853, 0.03785404562950134, 0.02759505622088909, 0.7090216875076294, 0.017242351546883583 ], [ 0.24628259241580963, 0.00540303997695446, 0.024443550035357475, 0.6950584650039673, 0.006999562494456768, 0.01274196058511734, 0.2717979848384857, 0.9466676115989685, 0.014795330353081226 ], [ 0.18779028952121735, 0.15636588633060455, 0.875288724899292, 0.04752778634428978, 0.0313674621284008, 0.03740233555436134, 0.07455025613307953, 0.09868764877319336, 0.06986863911151886, 0.015765303745865822 ], [ 0.16784092783927917, 0.03891419619321823, 0.07775678485631943, 0.8525193333625793, 0.5807410478591919, 0.9177135825157166, 0.934775710105896, 0.014980576932430267 ], [ 0.09485085308551788, 0.025819839909672737, 0.272282212972641, 0.06048984080553055, 0.09469520300626755, 0.2516901195049286, 0.013433651067316532, 0.13637392222881317, 0.08750656247138977, 0.849885106086731, 0.0024622653145343065, 0.03272586315870285, 0.0628308579325676, 0.08629591763019562, 0.05771786719560623, 0.011468278244137764, 0.05821498483419418, 0.02879137359559536 ], [ 0.09485126286745071, 0.019899040460586548, 0.3700141906738281, 0.09588626027107239, 0.14663654565811157, 0.3399977385997772, 0.005028433166444302, 0.1305544078350067, 0.08849512785673141, 0.577475368976593, 0.0018615020671859384, 0.03497102111577988, 0.050006210803985596, 0.050259023904800415, 0.0940607562661171, 0.019981930032372475, 0.026754241436719894, 0.045458752661943436, 0.1217942014336586, 0.2144024521112442, 0.04862130805850029 ], [ 0.2366660088300705, 0.09616091847419739, 0.18765686452388763, 0.002327457768842578, 0.013670279644429684, 0.05929836258292198, 0.4517110288143158, 0.14978806674480438 ], [ 0.1456175446510315, 0.7191399335861206, 0.5501298308372498, 0.28162163496017456, 0.33625227212905884, 0.1572844386100769, 0.021823987364768982 ] ] }, { "q_id": "10152_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9863536357879639, 0.8924579620361328, 0.05303419753909111, 0.9939104318618774 ], [ 0.977950930595398, 0.9680814743041992, 0.9971790313720703 ], [ 0.09916816651821136, 0.8699883818626404, 0.9920828342437744 ], [ 0.3802758455276489, 0.031563449651002884, 0.9245480895042419, 0.9974005222320557 ], [ 0.8172234892845154, 0.22956421971321106, 0.27376773953437805, 0.9965410828590393 ], [ 0.9802314639091492, 0.19404686987400055, 0.08048176765441895, 0.9971776008605957 ], [ 0.2804761528968811, 0.05319376662373543, 0.07880028337240219, 0.09409095346927643, 0.15275464951992035, 0.17229755222797394, 0.021948153153061867, 0.08712185174226761, 0.09420233964920044, 0.013342172838747501 ], [ 0.7981384992599487, 0.963295578956604, 0.997367799282074 ], [ 0.29364487528800964, 0.15939371287822723, 0.34966978430747986, 0.9914578795433044 ], [ 0.19427144527435303, 0.028625821694731712, 0.9188541173934937, 0.9944832921028137 ], [ 0.7981389760971069, 0.30920928716659546, 0.9322966933250427, 0.996562659740448 ], [ 0.7981406450271606, 0.028067203238606453, 0.07169471681118011, 0.6337043046951294, 0.9959565997123718 ], [ 0.2666681706905365, 0.7412844896316528, 0.996432900428772 ], [ 0.3161064386367798, 0.14742423593997955, 0.7098970413208008, 0.27643972635269165, 0.9696062803268433 ], [ 0.9502692222595215, 0.996364951133728 ], [ 0.1518668383359909, 0.08047018945217133, 0.06520695984363556, 0.037326786667108536, 0.009197902865707874 ] ] }, { "q_id": "9086_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 ], "rewards": [ [ 0.2835721969604492, 0.305642694234848, 0.5429128408432007, 0.2207665592432022, 0.0009001962025649846 ], [ 0.17527054250240326, 0.06942813098430634, 0.17131632566452026, 0.18438413739204407, 0.15297479927539825, 0.024340663105249405, 0.05779021233320236, 0.12363103032112122, 0.03273291140794754, 0.17416603863239288, 0.08118908107280731, 0.11883239448070526, 0.07344874739646912, 0.8634144067764282, 0.12473641335964203 ], [ 0.29490557312965393, 0.3323580026626587, 0.015134245157241821, 0.0360141322016716 ], [ 0.2559962868690491, 0.18235307931900024, 0.1653783619403839, 0.1480274647474289, 0.025324508547782898, 0.2215437889099121, 0.07318027317523956, 0.054323866963386536 ], [ 0.2949042022228241, 0.1828242838382721, 0.1369544118642807, 0.2270936667919159, 0.24752601981163025, 0.5220655798912048, 0.0009534700075164437 ], [ 0.2191505879163742, 0.07061336934566498, 0.09646451473236084, 0.021329106763005257, 0.0718289464712143, 0.17639516294002533, 0.041229575872421265, 0.18593767285346985, 0.05505778267979622, 0.4391850531101227, 0.6076215505599976, 0.0009801954729482532 ], [ 0.3288097083568573, 0.37590667605400085, 0.8703126907348633, 0.0009077749564312398 ], [ 0.3069719076156616, 0.28487005829811096, 0.18640343844890594, 0.8747673630714417, 0.0008973676012828946 ], [ 0.17527006566524506, 0.06942908465862274, 0.13511161506175995, 0.0461851991713047, 0.050643060356378555, 0.11706392467021942, 0.03280790522694588, 0.17966102063655853, 0.04714220017194748, 0.31292200088500977, 0.15224698185920715, 0.0504201240837574, 0.10049227625131607, 0.05747801065444946, 0.05639495328068733 ], [ 0.33357763290405273, 0.1875002086162567, 0.11739569157361984, 0.7885867953300476, 0.0009819631231948733 ], [ 0.2695225179195404, 0.1946718841791153, 0.4484768509864807, 0.7394519448280334, 0.0009016683325171471 ], [ 0.1629108041524887, 0.0670093223452568, 0.17194117605686188, 0.1460295170545578, 0.14624042809009552, 0.1194218322634697, 0.18022824823856354, 0.8398451209068298, 0.0007912683649919927 ], [ 0.17527179419994354, 0.06942803412675858, 0.10669486969709396, 0.03581041470170021, 0.04700107499957085, 0.060892071574926376, 0.1801903396844864, 0.1773088276386261, 0.5282571315765381, 0.0010954280151054263 ], [ 0.1629117876291275, 0.0670088455080986, 0.11308988183736801, 0.006058730650693178, 0.030343538150191307, 0.0754220262169838, 0.19177722930908203, 0.2132624238729477, 0.30578112602233887, 0.030473805963993073, 0.09036275744438171, 0.08953157067298889, 0.3582702875137329, 0.6107835173606873, 0.0013885796070098877 ], [ 0.15966500341892242, 0.07014292478561401, 0.11944214254617691, 0.02224099077284336, 0.0607977919280529, 0.08402764797210693, 0.19828005135059357, 0.20576460659503937, 0.31089356541633606, 0.44313275814056396, 0.3733389675617218, 0.0010846499353647232 ] ] }, { "q_id": "9668_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06717764586210251, 0.04440710321068764, 0.07068856805562973, 0.026720168069005013, 0.027322236448526382, 0.07551275193691254, 0.023787956684827805, 0.13469037413597107, 0.0015426677418872714, 0.032634906470775604, 0.032761700451374054, 0.012698700651526451, 0.0010196256916970015, 0.0014653165126219392 ], [ 0.08911274373531342, 0.05528700724244118, 0.07513649016618729, 0.045752763748168945, 0.09494985640048981, 0.012770473957061768, 0.025358356535434723, 0.03476235643029213, 0.011828484013676643, 0.0015818645479157567 ], [ 0.195531964302063, 0.06717947870492935, 0.1402771919965744, 0.019856426864862442, 0.028427641838788986, 0.034055523574352264, 0.1029980406165123, 0.000560292974114418, 0.07810144126415253, 0.03800075501203537, 0.025919359177350998, 0.005890236236155033, 0.0007279338897205889 ], [ 0.08504979312419891, 0.039388738572597504, 0.08736072480678558, 0.12106700241565704, 0.021164897829294205, 0.048934705555438995, 0.0757913812994957, 0.5774216651916504, 0.9978261590003967 ], [ 0.33177831768989563, 0.022903773933649063, 0.08782897144556046, 0.021560754626989365, 0.050285253673791885, 0.02160540409386158, 0.06727943569421768, 0.03029252588748932, 0.11220420151948929, 0.996650755405426, 0.9977534413337708 ], [ 0.11940082162618637, 0.05612078309059143, 0.07228033989667892, 0.02615155093371868, 0.5867079496383667, 0.9957309365272522 ], [ 0.3618236482143402, 0.040813468396663666, 0.029301365837454796, 0.0005047466256655753, 0.06790671497583389, 0.017651623114943504, 0.03217921778559685, 0.01736443303525448, 0.09585785865783691, 0.1013093888759613, 0.0007787365466356277, 0.06154318153858185, 0.03434697166085243, 0.01460198312997818, 0.08089546859264374, 0.9975687861442566 ], [ 0.19240698218345642, 0.05645861104130745, 0.11822597682476044, 0.14748089015483856, 0.013381557539105415, 0.04104181379079819, 0.004438956268131733, 0.12782137095928192, 0.03369086980819702, 0.9938619136810303, 0.9988195300102234 ], [ 0.2281607985496521, 0.05920886993408203, 0.0929718017578125, 0.1193426251411438, 0.0451749749481678, 0.087607242166996, 0.08046592772006989, 0.04872919246554375, 0.048929713666439056, 0.009139799512922764, 0.05158393830060959, 0.06989539414644241, 0.07370635867118835, 0.007178798317909241, 0.0025099492631852627 ], [ 0.14024756848812103, 0.04538252577185631, 0.14173156023025513, 0.120336152613163, 0.031533658504486084, 0.11721961200237274, 0.10898134112358093, 0.020090272650122643, 0.04581822082400322, 0.03139125555753708, 0.016147704795002937, 0.0008357493788935244 ], [ 0.3539736270904541, 0.06038021296262741, 0.08060646057128906, 0.03142724931240082, 0.0041347830556333065, 0.03183675929903984, 0.04624352976679802, 0.0244643222540617, 0.0009926339844241738 ], [ 0.28919875621795654, 0.03713364526629448, 0.08966513723134995, 0.12712082266807556, 0.015561694279313087, 0.08128538727760315, 0.01642381027340889, 0.04028666391968727, 0.016997136175632477, 0.012764576822519302, 0.0007289662025868893 ], [ 0.09317989647388458, 0.023323271423578262, 0.06043387949466705, 0.034552253782749176, 0.041214559227228165, 0.0877978503704071, 0.016151683405041695, 0.03739095479249954, 0.02671736665070057, 0.09135641157627106, 0.0008092892239801586 ], [ 0.14024889469146729, 0.06692799180746078, 0.13027390837669373, 0.03338770940899849, 0.9967516660690308 ], [ 0.15443240106105804, 0.03344873711466789, 0.07276538014411926, 0.021217435598373413, 0.06494992226362228, 0.05692572146654129, 0.00999817717820406, 0.05956563726067543, 0.02597864344716072, 0.0249142087996006, 0.014947142452001572, 0.9956580400466919 ] ] }, { "q_id": "10332_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9964767098426819, 0.9884753227233887, 0.9970707893371582, 0.9988279938697815 ], [ 0.9964767098426819, 0.9980521202087402, 0.9990341663360596 ], [ 0.9964765906333923, 0.9973674416542053, 0.9985982775688171 ], [ 0.9964765906333923, 0.997723400592804, 0.9986143112182617 ], [ 0.9964765906333923, 0.9972014427185059, 0.9988263249397278 ], [ 0.9964765906333923, 0.9978668093681335, 0.9989720582962036 ], [ 0.9964765906333923, 0.9970661997795105, 0.9989650249481201 ], [ 0.9964765906333923, 0.9970836043357849, 0.9986727237701416 ], [ 0.9964765906333923, 0.9850596189498901, 0.9967064261436462, 0.998781144618988 ], [ 0.9964765906333923, 0.9978747367858887, 0.9987722039222717 ], [ 0.9964765906333923, 0.9806674718856812, 0.9974566102027893, 0.9989768266677856 ], [ 0.9964765906333923, 0.9972014427185059, 0.9988262057304382 ], [ 0.9964765906333923, 0.9980869293212891, 0.9990102052688599 ], [ 0.9964765906333923, 0.9978747367858887, 0.9987722039222717 ], [ 0.9964765906333923, 0.9981106519699097, 0.9990177154541016 ], [ 0.9964765906333923, 0.9977914094924927, 0.9986845850944519 ] ] }, { "q_id": "9737_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.0467585027217865, 0.991222620010376, 0.0051644425839185715 ], [ 0.9245757460594177, 0.09083869308233261, 0.9910883903503418, 0.003873238107189536 ], [ 0.8945710062980652, 0.10904117673635483, 0.7928962707519531, 0.006596639286726713 ], [ 0.8769249320030212, 0.028385069221258163, 0.39097222685813904, 0.006003282964229584 ], [ 0.398436963558197, 0.7572090029716492, 0.9617195129394531, 0.0042798444628715515 ], [ 0.3495468199253082, 0.009228621609508991, 0.11081447452306747, 0.004519830923527479 ], [ 0.01835608296096325, 0.006923563778400421, 0.006498738192021847, 0.02262679673731327, 0.7208475470542908, 0.013726824894547462 ], [ 0.03365778550505638, 0.01747850328683853, 0.016442591324448586, 0.26221591234207153, 0.985936164855957, 0.005614906549453735 ], [ 0.8245199918746948, 0.013024670071899891, 0.036093566566705704, 0.6155781745910645, 0.005891576875001192 ], [ 0.014223549515008926, 0.09881246089935303, 0.010182053782045841, 0.9783469438552856, 0.005501326639205217 ], [ 0.6692790389060974, 0.016574809327721596, 0.1501934975385666, 0.034931521862745285, 0.009967954829335213 ], [ 0.7761588096618652, 0.018236853182315826, 0.04081813246011734, 0.0073657869361341 ], [ 0.8945685625076294, 0.033979494124650955, 0.02143203094601631, 0.04266079142689705, 0.9851860404014587, 0.005814091302454472 ], [ 0.01618719846010208, 0.012824908830225468, 0.11697939038276672, 0.9920797944068909, 0.004487515427172184 ], [ 0.9618958234786987, 0.054781850427389145, 0.02170252986252308, 0.15208357572555542, 0.014257519505918026, 0.5607931017875671, 0.007995415478944778 ], [ 0.9057593941688538, 0.08204454928636551, 0.9159387946128845, 0.012031291611492634 ] ] }, { "q_id": "9699_mmlu_physics", "cot_ids": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ], "rewards": [ [ 0.2595616281032562, 0.010843220166862011, 0.04492788016796112, 0.020950190722942352, 0.0004175656649749726, 0.12613621354103088, 0.006127858534455299, 0.014276389963924885, 0.048512134701013565, 0.10412250459194183, 0.08969686925411224, 0.00457795662805438, 0.12807103991508484, 0.0457838736474514, 0.7892151474952698, 0.0012776902876794338 ], [ 0.2595618963241577, 0.010843255557119846, 0.0449274517595768, 0.020950211212038994, 0.00041756208520382643, 0.12937679886817932, 0.006716674193739891, 0.11664722114801407, 0.018200520426034927, 0.049104154109954834, 0.11578847467899323, 0.11289364099502563, 0.005011868197470903, 0.13240233063697815, 0.051270097494125366, 0.13371336460113525, 0.8162162899971008, 0.0053499964997172356 ], [ 0.25956225395202637, 0.01084297988563776, 0.044927552342414856, 0.026011133566498756, 0.11149509251117706, 0.007922777906060219, 0.016216011717915535, 0.045869506895542145, 0.06065869331359863, 0.09171189367771149, 0.11215001344680786, 0.06436118483543396, 0.7395412921905518, 0.0014611153164878488 ], [ 0.34221839904785156, 0.03554447740316391, 0.0006533047999255359, 0.2642495334148407, 0.008849534206092358, 0.17803901433944702, 0.006900887005031109, 0.02065460942685604, 0.12109829485416412, 0.004682164639234543, 0.15110205113887787, 0.14917516708374023, 0.31474292278289795, 0.15809689462184906, 0.7495982050895691, 0.0012814000947400928 ], [ 0.2592359781265259, 0.009615643881261349, 0.045150276273489, 0.021504364907741547, 0.11518020927906036, 0.006926340516656637, 0.014339476823806763, 0.044689033180475235, 0.1042625680565834, 0.09141180664300919, 0.12634113430976868, 0.036168791353702545, 0.21898336708545685, 0.06773536652326584, 0.7230170369148254, 0.001407111994922161 ], [ 0.25923943519592285, 0.009615706279873848, 0.045150935649871826, 0.02150474488735199, 0.0004309536889195442, 0.12324774265289307, 0.01003667525947094, 0.015853773802518845, 0.047895919531583786, 0.10517619550228119, 0.0912797600030899, 0.004751802887767553, 0.12984144687652588, 0.0840691402554512, 0.21441395580768585, 0.07322727888822556, 0.7050809264183044, 0.0013666676823049784 ], [ 0.25956013798713684, 0.010843220166862011, 0.0532742477953434, 0.02057167887687683, 0.11260900646448135, 0.00839438196271658, 0.1152980625629425, 0.16913746297359467, 0.060615867376327515, 0.029730642214417458, 0.13511057198047638, 0.05410972982645035, 0.35932669043540955, 0.8185192942619324, 0.006320381537079811 ], [ 0.2595616281032562, 0.010843220166862011, 0.05327415093779564, 0.019438888877630234, 0.09822139889001846, 0.005376636981964111, 0.11497160792350769, 0.01208705548197031, 0.042670901864767075, 0.029301730915904045, 0.08314749598503113, 0.1232801079750061, 0.030383098870515823, 0.07528913021087646, 0.10310389846563339, 0.04567194730043411, 0.2012019008398056, 0.8594303131103516, 0.005750192329287529 ], [ 0.2595651149749756, 0.0076853740029037, 0.033713553100824356, 0.019733263179659843, 0.2038390338420868, 0.011087344028055668, 0.0767453983426094, 0.1486635059118271, 0.04857518523931503, 0.03442869707942009, 0.2076248675584793, 0.08238392323255539, 0.4382217526435852, 0.7730088829994202, 0.004592276178300381 ], [ 0.2595609724521637, 0.010843208990991116, 0.04492742940783501, 0.020950326696038246, 0.11917049437761307, 0.007254008669406176, 0.11686830222606659, 0.01570231467485428, 0.04657667875289917, 0.10536681115627289, 0.09102662652730942, 0.05509967729449272, 0.12652471661567688, 0.03525405749678612, 0.09296710044145584, 0.18231403827667236, 0.8138446807861328, 0.004178876988589764 ], [ 0.2595617175102234, 0.010843168944120407, 0.044928040355443954, 0.020950092002749443, 0.0004175752110313624, 0.1314944475889206, 0.005842391401529312, 0.009647036902606487, 0.04323112964630127, 0.10061799734830856, 0.08516537398099899, 0.004292297642678022, 0.12607978284358978, 0.03382176533341408, 0.050640515983104706, 0.04571133479475975, 0.7716034650802612, 0.004444765858352184 ], [ 0.2595595121383667, 0.010843107476830482, 0.05327442288398743, 0.019439078867435455, 0.0003843439626507461, 0.1053539589047432, 0.005767154041677713, 0.12012891471385956, 0.017159370705485344, 0.04433197155594826, 0.03225020691752434, 0.08187907189130783, 0.003496933961287141, 0.13885942101478577, 0.02659914456307888, 0.07802306115627289, 0.23893965780735016, 0.05170290544629097, 0.1753636747598648, 0.761844277381897, 0.006045627873390913 ], [ 0.2595612406730652, 0.010843225754797459, 0.04492718353867531, 0.02095014415681362, 0.0004175732610747218, 0.12937705218791962, 0.006716656032949686, 0.11664870381355286, 0.11553451418876648, 0.07141907513141632, 0.10190461575984955, 0.1659964621067047, 0.005295330658555031, 0.31041279435157776, 0.6961435079574585, 0.002276082755997777 ], [ 0.25923970341682434, 0.010823874734342098, 0.041884422302246094, 0.01653016172349453, 0.06288279592990875, 0.006636574398726225, 0.05477385222911835, 0.01637393981218338, 0.020233342424035072, 0.015162019059062004, 0.10003209859132767, 0.06129930168390274, 0.06692937761545181, 0.027941251173615456, 0.1510569155216217, 0.07877589017152786, 0.7177868485450745, 0.0069457548670470715 ] ] }, { "q_id": "10284_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.15144243836402893, 0.04470512270927429, 0.07426503300666809, 0.007430081255733967, 0.032265521585941315, 0.09944791346788406, 0.25676801800727844, 0.015834122896194458, 0.10085630416870117, 0.0077375625260174274, 0.03172096610069275, 0.0425078310072422, 0.044877246022224426, 0.04927212744951248, 0.06164010986685753, 0.008929620496928692, 0.04366600513458252, 0.06586036086082458, 0.25581714510917664, 0.007710174657404423 ], [ 0.15144267678260803, 0.058568183332681656, 0.0006549471290782094, 0.27706658840179443, 0.03797374293208122, 0.6227777004241943, 0.006654576398432255, 0.09163516759872437, 0.9794079065322876, 0.0022726645693182945 ], [ 0.7365342974662781, 0.010965419933199883, 0.06371667236089706, 0.0005413814214989543, 0.11317834258079529, 0.1444890946149826, 0.10945215821266174, 0.18330542743206024, 0.01299973949790001, 0.07429218292236328, 0.0119926193729043 ], [ 0.15143953263759613, 0.11431516706943512, 0.0005423485417850316, 0.23029157519340515, 0.12341679632663727, 0.12171801179647446, 0.08551722019910812, 0.15318015217781067, 0.04563696309924126, 0.22596792876720428, 0.5346688628196716, 0.006924510933458805, 0.0941324532032013, 0.9791466593742371, 0.002816531341522932 ], [ 0.15144212543964386, 0.08494095504283905, 0.15366175770759583, 0.056826069951057434, 0.06739716231822968, 0.001721779233776033 ], [ 0.6724303364753723, 0.015725495293736458, 0.07815950363874435, 0.0005046475562267005, 0.2576436698436737, 0.07473752647638321, 0.7564696669578552, 0.03563118353486061, 0.07187057286500931, 0.0473184771835804, 0.9621286392211914, 0.002301759785041213 ], [ 0.1514418125152588, 0.13625052571296692, 0.355341374874115, 0.1351235955953598, 0.11286848783493042, 0.022106505930423737, 0.17952284216880798, 0.5789494514465332, 0.00633117463439703, 0.04940197244286537, 0.08376407623291016, 0.978600800037384, 0.0022055443841964006 ], [ 0.2348478138446808, 0.04944821447134018, 0.0674562007188797, 0.002670636400580406, 0.04362446814775467, 0.1660265028476715, 0.1209268644452095, 0.332057386636734, 0.022160790860652924, 0.07381970435380936, 0.011686200276017189 ], [ 0.15144243836402893, 0.0660155788064003, 0.0018336751963943243, 0.20226100087165833, 0.3683333694934845, 0.45678219199180603, 0.01927492395043373, 0.031317442655563354, 0.9659752249717712, 0.002618425525724888 ], [ 0.15144015848636627, 0.09710126370191574, 0.25592753291130066, 0.11380095034837723, 0.022067420184612274, 0.1519801914691925, 0.3207825720310211, 0.008493972010910511, 0.04302753508090973, 0.05373514071106911, 0.0948825478553772, 0.9648489356040955, 0.0032428561244159937 ], [ 0.7639864683151245, 0.014591092243790627, 0.06587096303701401, 0.17056000232696533, 0.029026919975876808, 0.5719864368438721, 0.01574661210179329, 0.9645639061927795, 0.002672703703865409 ], [ 0.6807128190994263, 0.011958169750869274, 0.055859293788671494, 0.0006789370672777295, 0.1057552620768547, 0.11127519607543945, 0.2129959762096405, 0.024466438218951225, 0.3552985191345215, 0.3863072991371155, 0.0017939652316272259 ], [ 0.1514418125152588, 0.11431457847356796, 0.0005423739203251898, 0.5409783124923706, 0.04981866478919983, 0.21402931213378906, 0.8187794089317322, 0.0100426459684968, 0.09189922362565994, 0.10093594342470169, 0.9855453372001648, 0.0031089598778635263 ], [ 0.15144145488739014, 0.13129891455173492, 0.5574199557304382, 0.07387380301952362, 0.5712521076202393, 0.010744397528469563, 0.08610232919454575, 0.9806700944900513, 0.0019791543018072844 ], [ 0.15144206583499908, 0.08084800839424133, 0.187080979347229, 0.12030522525310516, 0.06260434538125992, 0.03198658674955368, 0.04941438138484955, 0.09385175257921219, 0.09522560983896255, 0.01796845719218254, 0.07334331423044205, 0.9483650922775269, 0.002536641899496317 ] ] }, { "q_id": "9701_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.477181077003479, 0.49604278802871704, 0.8569521903991699, 0.006202147342264652, 0.3544243574142456, 0.02228783816099167, 0.031838152557611465 ], [ 0.6026525497436523, 0.11407827585935593, 0.13339757919311523, 0.0004575141065288335, 0.6665845513343811, 0.06422027945518494, 0.5786361694335938, 0.030785763636231422, 0.3126468360424042, 0.46849745512008667, 0.021222781389951706 ], [ 0.4771829843521118, 0.5630506873130798, 0.0008102005813270807, 0.8858352899551392, 0.003946632146835327, 0.32546862959861755, 0.023854685947299004, 0.03181980177760124 ], [ 0.47718408703804016, 0.49604231119155884, 0.8628650903701782, 0.8868258595466614, 0.23162370920181274, 0.9167459607124329, 0.019762257114052773 ], [ 0.465129554271698, 0.5559697151184082, 0.8959444761276245, 0.5530352592468262, 0.10070756077766418, 0.38929662108421326, 0.52691251039505, 0.014506272040307522 ], [ 0.5174810886383057, 0.24323846399784088, 0.6391264200210571, 0.859896183013916, 0.18564417958259583, 0.86542147397995, 0.02599666826426983 ], [ 0.47718024253845215, 0.49604469537734985, 0.8551400303840637, 0.6228022575378418, 0.5475895404815674, 0.02803150750696659, 0.02611049823462963 ], [ 0.4485274851322174, 0.47982263565063477, 0.8431844711303711, 0.012877045199275017, 0.37494421005249023, 0.029880110174417496, 0.032917141914367676 ], [ 0.4026516377925873, 0.41598668694496155, 0.8019431829452515, 0.8825665712356567, 0.22140492498874664, 0.9047160744667053, 0.031117871403694153 ], [ 0.9011757373809814, 0.5573093891143799, 0.6698203682899475, 0.0581439733505249 ], [ 0.5354315042495728, 0.31825441122055054, 0.612105667591095, 0.009018518961966038, 0.023759713396430016, 0.03241067752242088 ], [ 0.5053675174713135, 0.1200496181845665, 0.13636089861392975, 0.6322357058525085, 0.06910090148448944, 0.6785783767700195, 0.05620856583118439, 0.2795785367488861, 0.025984929874539375, 0.019406015053391457 ], [ 0.5174765586853027, 0.2432379275560379, 0.9263899326324463, 0.22905422747135162, 0.7234028577804565, 0.04581461101770401 ], [ 0.47718337178230286, 0.49604329466819763, 0.8628630638122559, 0.8559108972549438, 0.9860941171646118, 0.9875183701515198 ], [ 0.6026541590690613, 0.11407742649316788, 0.16761772334575653, 0.7251169681549072, 0.002569120144471526, 0.300056129693985, 0.5261948704719543, 0.04049869254231453, 0.030880032107234 ], [ 0.47718551754951477, 0.49604254961013794, 0.8551408648490906, 0.00232964800670743, 0.06733712553977966, 0.11798832565546036, 0.8296701908111572, 0.23866185545921326, 0.40753811597824097, 0.7819952964782715, 0.01909121684730053 ] ] }, { "q_id": "9541_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5733746290206909, 0.92339688539505, 0.9977548718452454, 0.999687671661377 ], [ 0.9720723032951355, 0.7163941860198975, 0.9984642267227173, 0.9997323155403137 ], [ 0.5405541658401489, 0.8744476437568665, 0.8325227499008179, 0.9977551102638245, 0.9996452331542969 ], [ 0.5000907182693481, 0.5224161148071289, 0.7633383274078369, 0.9993089437484741, 0.9998601675033569 ], [ 0.8621271252632141, 0.9208046793937683, 0.9982126951217651, 0.999735414981842 ], [ 0.9383906126022339, 0.3378976583480835, 0.9978627562522888, 0.9997076392173767 ], [ 0.14731137454509735, 0.6058611273765564, 0.9984305500984192, 0.9996881484985352 ], [ 0.744205117225647, 0.6145922541618347, 0.843560516834259, 0.9980471134185791, 0.999594509601593 ], [ 0.7931010127067566, 0.49329739809036255, 0.9978405237197876, 0.9995434880256653 ], [ 0.9033037424087524, 0.8211498856544495, 0.9982258677482605, 0.9996225833892822 ], [ 0.540553092956543, 0.9318544864654541, 0.998134970664978, 0.9995800852775574 ], [ 0.9835741519927979, 0.8027563691139221, 0.39680272340774536, 0.4434763789176941, 0.9993357062339783, 0.9998947381973267 ], [ 0.7630072236061096, 0.8837308287620544, 0.998292863368988, 0.9996102452278137 ], [ 0.18269401788711548, 0.9971210360527039, 0.9995427131652832 ], [ 0.9742810130119324, 0.7830491065979004, 0.9982888102531433, 0.9996979236602783 ], [ 0.9713190793991089, 0.9985330104827881, 0.999702513217926, 0.9990434050559998 ] ] }, { "q_id": "9049_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.1387559026479721, 0.6167162656784058, 0.9919415712356567, 0.9998595714569092 ], [ 0.9219262599945068, 0.7813883423805237, 0.9935675263404846, 0.9998873472213745 ], [ 0.9878913164138794, 0.9967151880264282, 0.99988853931427 ], [ 0.9219266772270203, 0.9847930669784546, 0.9998551607131958 ], [ 0.9578847885131836, 0.8616019487380981, 0.029470188543200493, 0.9826506972312927, 0.9998602867126465 ], [ 0.9889633655548096, 0.9948252439498901, 0.9998458623886108 ], [ 0.8990983963012695, 0.9406569004058838, 0.563323974609375, 0.9998409748077393 ], [ 0.9219266772270203, 0.9879760146141052, 0.9959051609039307, 0.9998515844345093 ], [ 0.1387525051832199, 0.5595307350158691, 0.9958635568618774, 0.9998770952224731 ], [ 0.9219268560409546, 0.9969154596328735, 0.9998745918273926 ], [ 0.9261232614517212, 0.8911054134368896, 0.9954010248184204, 0.9998844861984253 ], [ 0.9856654405593872, 0.9952279329299927, 0.9998897314071655 ], [ 0.992428719997406, 0.9890679717063904, 0.9998509883880615 ], [ 0.9648301601409912, 0.9557682871818542, 0.999841570854187, 0.9997802376747131 ], [ 0.6422606706619263, 0.9946422576904297, 0.9998985528945923 ], [ 0.9739607572555542, 0.6746967434883118, 0.9941245913505554, 0.9998843669891357 ] ] }, { "q_id": "9772_mmlu_physics", "cot_ids": [ 1, 2, 4, 5, 7, 8, 9, 12, 13 ], "rewards": [ [ 0.4683971107006073, 0.0034399337600916624, 0.01746227964758873, 0.02945731207728386, 0.023237163200974464, 0.14493703842163086, 0.248880073428154, 0.1556720733642578, 0.0689968690276146, 0.029816072434186935, 0.15008077025413513, 0.16109560430049896, 0.033296555280685425, 0.29066163301467896, 0.1899344027042389, 0.29913297295570374, 0.051256973296403885, 0.6879554986953735, 0.00036598893348127604 ], [ 0.4683971107006073, 0.0031701531261205673, 0.01731574721634388, 0.002279657870531082, 0.01145611610263586, 0.0011104763252660632, 0.01480904221534729, 0.22721923887729645, 0.017968716099858284, 0.06601284444332123, 0.02648307755589485, 0.003941270988434553, 0.004030819050967693, 0.0005594727699644864 ], [ 0.46839961409568787, 0.0021522322203963995, 0.009901017881929874, 0.0028694632928818464, 0.06788067519664764, 0.0024333097971975803, 0.06166035309433937, 0.005692340433597565, 0.05681338906288147, 0.004763742908835411, 0.022331969812512398, 0.020472675561904907, 0.27585846185684204, 0.3019251525402069, 0.9997665286064148 ], [ 0.3025510609149933, 0.14139766991138458, 0.09511789679527283, 0.33000099658966064, 0.4721772074699402, 0.5442188382148743, 0.8470757603645325, 0.00039451790507882833 ], [ 0.1873607635498047, 0.020754599943757057, 0.0008217217400670052, 0.04986904188990593, 0.02655062824487686, 0.0924820676445961, 0.06207071989774704, 0.12766006588935852, 0.25133830308914185, 0.31219568848609924, 0.2383323311805725, 0.2865417003631592, 0.5213087201118469, 0.9998331069946289 ], [ 0.27805095911026, 0.004296963568776846, 0.14037087559700012, 0.0018403517315164208, 0.1012297049164772, 0.10870318114757538, 0.2875327467918396, 0.7428091764450073, 0.8749533295631409, 0.7863971590995789, 0.9998477697372437 ], [ 0.03755079209804535, 0.040167585015296936, 0.03067787177860737, 0.0014843421522527933, 0.05657971277832985, 0.0012339719105511904, 0.0067731156013906, 0.007117578759789467, 0.013682539574801922, 0.03813426196575165, 0.2812107801437378, 0.21207399666309357, 0.13499225676059723, 0.027186352759599686, 0.1290266364812851, 0.2458144724369049, 0.00030560060986317694 ], [ 0.46839770674705505, 0.001939389854669571, 0.002846694551408291, 0.00970720686018467, 0.0009964064229279757, 0.13560707867145538, 0.010151457972824574, 0.005234852898865938, 0.0025102524086833, 0.03930291160941124, 0.0014211836969479918, 0.008369864895939827, 0.006088636349886656, 0.006571731995791197, 0.03899892047047615, 0.040401771664619446, 0.00817230436950922, 0.5705780982971191, 0.515520453453064, 0.00034533810685388744 ], [ 0.46839639544487, 0.008600662462413311, 0.028778240084648132, 0.0015771856997162104, 0.01639961637556553, 0.12498922646045685, 0.0009388815378770232, 0.034162864089012146, 0.028473785147070885, 0.3419729769229889, 0.06220630556344986, 0.015537374652922153, 0.2865777611732483, 0.0011036151554435492, 0.0005125509342178702 ] ] }, { "q_id": "9898_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15 ], "rewards": [ [ 0.0597371906042099, 0.024615364149212837, 0.020220475271344185, 0.0204270351678133, 0.015064540319144726, 0.005676610860973597 ], [ 0.40632539987564087, 0.14412879943847656, 0.1151864305138588, 0.027142034843564034, 0.049381155520677567, 0.009660481475293636 ], [ 0.7522656321525574, 0.06354331970214844, 0.004139112774282694, 0.026150749996304512, 0.00018377475498709828, 0.028601529076695442, 0.2003922164440155, 0.005405507981777191 ], [ 0.705375075340271, 0.17777211964130402, 0.04705509915947914, 0.012503281235694885 ], [ 0.08711150288581848, 0.04212500527501106, 0.05209920182824135, 0.060192279517650604, 0.011667458340525627 ], [ 0.6639992594718933, 0.036886684596538544, 0.02461693435907364, 0.03524111583828926, 0.03444812446832657 ], [ 0.2913714051246643, 0.0055929264053702354, 0.00348953390493989, 0.010556613095104694, 0.0008784712990745902, 0.016904909163713455, 0.001720402855426073, 0.0008753405418246984, 0.02916077710688114, 0.07850488275289536 ], [ 0.3472961485385895, 0.004600848071277142, 0.016296202316880226, 0.01902211271226406, 0.009993736632168293, 0.035291992127895355, 0.0061203185468912125 ], [ 0.2274610549211502, 0.04656587913632393, 0.029989348724484444, 0.0005111965583637357, 0.030700255185365677, 0.010242667980492115 ], [ 0.03665664792060852, 0.03859744220972061, 0.03111121617257595, 0.028487537056207657, 0.02026473358273506, 0.028058556839823723 ], [ 0.249045267701149, 0.07167256623506546, 0.03425446152687073, 0.02859739400446415, 0.005003504920750856 ], [ 0.571591317653656, 0.1399453580379486, 0.01628214307129383, 0.02009488083422184, 0.0467476062476635, 0.018511826172471046 ], [ 0.6179414987564087, 0.0570574626326561, 0.0004513401072472334, 0.031962454319000244, 0.011965151876211166 ], [ 0.27144140005111694, 0.047377318143844604, 0.00037937460001558065, 0.0310598686337471, 0.010923662222921848 ], [ 0.3005618155002594, 0.019678952172398567, 0.022647799924016, 0.039154838770627975, 0.03695785999298096, 0.00652811536565423 ] ] }, { "q_id": "9707_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06908219307661057, 0.036469683051109314, 0.06707583367824554, 0.2170574814081192, 0.03084731660783291, 0.18898752331733704, 0.052576448768377304, 0.3751303255558014, 0.08508771657943726, 0.07737800478935242, 0.7755641341209412 ], [ 0.05256357416510582, 0.07005977630615234, 0.05989981070160866, 0.13761824369430542, 0.3735128939151764, 0.06160448119044304, 0.06092900410294533, 0.07602997124195099, 0.4460396468639374, 0.981368899345398 ], [ 0.38607898354530334, 0.28047335147857666, 0.04886172339320183, 0.6924459934234619, 0.08796878904104233, 0.3909647464752197, 0.19917334616184235, 0.9791967272758484 ], [ 0.08934811502695084, 0.026141133159399033, 0.06177094206213951, 0.29667454957962036, 0.03259129077196121, 0.1383497714996338, 0.5969040393829346, 0.9677599668502808 ], [ 0.08163292706012726, 0.0973554477095604, 0.09072455018758774, 0.004522333852946758, 0.5819306969642639, 0.00913020595908165, 0.19007286429405212, 0.33770856261253357, 0.051231496036052704, 0.4546597898006439, 0.9902315735816956 ], [ 0.1519157886505127, 0.21492207050323486, 0.21000373363494873, 0.010552192106842995, 0.6954649090766907, 0.02689264342188835, 0.1544647365808487, 0.051958777010440826, 0.8049753904342651, 0.995964527130127 ], [ 0.08166737109422684, 0.08495959639549255, 0.004062287975102663, 0.4676894247531891, 0.018112290650606155, 0.2471439689397812, 0.061393093317747116, 0.5287579894065857, 0.9936843514442444 ], [ 0.8264917135238647, 0.7125506401062012, 0.006372706964612007, 0.20685556530952454, 0.7563420534133911, 0.9905704259872437 ], [ 0.05837278440594673, 0.12205878645181656, 0.1289663016796112, 0.005065527278929949, 0.7284762263298035, 0.007487846538424492, 0.07679028809070587, 0.2448323369026184, 0.05292600393295288, 0.7418647408485413, 0.001685886294580996 ], [ 0.052062906324863434, 0.09223983436822891, 0.11805137246847153, 0.004292753059417009, 0.26685309410095215, 0.017229409888386726, 0.036510538309812546, 0.026219569146633148, 0.12057369202375412, 0.9801367521286011 ], [ 0.04691699892282486, 0.03551869094371796, 0.030142059549689293, 0.03303695097565651, 0.0001243073638761416, 0.5409801006317139, 0.057448700070381165, 0.5572665333747864, 0.02886335179209709, 0.04791001230478287, 0.05681507661938667, 0.006936338264495134, 0.2943299412727356, 0.06768392026424408, 0.6867457628250122, 0.9873599410057068 ], [ 0.2702445983886719, 0.14255762100219727, 0.4498884975910187, 0.0392347127199173, 0.01723032258450985, 0.9476684927940369 ], [ 0.08934842795133591, 0.02575795166194439, 0.03640798106789589, 0.013335208408534527, 0.000143717261380516, 0.3942323923110962, 0.046733006834983826, 0.6066454648971558, 0.0210528876632452, 0.04578887298703194, 0.01917102560400963, 0.004299878142774105, 0.0438276045024395, 0.04982110112905502, 0.046092066913843155, 0.24559564888477325, 0.060931675136089325, 0.5881439447402954, 0.0021442242432385683 ], [ 0.2884162962436676, 0.21685197949409485, 0.22312240302562714, 0.006794152315706015, 0.7367134094238281, 0.015087026171386242, 0.01600615866482258, 0.06119643151760101, 0.1442674994468689, 0.04165194556117058, 0.8616625666618347, 0.0018716922495514154 ], [ 0.08771131932735443, 0.025552092120051384, 0.04645425081253052, 0.029266923666000366, 0.066277876496315, 0.0032563754357397556, 0.5438480973243713, 0.028440549969673157, 0.04585965722799301, 0.013703545555472374, 0.05489182844758034, 0.04808462783694267, 0.13609178364276886, 0.05024136230349541, 0.3018655776977539, 0.9674996733665466 ], [ 0.057982828468084335, 0.07232726365327835, 0.0399368554353714, 0.024914490059018135, 0.0687633752822876, 0.17441371083259583, 0.2577108144760132, 0.5297028422355652, 0.5172556042671204, 0.0022016442380845547 ] ] }, { "q_id": "10308_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.570905864238739, 0.02146807312965393, 0.517939031124115, 0.9503398537635803, 0.0208871029317379, 0.13537311553955078, 0.08577337861061096, 0.07944846898317337, 0.1935928910970688, 0.9243538975715637, 0.9958863854408264 ], [ 0.57090824842453, 0.02146819233894348, 0.30514460802078247, 0.8132643103599548, 0.022856013849377632, 0.15533317625522614, 0.25588423013687134, 0.09447173774242401, 0.24002507328987122, 0.8503391742706299, 0.9945333003997803 ], [ 0.5709065794944763, 0.011924928985536098, 0.6850217580795288, 0.019196175038814545, 0.26555392146110535, 0.10152427107095718, 0.9333568215370178, 0.9967787861824036 ], [ 0.5709054470062256, 0.021467993035912514, 0.22613561153411865, 0.8211466670036316, 0.025152264162898064, 0.04886415973305702, 0.04226784035563469, 0.899321436882019, 0.9938719272613525 ], [ 0.5709014534950256, 0.010696017183363438, 0.10968118906021118, 0.7661315202713013, 0.01710846833884716, 0.12085019052028656, 0.06173044070601463, 0.10931126773357391, 0.236021488904953, 0.8540900945663452, 0.9883963465690613 ], [ 0.570905864238739, 0.02146807312965393, 0.3535955846309662, 0.9554733633995056, 0.012438162229955196, 0.0632026270031929, 0.06678131967782974, 0.058351606130599976, 0.1450958400964737, 0.9281637072563171, 0.9956127405166626 ], [ 0.5709037780761719, 0.013675834983587265, 0.32316938042640686, 0.9407010078430176, 0.01427491381764412, 0.09201095253229141, 0.09610547870397568, 0.1021517962217331, 0.19099369645118713, 0.9310832023620605, 0.9961601495742798 ], [ 0.5709033012390137, 0.011924761347472668, 0.09734471887350082, 0.7937807440757751, 0.021540876477956772, 0.355977326631546, 0.08098965138196945, 0.9119554758071899, 0.995898425579071 ], [ 0.5709016919136047, 0.016082406044006348, 0.897199273109436, 0.01245089154690504, 0.0781237930059433, 0.07181184738874435, 0.7102106213569641, 0.9900873303413391 ], [ 0.5709054470062256, 0.01726614497601986, 0.2425946146249771, 0.9072379469871521, 0.033133357763290405, 0.2862450182437897, 0.1028175875544548, 0.8904996514320374, 0.9964935183525085 ], [ 0.5709063410758972, 0.0220465287566185, 0.2792365550994873, 0.9491288065910339, 0.012244608253240585, 0.06462137401103973, 0.07685663551092148, 0.060745373368263245, 0.16988708078861237, 0.9312386512756348, 0.9955222606658936 ], [ 0.5709047317504883, 0.021468130871653557, 0.2925082743167877, 0.9519628286361694, 0.024370862171053886, 0.11084046959877014, 0.10300089418888092, 0.08283264935016632, 0.21131493151187897, 0.9141204357147217, 0.9948570728302002 ], [ 0.14664560556411743, 0.02683190442621708, 0.003949545789510012, 0.09053504467010498, 0.008255868218839169, 0.2574014961719513, 0.03498154506087303, 0.9373117089271545, 0.007258151657879353, 0.09334239363670349, 0.12648899853229523, 0.10261069983243942, 0.13231000304222107, 0.42971071600914, 0.029461296275258064, 0.1353905349969864, 0.3914145827293396, 0.2502497732639313, 0.2265191674232483, 0.965340256690979, 0.9994913339614868 ], [ 0.570904016494751, 0.021467791870236397, 0.8880942463874817, 0.025085637345910072, 0.0816524550318718, 0.06477557867765427, 0.8678519129753113, 0.9937846660614014 ], [ 0.5709054470062256, 0.020496193319559097, 0.45206981897354126, 0.8548895716667175, 0.013913320377469063, 0.12928007543087006, 0.3044351041316986, 0.07825654745101929, 0.22111934423446655, 0.933893620967865, 0.9957802295684814 ], [ 0.5709035396575928, 0.02146817184984684, 0.9612168669700623, 0.013195164501667023, 0.3381703794002533, 0.05858743190765381, 0.9932093024253845, 0.9996507167816162 ] ] }, { "q_id": "10058_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9206884503364563, 0.9636910557746887, 0.24534174799919128 ], [ 0.9206856489181519, 0.009915009140968323, 0.00966634415090084 ], [ 0.9206856489181519, 0.09254015237092972, 0.009999494068324566 ], [ 0.9591954350471497, 0.5068274140357971, 0.01030042301863432 ], [ 0.9206867218017578, 0.8601400852203369, 0.2763342559337616 ], [ 0.9206867218017578, 0.5380772948265076, 0.010181136429309845 ], [ 0.9088068604469299, 0.6139615774154663, 0.005229067523032427 ], [ 0.9183125495910645, 0.5709826946258545, 0.009923713281750679 ], [ 0.9206881523132324, 0.17297957837581635, 0.010600103065371513 ], [ 0.9206856489181519, 0.3058108985424042, 0.009716033935546875 ], [ 0.9206846356391907, 0.8552008867263794, 0.00867186114192009 ], [ 0.918312668800354, 0.1796475350856781, 0.01015705056488514 ], [ 0.9206867218017578, 0.9526785612106323, 0.32168659567832947 ], [ 0.9206855297088623, 0.32763341069221497, 0.0061689275316894054 ], [ 0.9206855297088623, 0.30834877490997314, 0.009140970185399055 ], [ 0.9206856489181519, 0.9588831663131714, 0.011637391522526741 ] ] }, { "q_id": "10068_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5610886812210083, 0.0627872422337532, 0.6168704628944397, 0.3659796714782715, 0.0025745437014847994, 0.35092172026634216, 0.9380338788032532, 0.9976223111152649 ], [ 0.561089038848877, 0.06278792023658752, 0.6168684959411621, 0.17500858008861542, 0.43485593795776367, 0.002691732021048665, 0.37169769406318665, 0.9103419184684753, 0.9974855184555054 ], [ 0.5610871911048889, 0.06278746575117111, 0.5562745928764343, 0.35185569524765015, 0.0025955205783247948, 0.34016403555870056, 0.95305997133255, 0.9974276423454285 ], [ 0.8616431355476379, 0.26790186762809753, 0.008896900340914726, 0.9767988920211792, 0.9985426664352417 ], [ 0.9503893852233887, 0.0739053264260292, 0.23658651113510132, 0.04395325854420662, 0.9758943319320679, 0.9990399479866028 ], [ 0.5076097249984741, 0.06300747394561768, 0.6089897155761719, 0.290912002325058, 0.0026569736655801535, 0.41260990500450134, 0.005665130447596312, 0.00511980289593339 ], [ 0.9476550221443176, 0.24400140345096588, 0.3744800090789795, 0.9783049821853638, 0.9984095692634583 ], [ 0.5610851049423218, 0.0741744413971901, 0.5890592336654663, 0.34612441062927246, 0.0023769475519657135, 0.14463308453559875, 0.16976095736026764, 0.19565321505069733, 0.3783336877822876, 0.9654290080070496, 0.9993371367454529 ], [ 0.5610865950584412, 0.07986761629581451, 0.5828602313995361, 0.290529727935791, 0.0012074450496584177, 0.5620701313018799, 0.9628661274909973, 0.9984373450279236 ], [ 0.5610871911048889, 0.08680616319179535, 0.5647725462913513, 0.2665324807167053, 0.28446924686431885, 0.24641554057598114, 0.05644572898745537, 0.9314889907836914, 0.9994459748268127 ], [ 0.561083972454071, 0.06278667598962784, 0.5803861618041992, 0.37938761711120605, 0.0023235559929162264, 0.41817614436149597, 0.9319820404052734, 0.9977099895477295 ], [ 0.9652540683746338, 0.29858142137527466, 0.9904113411903381, 0.9990808963775635 ], [ 0.9575306177139282, 0.1551709622144699, 0.9883982539176941, 0.9990204572677612 ], [ 0.6247437000274658, 0.07621724158525467, 0.6343460083007812, 0.37736719846725464, 0.013466870412230492, 0.44492533802986145, 0.0026001392398029566, 0.38718312978744507, 0.9165624976158142, 0.9976032376289368 ], [ 0.5610862374305725, 0.0627862885594368, 0.6168689131736755, 0.30893269181251526, 0.0023049276787787676, 0.39498284459114075, 0.9264707565307617, 0.9976992011070251 ], [ 0.5610852837562561, 0.06278713047504425, 0.6417837738990784, 0.05368843302130699, 0.09136675298213959, 0.42614737153053284, 0.6658874750137329, 0.06795870512723923, 0.300887793302536, 0.9177520275115967, 0.9972352385520935 ] ] }, { "q_id": "9454_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.2197595089673996, 0.12590144574642181, 0.0664391741156578, 0.04582931473851204, 0.06963259726762772, 0.030555032193660736, 0.02157193422317505, 0.045819200575351715, 0.01956907846033573, 0.01856525056064129, 0.01238455530256033, 0.019275888800621033, 0.024704834446310997, 0.9997584223747253 ], [ 0.0731944739818573, 0.028061259537935257, 0.05683789774775505, 0.03838639333844185, 0.01261966023594141, 0.015541218221187592, 0.0023035367485135794, 0.014474875293672085, 0.024380430579185486, 0.1601213812828064, 0.03918922692537308, 0.09347343444824219, 0.026405446231365204, 0.043540313839912415, 0.06885537505149841, 0.00033117408747784793 ], [ 0.09449699521064758, 0.02953125536441803, 0.10019861161708832, 0.07352370023727417, 0.013168045319616795, 0.01479346863925457, 0.012146437540650368, 0.008014116436243057, 0.007894344627857208, 0.00792419072240591, 0.9997473359107971 ], [ 0.9019519686698914, 0.0948667824268341, 0.1439231038093567, 0.04393002763390541, 0.10182495415210724, 0.0003044628829229623 ], [ 0.2908843755722046, 0.040215663611888885, 0.028288597241044044, 0.06862619519233704, 0.02800602652132511, 0.03822845593094826, 0.055709924548864365, 0.28586506843566895, 0.06831575185060501, 0.9996289014816284 ], [ 0.7938812375068665, 0.016322288662195206, 0.018846863880753517, 0.024177296087145805, 0.022722361609339714, 0.008124577812850475, 0.03255842998623848, 0.000922895735129714, 0.030571352690458298, 0.02656501904129982, 0.014574946835637093, 0.1522519737482071, 0.018030785024166107, 0.0967610701918602, 0.08234517276287079, 0.0003952734696213156 ], [ 0.05353299528360367, 0.02898087166249752, 0.08554261922836304, 0.008564628660678864, 0.014134481549263, 0.02637345716357231, 0.11659356951713562, 0.05508681759238243, 0.05611345171928406, 0.02601599134504795, 0.014831914566457272, 0.9997084736824036 ], [ 0.03832067549228668, 0.03423480689525604, 0.02457592263817787, 0.026201071217656136, 0.03383145481348038, 0.13091443479061127, 0.04792763292789459, 0.05327468365430832, 0.0446477048099041, 0.03200964257121086, 0.9997534155845642 ], [ 0.09449777752161026, 0.22253477573394775, 0.13698092103004456, 0.05565840005874634, 0.0743240937590599, 0.04684117063879967, 0.0640508234500885, 0.8205716013908386, 0.0002526401076465845 ], [ 0.22752782702445984, 0.09469593316316605, 0.08433616906404495, 0.24127808213233948, 0.00046514233690686524 ], [ 0.08491523563861847, 0.13133834302425385, 0.034322720021009445, 0.04505538195371628, 0.022397277876734734, 0.05651148781180382, 0.10709427297115326, 0.0268056932836771, 0.02229670062661171, 0.00400798162445426, 0.0004893598379567266 ], [ 0.3122953474521637, 0.1965465396642685, 0.11556735634803772, 0.04007600247859955, 0.03332453593611717, 0.025959309190511703, 0.028909368440508842, 0.0858440101146698, 0.08492905646562576, 0.08011166751384735, 0.08924566954374313, 0.026682065799832344, 0.02018730528652668, 0.04190428927540779, 0.992620050907135, 0.9998928308486938 ], [ 0.9358223080635071, 0.7860323786735535, 0.043011751025915146, 0.0690794363617897, 0.16188746690750122, 0.10472424328327179, 0.015530467964708805, 0.9997496008872986 ], [ 0.2908821105957031, 0.0568130798637867, 0.053352177143096924, 0.050140030682086945, 0.033088281750679016, 0.19766058027744293, 0.9959242343902588, 0.9998800754547119 ], [ 0.3145824670791626, 0.050891391932964325, 0.12163680046796799, 0.14959536492824554, 0.1021452397108078, 0.03386343643069267, 0.028904898092150688, 0.0112367644906044, 0.05279222130775452, 0.0204266756772995, 0.17059729993343353, 0.0003237968485336751 ] ] }, { "q_id": "9418_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.006743309553712606, 0.0014244085177779198, 0.08694972097873688, 0.0065786028280854225, 0.002024557674303651, 0.06293421238660812, 0.12394528090953827, 0.008777972310781479 ], [ 0.05254816263914108, 0.035103268921375275, 0.09593784809112549, 0.2423466593027115, 0.008647704496979713 ], [ 0.06404653191566467, 0.7350393533706665, 0.696794331073761, 0.9951187372207642 ], [ 0.05841700732707977, 0.14819447696208954, 0.4006367027759552, 0.31823495030403137, 0.008563377894461155 ], [ 0.07147237658500671, 0.3741658627986908, 0.4448261857032776, 0.9947100877761841 ], [ 0.24204647541046143, 0.08215522021055222, 0.0545646995306015, 0.201448455452919, 0.17207705974578857, 0.9940981864929199 ], [ 0.036395251750946045, 0.08088599890470505, 0.03824186697602272, 0.2460099756717682, 0.12521719932556152, 0.009537828154861927 ], [ 0.22540247440338135, 0.10498965531587601, 0.5181035399436951, 0.007343284785747528 ], [ 0.06360074132680893, 0.09815961867570877, 0.32192832231521606, 0.00900549627840519 ], [ 0.6048376560211182, 0.4306521415710449, 0.7367904782295227, 0.9956692457199097, 0.9966408014297485 ], [ 0.058417871594429016, 0.19271349906921387, 0.1729343682527542, 0.04840703308582306, 0.009448960423469543 ], [ 0.018876856192946434, 0.03030265122652054, 0.002187036909162998, 0.48883554339408875, 0.007325441110879183 ], [ 0.006481738295406103, 0.001488290959969163, 0.10325908660888672, 0.012013066560029984, 0.042743559926748276, 0.02274463139474392, 0.009388918057084084 ], [ 0.06623061746358871, 0.2145378291606903, 0.27174118161201477, 0.007383253425359726 ], [ 0.0732278972864151, 0.03954734653234482, 0.3342086374759674, 0.336990624666214, 0.12061227858066559, 0.011328116990625858 ] ] }, { "q_id": "9462_mmlu_physics", "cot_ids": [ 0, 2, 5, 6, 7, 9, 10, 12, 14, 15 ], "rewards": [ [ 0.06320386379957199, 0.05713630095124245, 0.04078720510005951, 0.03580861911177635, 0.024685392156243324, 0.03467537835240364, 0.018808966502547264 ], [ 0.06256453692913055, 0.04694066569209099, 0.06584907323122025, 0.0001613693602848798, 0.04926028847694397, 0.044286441057920456, 0.04175355285406113, 0.06973878294229507, 0.019600657746195793, 0.024338770657777786 ], [ 0.05349335819482803, 0.0012280108639970422, 0.0923076793551445, 0.0014818762429058552, 0.025525806471705437, 0.026212960481643677, 0.007936123758554459, 0.028997743502259254, 0.002445060992613435, 0.02254609763622284, 0.016916610300540924, 0.049330685287714005, 0.06107348948717117 ], [ 0.04148784652352333, 0.06202856823801994, 0.00012073411198798567, 0.058338847011327744, 0.023488454520702362, 0.019353028386831284, 0.10260024666786194, 0.09010057151317596, 0.031117381528019905, 0.12411583960056305, 0.02030567079782486, 0.07230012863874435, 0.03426048532128334, 0.023650528863072395 ], [ 0.5409788489341736, 0.07764698565006256, 0.03270908445119858, 0.05737131088972092, 0.05572977662086487, 0.04792332649230957, 0.034074630588293076, 0.037394870072603226, 0.026460014283657074 ], [ 0.06726890802383423, 0.023287847638130188, 0.020719828084111214, 0.012096510268747807, 0.05124426633119583, 0.04805542901158333, 0.0975678488612175, 0.09363315254449844, 0.21880660951137543, 0.032438114285469055, 0.05342334136366844, 0.022161968052387238, 0.02087639831006527 ], [ 0.07765323668718338, 0.0056402613408863544, 0.028763651847839355, 0.12380901724100113, 0.011758373118937016, 0.05537334829568863, 0.04458383843302727, 0.07477888464927673, 0.9823106527328491, 0.9813278317451477 ], [ 0.04221082106232643, 0.05113208293914795, 0.054371513426303864, 0.0359019935131073, 0.024046123027801514, 0.06559835374355316, 0.09158128499984741, 0.043275583535432816, 0.05801716819405556, 0.03714121878147125, 0.08535991609096527, 0.02797989547252655 ], [ 0.037364840507507324, 0.06705891340970993, 0.16252265870571136, 0.023614823818206787, 0.0741485059261322, 0.1317475140094757, 0.24240882694721222, 0.05892680585384369, 0.05214950442314148, 0.9728435277938843, 0.969992995262146 ], [ 0.037365250289440155, 0.05210386961698532, 0.04180615022778511, 0.021787004545331, 0.032785672694444656, 0.02301168255507946, 0.011628175154328346 ] ] }, { "q_id": "9331_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.2659691870212555, 0.06071724370121956, 0.0542958565056324, 0.2343510389328003, 0.061489611864089966, 0.7197384834289551, 0.06428910046815872, 0.05678332597017288, 0.00146377831697464 ], [ 0.8775492310523987, 0.15381065011024475, 0.016940830275416374, 0.6268495321273804, 0.7309222221374512, 0.037955932319164276, 0.05062012001872063, 0.18353724479675293 ], [ 0.767167866230011, 0.13525539636611938, 0.038393013179302216, 0.7077606320381165, 0.04433932527899742, 0.3077768385410309, 0.08012379705905914, 0.04589021950960159, 0.05941367149353027 ], [ 0.1606132537126541, 0.10413055866956711, 0.2625407874584198, 0.09796246141195297, 0.8387215733528137, 0.41194644570350647, 0.4029000997543335, 0.10905317962169647 ], [ 0.2589587867259979, 0.10078039765357971, 0.4529435336589813, 0.3304106295108795, 0.04200529679656029, 0.0016020959010347724 ], [ 0.2589610517024994, 0.06324218958616257, 0.4308916926383972, 0.8409568071365356, 0.07140810042619705, 0.06540276110172272, 0.037387728691101074 ], [ 0.16046859323978424, 0.4480964243412018, 0.851858377456665, 0.05499346926808357, 0.16297492384910583 ], [ 0.26596778631210327, 0.046115219593048096, 0.2505657374858856, 0.011472252197563648, 0.30628079175949097, 0.03738362714648247, 0.4131004512310028, 0.0027458379045128822, 0.0504908487200737, 0.041667405515909195 ], [ 0.25895923376083374, 0.06359787285327911, 0.29741743206977844, 0.07233371585607529, 0.8079911470413208, 0.1061091497540474, 0.0375804603099823, 0.05566123127937317 ], [ 0.32389041781425476, 0.18608221411705017, 0.6047072410583496, 0.6944059133529663, 0.8016889691352844, 0.07117243111133575 ], [ 0.26596948504447937, 0.06532496213912964, 0.43260711431503296, 0.1579752117395401, 0.4138900339603424, 0.03576575219631195, 0.0015324894338846207 ], [ 0.2589571177959442, 0.15529315173625946, 0.4339856803417206, 0.055973198264837265, 0.13465091586112976 ], [ 0.8693804144859314, 0.0203075110912323, 0.6636186242103577, 0.6938256025314331, 0.06389107555150986, 0.03392000496387482 ], [ 0.8634318113327026, 0.14152340590953827, 0.016650762408971786, 0.6360588073730469, 0.17164210975170135, 0.7376909255981445, 0.11312159895896912, 0.05808751657605171, 0.05243723839521408, 0.03864675760269165 ], [ 0.2589586675167084, 0.03316667675971985, 0.21334291994571686, 0.014195503666996956, 0.25050222873687744, 0.0364607498049736, 0.18836385011672974, 0.0026453149039298296, 0.04390377923846245, 0.050828393548727036, 0.026962898671627045, 0.07003836333751678, 0.021571703255176544 ], [ 0.2659704089164734, 0.04912981018424034, 0.33647632598876953, 0.3468136787414551, 0.532675564289093, 0.03412463515996933, 0.0012896169209852815 ] ] }, { "q_id": "10139_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 ], "rewards": [ [ 0.40006983280181885, 0.1338965743780136, 0.3370843827724457, 0.5920478105545044, 0.06444565951824188, 0.5032185912132263, 0.05827075242996216, 0.25549256801605225, 0.08592324703931808, 0.9931719303131104, 0.9995613694190979 ], [ 0.6949188709259033, 0.5084484815597534, 0.9897777438163757, 0.9977895021438599 ], [ 0.32403799891471863, 0.2056722790002823, 0.25552964210510254, 0.017716165632009506, 0.2512851655483246, 0.10208000987768173, 0.0908377394080162, 0.016463665291666985, 0.009401978924870491 ], [ 0.4357670247554779, 0.5215839743614197, 0.9848740100860596, 0.9974237680435181 ], [ 0.43576741218566895, 0.10082941502332687, 0.030963663011789322, 0.16442497074604034, 0.0467899926006794, 0.14183002710342407, 0.04656977206468582, 0.17935138940811157, 0.039784036576747894, 0.9937269687652588, 0.9988258481025696 ], [ 0.43576622009277344, 0.7552611231803894, 0.35239091515541077, 0.9967785477638245, 0.9991135001182556 ], [ 0.43576353788375854, 0.2811911106109619, 0.9871416091918945, 0.9955040812492371 ], [ 0.12082638591527939, 0.023463204503059387, 0.13586585223674774, 0.19662010669708252, 0.026093021035194397, 0.15784615278244019, 0.052031729370355606, 0.9763744473457336, 0.9968357682228088 ], [ 0.33401229977607727, 0.14560741186141968, 0.5685979723930359, 0.9918915033340454, 0.9988806843757629 ], [ 0.43576285243034363, 0.30291423201560974, 0.6645305156707764, 0.9929171800613403, 0.9989326596260071 ], [ 0.45476335287094116, 0.025801805779337883, 0.035709865391254425, 0.07600890845060349, 0.012279798276722431, 0.25358542799949646, 0.326622873544693, 0.07648329436779022, 0.12081504613161087, 0.07072187215089798, 0.07591034471988678, 0.04093862697482109, 0.9899455904960632, 0.9986820816993713 ], [ 0.43576493859291077, 0.21703796088695526, 0.013227121904492378, 0.5441409945487976, 0.058812547475099564, 0.9947715401649475, 0.9993041753768921 ], [ 0.4357661008834839, 0.3967227041721344, 0.30662021040916443, 0.9817459583282471, 0.9972617626190186 ], [ 0.4357618987560272, 0.022531874477863312, 0.3401102125644684, 0.9785276055335999, 0.9951611161231995 ], [ 0.43576374650001526, 0.136158749461174, 0.2346602827310562, 0.9947696328163147, 0.9991070628166199 ] ] }, { "q_id": "10118_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8055446147918701, 0.044286441057920456, 0.12613941729068756, 0.0002935860538855195, 0.16227267682552338, 0.000222153976210393, 0.13187547028064728, 0.0552416555583477, 0.9998685121536255 ], [ 0.9793624877929688, 0.024707641452550888, 0.05116119608283043, 0.10676251351833344, 0.06584707647562027, 0.0754811018705368, 0.06363578885793686, 0.9993315935134888, 0.9999322891235352 ], [ 0.8973061442375183, 0.10693971812725067, 0.06924247741699219, 0.007611249107867479, 0.0895034670829773, 0.008320999331772327, 0.22601813077926636, 0.5226302146911621, 0.9999344348907471 ], [ 0.08827969431877136, 0.06775431334972382, 0.09166458994150162, 0.0632481798529625, 0.017552830278873444, 0.057665448635816574, 0.999622106552124, 0.9999529123306274 ], [ 0.8253060579299927, 0.10253536701202393, 0.037652239203453064, 0.047572553157806396, 0.00037261989200487733, 0.07825081795454025, 0.08451488614082336, 0.01826341450214386, 0.06953863054513931, 0.006009067874401808, 0.032850030809640884, 0.007529404014348984, 0.9990924596786499, 0.99993896484375 ], [ 0.8983957767486572, 0.02824728563427925, 0.051878105849027634, 0.00032653071684762836, 0.08414275199174881, 0.05892416834831238, 0.026501279324293137, 0.0529310517013073, 0.02611464448273182, 0.1519351452589035, 0.9995560050010681, 0.9999476671218872 ], [ 0.8253037929534912, 0.029200222343206406, 0.04874611273407936, 0.07434433698654175, 0.3447377383708954, 0.9998766183853149 ], [ 0.8253061175346375, 0.02920011430978775, 0.04451921582221985, 0.00034067447995767, 0.07457749545574188, 0.05667722225189209, 0.06257303804159164, 0.11593086272478104, 0.9998756647109985 ], [ 0.08902522921562195, 0.059377603232860565, 0.00035064283292740583, 0.09799061715602875, 0.03631271794438362, 0.13976317644119263, 0.03492056205868721, 0.12203063070774078, 0.010263249278068542, 0.9992250204086304, 0.9999542236328125 ], [ 0.5085619688034058, 0.03018464520573616, 0.00020968008902855217, 0.05587976425886154, 0.03713879734277725, 0.017703982070088387, 0.09360774606466293, 0.05389883741736412, 0.02703278325498104, 0.17469802498817444, 0.9997256398200989, 0.9999375343322754 ], [ 0.8253040313720703, 0.07196357101202011, 0.020919110625982285, 0.12130003422498703, 0.13597562909126282, 0.052606288343667984, 0.05343344435095787, 0.04905577376484871, 0.03183605149388313, 0.9990609288215637, 0.9999489784240723 ], [ 0.08534472435712814, 0.05529371276497841, 0.09394469112157822, 0.07418704777956009, 0.019867239519953728, 0.0576171949505806, 0.018887721002101898, 0.14059780538082123, 0.10439347475767136, 0.999506950378418, 0.9999562501907349 ], [ 0.29230424761772156, 0.028005817905068398, 0.0002079140249406919, 0.039724480360746384, 0.05567767843604088, 0.21497398614883423, 0.06329870969057083, 0.03862355276942253, 0.9992899894714355, 0.9999531507492065 ], [ 0.9396256804466248, 0.06421232223510742, 0.00032146775629371405, 0.11126020550727844, 0.009343484416604042, 0.022018030285835266, 0.005381613504141569, 0.035389743745326996, 0.004289828706532717, 0.05966896191239357, 0.9992720484733582, 0.9999160766601562 ], [ 0.8983951807022095, 0.03501668944954872, 0.04930049926042557, 0.09176842123270035, 0.09364615380764008, 0.07789719849824905, 0.02057194523513317, 0.10998939722776413, 0.26281583309173584, 0.9990010857582092, 0.999942421913147 ] ] }, { "q_id": "10299_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9959017634391785, 0.38411274552345276, 0.9978591799736023, 0.9999717473983765 ], [ 0.9962942004203796, 0.9985468983650208, 0.9999691247940063 ], [ 0.996403694152832, 0.9978339076042175, 0.9999649524688721 ], [ 0.9973830580711365, 0.9951816201210022, 0.9999663829803467 ], [ 0.9962100982666016, 0.9961113333702087, 0.9491196274757385, 0.9999566078186035 ], [ 0.9965077042579651, 0.12026692926883698, 0.9984527826309204, 0.9999713897705078 ], [ 0.9907246232032776, 0.9967617988586426, 0.999966025352478 ], [ 0.9967045187950134, 0.12229593098163605, 0.9984476566314697, 0.999970555305481 ], [ 0.9956348538398743, 0.9980656504631042, 0.9999651908874512 ], [ 0.9964035749435425, 0.9981720447540283, 0.9999638795852661 ], [ 0.996209979057312, 0.3520628809928894, 0.9932416677474976, 0.9999657869338989 ], [ 0.9962100982666016, 0.040756139904260635, 0.9977260231971741, 0.9999675750732422 ], [ 0.996209979057312, 0.996771514415741, 0.9999642372131348 ], [ 0.9964035749435425, 0.3964984714984894, 0.9965770840644836, 0.9999687671661377 ], [ 0.9954909682273865, 0.0708111822605133, 0.9975234866142273, 0.9999668598175049 ], [ 0.9954909682273865, 0.9959557056427002, 0.9999589920043945 ] ] }, { "q_id": "10063_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8626900315284729, 0.9390761852264404, 0.9858965277671814 ], [ 0.9925271272659302, 0.9260869026184082, 0.9972803592681885 ], [ 0.8383561372756958, 0.9943906664848328, 0.9736721515655518, 0.000886636262293905 ], [ 0.6723418831825256, 0.5955353379249573, 0.0013397256843745708 ], [ 0.7668408155441284, 0.8830044865608215, 0.0014160149730741978 ], [ 0.9987188577651978, 0.898561954498291, 0.9689313173294067, 0.00224151648581028 ], [ 0.9987188577651978, 0.7843943238258362, 0.995244562625885 ], [ 0.771047830581665, 0.3171760141849518, 0.7806709408760071, 0.0011193702230229974 ], [ 0.9987188577651978, 0.9112723469734192, 0.805780291557312, 0.9969133138656616 ], [ 0.6936543583869934, 0.01014900952577591, 0.9645689129829407 ], [ 0.9980542659759521, 0.995999813079834 ], [ 0.9987188577651978, 0.9684703350067139, 0.9800743460655212, 0.001899127964861691 ], [ 0.6936486959457397, 0.4331592619419098, 0.9171232581138611, 0.0017154900124296546 ], [ 0.6936538815498352, 0.9820484519004822, 0.9935622215270996 ], [ 0.991755485534668, 0.2845129072666168, 0.7283685803413391, 0.0006344648427329957 ], [ 0.9987188577651978, 0.9476633667945862, 0.9963656663894653 ] ] }, { "q_id": "9955_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5569614768028259, 0.048368893563747406, 0.01338815689086914, 0.0565590001642704, 0.0426134392619133, 0.04190827161073685, 0.05336523428559303, 0.051736507564783096, 0.024683361873030663, 0.07757936418056488, 0.03242886811494827, 0.0213021170347929, 0.001376324100419879 ], [ 0.16586242616176605, 0.08916912227869034, 0.016345111653208733, 0.0012860071146860719 ], [ 0.3239634931087494, 0.05991555005311966, 0.04276910424232483, 0.024350164458155632, 0.1454227715730667, 0.05207328498363495, 0.07209376245737076, 0.05903439596295357, 0.43776458501815796, 0.054833825677633286 ], [ 0.13492907583713531, 0.015997620299458504, 0.09867195785045624, 0.025415590032935143, 0.05418660491704941, 0.03413684666156769, 0.015742013230919838, 0.001104772207327187 ], [ 0.048195451498031616, 0.015378760173916817, 0.07568500190973282, 0.02502385713160038, 0.12116257101297379, 0.055430516600608826, 0.01998841017484665, 0.0014649147633463144 ], [ 0.0223168283700943, 0.018698275089263916, 0.15132413804531097, 0.08358047902584076, 0.0736282616853714, 0.035264600068330765 ], [ 0.02277090772986412, 0.017353517934679985, 0.19148901104927063, 0.26383206248283386, 0.039166953414678574, 0.09300670772790909, 0.11726981401443481, 0.06669113039970398, 0.013105862773954868, 0.0010556948836892843 ], [ 0.02108774520456791, 0.01623007468879223, 0.030469540506601334, 0.1369527280330658, 0.1463581770658493, 0.024507397785782814, 0.0016665434231981635 ], [ 0.01572146639227867, 0.013814926147460938, 0.025519343093037605, 0.03844769671559334, 0.07552460581064224, 0.05577980726957321, 0.018576158210635185, 0.0661947950720787, 0.05952077731490135, 0.03865612670779228 ], [ 0.021087942644953728, 0.015593516640365124, 0.025841474533081055, 0.08886904269456863, 0.049356698989868164, 0.022189389914274216, 0.0016729732742533088 ], [ 0.43427348136901855, 0.06953281909227371, 0.11338242888450623, 0.0314934141933918, 0.042738623917102814, 0.017544833943247795, 0.0011280188336968422 ], [ 0.015358483418822289, 0.015106744132936, 0.02908262610435486, 0.04158714786171913, 0.0808248370885849, 0.05931216850876808, 0.15201884508132935, 0.05362071469426155, 0.05005280300974846, 0.04147882014513016 ], [ 0.022317033261060715, 0.01649523712694645, 0.017627520486712456, 0.0338326059281826, 0.07739908248186111, 0.018441036343574524, 0.06531316041946411, 0.0404459573328495, 0.02166943997144699, 0.0075454446487128735, 0.0018067591590806842 ], [ 0.4006946384906769, 0.14887070655822754, 0.031541552394628525, 0.1332234889268875, 0.056909359991550446, 0.06391163915395737, 0.016065800562500954, 0.00131900270935148 ], [ 0.04305524379014969, 0.15121449530124664, 0.07559029757976532, 0.00113748200237751 ], [ 0.2291126698255539, 0.02606373466551304, 0.13002321124076843, 0.017578834667801857, 0.049376972019672394, 0.02153548039495945, 0.001129636657424271 ] ] }, { "q_id": "9098_mmlu_physics", "cot_ids": [ 1, 2, 3, 9, 12 ], "rewards": [ [ 0.3933146893978119, 0.00016454621800221503, 0.03067999705672264, 0.000507847813423723, 0.06658536940813065, 9.286895510740578e-05, 0.022591285407543182, 0.00030059859273023903, 0.010741028003394604, 0.02181713655591011, 0.002160952892154455, 0.042384564876556396, 0.018447700887918472, 0.010210649110376835 ], [ 0.036230143159627914, 0.04794821888208389, 0.0036123283207416534, 0.02919797971844673, 0.03887907788157463, 0.09941717237234116, 0.01588214561343193, 0.0745389312505722, 0.05843791365623474, 0.008016686886548996 ], [ 0.39331310987472534, 0.00016454842989332974, 0.10060510039329529, 0.0010730538051575422, 0.0161883682012558, 0.00040387583430856466, 0.014122155494987965, 0.003824349259957671, 0.08765272051095963, 0.002732273656874895, 0.0036220019683241844, 0.04830699786543846, 0.026240531355142593, 0.01945999450981617, 0.004276236519217491 ], [ 0.3933156132698059, 0.00047656765673309565, 0.05509195104241371, 8.548790356144309e-05, 0.034567851573228836, 0.0010018596658483148, 0.10268553346395493, 0.0014500707620754838, 0.131849005818367, 0.03358845412731171, 0.06587597727775574, 0.016535837203264236, 0.0567031092941761, 0.0760699212551117, 0.07657036930322647, 0.02751052938401699, 0.06599414348602295, 0.9358882904052734, 0.9761364459991455 ], [ 0.3933151364326477, 0.0003590316919144243, 0.013014291413128376, 0.0002383889222983271, 0.015324289910495281, 0.017843088135123253, 0.036355629563331604, 0.02145407162606716, 0.13188377022743225, 0.04204706847667694, 0.00575191481038928, 0.012661539949476719, 0.00644242949783802 ] ] }, { "q_id": "9517_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.25923970341682434, 0.028090065345168114, 0.2250819206237793, 0.8569080829620361, 0.6124564409255981 ], [ 0.08997482061386108, 0.0468376986682415, 0.049382321536540985, 0.009334268048405647, 0.12259843200445175, 0.10927817225456238, 0.62964928150177, 0.01684776321053505, 0.8431000113487244, 0.3877308666706085 ], [ 0.11799382418394089, 0.0775623694062233, 0.011156084015965462, 0.23873291909694672, 0.9593616127967834, 0.8211979866027832 ], [ 0.2625698447227478, 0.1523887664079666, 0.1032416820526123, 0.021935025230050087, 0.07815185189247131, 0.9588749408721924, 0.7510924935340881 ], [ 0.2882035970687866, 0.39968568086624146, 0.877407431602478, 0.20095139741897583 ], [ 0.21593643724918365, 0.07633087038993835, 0.20329588651657104, 0.0682373121380806, 0.028436124324798584, 0.07426847517490387, 0.14086493849754333, 0.02744177356362343, 0.8684253096580505, 0.9474024176597595 ], [ 0.07731974124908447, 0.05224660411477089, 0.050516754388809204, 0.13591702282428741, 0.005128899123519659, 0.12066063284873962, 0.026106607168912888, 0.10963639616966248, 0.19798095524311066, 0.060916971415281296 ], [ 0.07868135720491409, 0.1403866410255432, 0.007575287017971277, 0.12328370660543442, 0.49958062171936035, 0.011330033652484417, 0.28733429312705994, 0.052895162254571915, 0.6878147721290588, 0.6895936727523804 ], [ 0.25923797488212585, 0.28383052349090576, 0.09813126921653748, 0.04133325442671776 ], [ 0.07731865346431732, 0.053631048649549484, 0.054165422916412354, 0.24670159816741943, 0.5752662420272827, 0.09993693232536316 ], [ 0.07232559472322464, 0.05540041625499725, 0.05772847309708595, 0.15115012228488922, 0.005092480685561895, 0.1259356141090393, 0.9105629920959473, 0.1790752410888672 ], [ 0.2592393457889557, 0.2533414661884308, 0.0959126278758049, 0.7172236442565918, 0.49198126792907715 ], [ 0.23731008172035217, 0.4804396331310272, 0.020678890869021416, 0.1451239436864853, 0.9028668403625488, 0.45113345980644226 ], [ 0.25923678278923035, 0.31284770369529724, 0.18035297095775604, 0.2757979929447174, 0.07341156154870987 ], [ 0.2592374384403229, 0.019898071885108948, 0.46540123224258423, 0.16394637525081635, 0.9577941298484802, 0.8223273158073425 ], [ 0.2592408061027527, 0.3289511501789093, 0.8612478971481323, 0.10835371166467667 ] ] }, { "q_id": "10098_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.10439088940620422, 0.042055387049913406, 0.03558361530303955, 0.9924638271331787 ], [ 0.362661212682724, 0.5242891907691956, 0.9962767958641052, 0.998264729976654 ], [ 0.4443431794643402, 0.097981296479702, 0.08503617346286774, 0.5212566256523132, 0.21981601417064667, 0.9981155395507812 ], [ 0.24987834692001343, 0.11504629999399185, 0.21958287060260773, 0.30836576223373413, 0.9212118983268738, 0.9978364109992981 ], [ 0.19732026755809784, 0.9975054860115051, 0.9965704679489136 ], [ 0.24987921118736267, 0.9698445200920105, 0.9969860911369324 ], [ 0.2799830436706543, 0.9674272537231445, 0.9976897239685059 ], [ 0.24987781047821045, 0.5274843573570251, 0.9571662545204163, 0.9982998967170715 ], [ 0.24987941980361938, 0.05758266896009445, 0.9986433386802673, 0.9990614056587219 ], [ 0.10438759624958038, 0.0840107724070549, 0.99921715259552, 0.9990503191947937 ], [ 0.303274005651474, 0.3213717043399811, 0.017993496730923653, 0.9982829093933105 ], [ 0.24987834692001343, 0.05644042044878006, 0.03142167627811432, 0.48897087574005127, 0.9872511625289917, 0.9987202882766724 ], [ 0.3626643121242523, 0.9744807481765747, 0.9900578856468201, 0.9983435869216919 ], [ 0.9072810411453247, 0.9971020817756653, 0.9921979308128357, 0.9980399012565613 ], [ 0.42477917671203613, 0.525371789932251, 0.89876788854599, 0.972496747970581, 0.9983162879943848 ], [ 0.36266693472862244, 0.9846675992012024, 0.9980347752571106 ] ] }, { "q_id": "9713_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ], "rewards": [ [ 0.17983172833919525, 0.02043478563427925, 0.014156107790768147, 0.1583903431892395, 0.0032923580147325993, 0.08841364830732346, 0.04044083133339882 ], [ 0.11596781015396118, 0.19559340178966522, 0.11309384554624557, 0.03179340064525604 ], [ 0.1798308938741684, 0.022203093394637108, 0.4005867540836334, 0.07482489198446274, 0.13895922899246216, 0.05432582646608353 ], [ 0.17983172833919525, 0.017203614115715027, 0.026095297187566757, 0.019859962165355682, 0.04270215705037117, 0.05300501361489296, 0.03784284368157387, 0.02378643862903118 ], [ 0.17983292043209076, 0.022203577682375908, 0.07583805918693542, 0.108683742582798, 0.031574003398418427, 0.06919009983539581, 0.11585977673530579, 0.00972610991448164, 0.239293172955513, 0.03017038106918335 ], [ 0.17982997000217438, 0.025502070784568787, 0.1097622811794281, 0.07082121819257736, 0.03694877028465271 ], [ 0.2806513011455536, 0.09249963611364365, 0.35379236936569214, 0.12371242046356201, 0.0035054716281592846 ], [ 0.17983490228652954, 0.022203588858246803, 0.07387714087963104, 0.1460076868534088, 0.1977282017469406, 0.7498571276664734 ], [ 0.17983172833919525, 0.02220313437283039, 0.08122438192367554, 0.09792618453502655, 0.005002161487936974, 0.010131358169019222, 0.04509936273097992, 0.05870189890265465, 0.0697028860449791, 0.04814116284251213 ], [ 0.17983172833919525, 0.022203370928764343, 0.08122452348470688, 0.24318501353263855, 0.23078709840774536, 0.8793730139732361 ], [ 0.15267138183116913, 0.1240653544664383, 0.13383017480373383, 0.22183267772197723, 0.1839519590139389, 0.020529992878437042 ], [ 0.17983102798461914, 0.022203218191862106, 0.09741798043251038, 0.09701785445213318, 0.125279039144516, 0.3657680153846741, 0.5445281863212585 ], [ 0.17983172833919525, 0.012476692907512188, 0.042544156312942505, 0.019827835261821747, 0.03335161134600639, 0.11684439331293106, 0.046254612505435944, 0.03995507210493088 ], [ 0.17983369529247284, 0.019648941233754158, 0.08523666113615036, 0.0880182608962059, 0.18537867069244385, 0.07601886242628098, 0.04186645522713661 ], [ 0.17983299493789673, 0.019649049267172813, 0.09229306876659393, 0.4189492464065552, 0.02426185831427574, 0.02348032221198082 ] ] }, { "q_id": "9631_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.7349201440811157, 0.12713998556137085, 0.5046846866607666, 0.3669571876525879, 0.3017716407775879, 0.10944044589996338, 0.06997718662023544 ], [ 0.8591012954711914, 0.02341870218515396, 0.003277062438428402, 0.047359760850667953, 0.06111336499452591 ], [ 0.859101414680481, 0.024861697107553482, 0.03480265289545059, 4.1016632167156786e-05, 0.023160098120570183, 0.02734489180147648, 0.07744148373603821, 0.06299779564142227, 0.05818440020084381, 0.4497220814228058, 0.6647272706031799 ], [ 0.7340593934059143, 0.8415113687515259, 0.3727874755859375, 0.5915102362632751, 0.09906015545129776, 0.0006990220281295478, 0.2929801940917969, 0.9752354621887207, 0.049997467547655106 ], [ 0.7349210381507874, 0.8546994924545288, 0.12076885253190994, 0.3656291961669922, 0.037066973745822906, 0.10593699663877487, 0.6055346131324768, 0.08887629210948944, 0.12706226110458374, 0.2995138168334961, 0.5343345999717712, 0.9886985421180725, 0.995254635810852 ], [ 0.36855894327163696, 0.8661475777626038, 0.3531009256839752, 0.05856987088918686, 0.23441846668720245, 0.9549182057380676, 0.9775975346565247 ], [ 0.72151780128479, 0.5110899806022644, 0.506689190864563, 0.0746598094701767 ], [ 0.7228953242301941, 0.7598720192909241, 0.6546421647071838, 0.076253242790699, 0.16430839896202087, 0.017395606264472008, 0.041987817734479904, 0.9237841963768005, 0.9903935790061951, 0.9933069348335266 ], [ 0.8578631281852722, 0.1883322298526764, 0.5081219673156738, 0.03560607507824898, 0.11629490554332733, 0.34615764021873474, 0.028338566422462463 ], [ 0.8715880513191223, 0.3320905864238739, 0.356596976518631, 0.5441634654998779, 0.08951936662197113, 0.06351599097251892 ], [ 0.8591027855873108, 0.4437169134616852, 0.45751988887786865, 0.22649921476840973, 0.3921315670013428, 0.11000616103410721, 0.015666162595152855, 0.43720436096191406, 0.9759154319763184, 0.9780516028404236 ], [ 0.8591016530990601, 0.15260033309459686, 0.6268271207809448, 0.09194253385066986, 0.013843356631696224, 0.009035995230078697, 0.02996954694390297, 0.8739914298057556, 0.0075491308234632015 ], [ 0.7913076877593994, 0.015728041529655457, 0.03659428283572197, 0.03550288826227188, 0.08783895522356033, 0.04762203246355057 ], [ 0.7446573376655579, 0.247700035572052, 0.582789957523346, 0.07504019141197205, 0.15288110077381134 ], [ 0.6585292220115662, 0.7163669466972351, 0.22153756022453308, 0.5362851619720459, 0.033842820674180984, 0.6374666094779968, 0.028160763904452324, 0.03171735256910324, 0.8772148489952087, 0.9208821058273315 ], [ 0.8948503136634827, 0.11962255835533142, 0.021243326365947723, 3.8123675039969385e-05, 0.019131658598780632, 0.04346933215856552, 0.054330211132764816 ] ] }, { "q_id": "9861_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15 ], "rewards": [ [ 0.2177094966173172, 0.0274199191480875, 0.10268838703632355, 0.0023269408848136663, 0.14667527377605438, 0.014751870185136795, 0.08759351819753647, 0.18091034889221191, 0.010118473321199417, 0.15242788195610046, 0.11226335167884827, 0.02091074548661709, 0.08910147845745087, 0.708262026309967, 0.06102444976568222, 0.8329014778137207, 0.007668769918382168 ], [ 0.20448341965675354, 0.03690091148018837, 0.2883952856063843, 0.2612370550632477, 0.18798352777957916, 0.1252494752407074, 0.175251305103302, 0.05078672617673874 ], [ 0.25342726707458496, 0.04049006104469299, 0.14825469255447388, 0.0706397220492363, 0.09809447079896927, 0.2379811555147171, 0.08121541142463684, 0.453996479511261, 0.9279789924621582, 0.012037334963679314 ], [ 0.20448286831378937, 0.02344101294875145, 0.023205215111374855, 0.288766086101532, 0.09952779859304428, 0.08351034671068192, 0.09230481833219528, 0.11416183412075043, 0.04352341964840889, 0.25438937544822693, 0.8738894462585449, 0.9778242111206055, 0.0064050438813865185 ], [ 0.10607680678367615, 0.05060923472046852, 0.1375509649515152, 0.3317756950855255, 0.09591755270957947, 0.7498066425323486, 0.9427295923233032, 0.014849823899567127 ], [ 0.2044791579246521, 0.023857228457927704, 0.020736347883939743, 0.0004634741635527462, 0.4014982581138611, 0.21262723207473755, 0.057640086859464645, 0.04925635829567909, 0.0026686317287385464, 0.10344211012125015, 0.07979772984981537, 0.0548701137304306, 0.041619740426540375, 0.006329599302262068, 0.147892564535141, 0.937593400478363, 0.007824953645467758 ], [ 0.21255022287368774, 0.06848527491092682, 0.23038025200366974, 0.17823678255081177, 0.08123871684074402, 0.1378302425146103, 0.028339523822069168, 0.34207919239997864, 0.941210925579071, 0.9208560585975647, 0.013838245533406734 ], [ 0.5249825119972229, 0.08871854096651077, 0.11275113373994827, 0.08367794007062912, 0.07078376412391663, 0.10167983174324036, 0.31875544786453247, 0.07764890044927597, 0.22930550575256348, 0.05630800500512123 ], [ 0.23195096850395203, 0.1645413637161255, 0.5095512270927429, 0.9397395849227905, 0.015295082703232765 ], [ 0.028707848861813545, 0.21964603662490845, 0.1778644174337387, 0.03912297263741493, 0.24226786196231842, 0.05410162732005119 ], [ 0.4887380599975586, 0.23288951814174652, 0.08304206281900406, 0.06526599824428558, 0.37192603945732117, 0.2658310532569885, 0.1003008484840393, 0.0638733059167862 ], [ 0.44517406821250916, 0.43355822563171387, 0.9731073975563049, 0.9114161729812622, 0.014715970493853092 ], [ 0.48874175548553467, 0.15244506299495697, 0.07860926538705826, 0.07709336280822754, 0.042574234306812286, 0.071157306432724, 0.16685231029987335, 0.39263391494750977, 0.018682723864912987, 0.08331030607223511, 0.1365589052438736, 0.15706095099449158, 0.25535017251968384, 0.0681084468960762 ], [ 0.25342950224876404, 0.03422780707478523, 0.0003325129800941795, 0.515483558177948, 0.011060589924454689, 0.039815980941057205, 0.16469836235046387, 0.053482089191675186, 0.18955771625041962, 0.0010154378833249211, 0.7964109778404236, 0.9775199294090271, 0.004297069739550352 ] ] }, { "q_id": "9179_mmlu_physics", "cot_ids": [ 3, 4, 6, 8, 10, 13, 14, 15 ], "rewards": [ [ 0.1547836810350418, 0.01884881965816021, 0.07313358783721924, 0.013575196266174316, 0.003333302913233638, 0.05397222563624382, 0.1195443868637085, 0.13333354890346527, 0.016817936673760414, 0.16105371713638306, 0.08270863443613052, 0.0664086863398552, 0.09548687934875488, 0.01774442568421364, 0.08517462760210037, 0.0541241317987442, 0.08273681253194809, 0.0030185477808117867 ], [ 0.15478505194187164, 0.2542264461517334, 0.3078514039516449, 0.4808712601661682, 0.002848480362445116, 0.04400850087404251, 0.0024601102340966463, 0.0018035577377304435, 0.008034419268369675, 0.06850364804267883, 0.0034951164852827787, 0.05539168044924736, 0.04317530617117882 ], [ 0.15478648245334625, 0.018849048763513565, 0.02198207750916481, 0.008862068876624107, 0.04492071643471718, 0.14853550493717194, 0.014069818891584873, 0.22665688395500183, 0.0719221830368042, 0.026739520952105522, 0.14305728673934937, 0.011517141945660114, 0.11056386679410934, 0.24749289453029633 ], [ 0.1547849178314209, 0.018848801031708717, 0.07313310354948044, 0.013574991375207901, 0.003333280561491847, 0.05397222563624382, 0.1413368433713913, 0.01119101420044899, 0.039577893912792206, 0.03837314620614052, 0.024047037586569786, 0.1510152816772461, 0.04133884981274605, 0.10204023867845535, 0.06822003424167633 ], [ 0.15478530526161194, 0.018849490210413933, 0.06020978465676308, 0.020041020587086678, 0.08855807036161423, 0.05616380274295807, 0.09634742140769958, 0.023011265322566032, 0.05251458287239075, 0.03269318863749504, 0.013805449940264225, 0.06919132173061371, 0.028887784108519554, 0.8037344217300415, 0.006032496225088835 ], [ 0.38664042949676514, 0.03116271086037159, 0.0006509865052066743, 0.14162643253803253, 0.002595830475911498, 0.19456300139427185, 0.05107952654361725, 0.08875926584005356, 0.18185819685459137, 0.14793457090854645, 0.22576189041137695, 0.2207922488451004, 0.3114626407623291 ], [ 0.15478497743606567, 0.0188489630818367, 0.07313426584005356, 0.013080705888569355, 0.0005025096470490098, 0.05574430152773857, 0.20500041544437408, 0.061383143067359924, 0.16309861838817596, 0.02214202471077442, 0.1477283537387848, 0.07082413882017136, 0.02061256766319275, 0.05499141290783882, 0.023368479683995247, 0.3583909869194031, 0.5106249451637268 ], [ 0.15478509664535522, 0.0188489630818367, 0.07873745262622833, 0.00959126278758049, 0.0467921644449234, 0.07180441170930862, 0.00821300595998764, 0.06919936835765839, 0.0062051573768258095, 0.0397840179502964, 0.01700342446565628, 0.040100350975990295, 0.006381372455507517 ] ] }, { "q_id": "9746_mmlu_physics", "cot_ids": [ 3, 7, 8, 15 ], "rewards": [ [ 0.21438045799732208, 0.0016305604949593544, 0.11209741234779358, 0.004664157517254353, 0.020198097452521324, 0.07978509366512299, 0.0011052570771425962, 0.8470112681388855, 0.012938212603330612, 0.07275442034006119, 0.013704616576433182, 0.05495224520564079, 0.2335725724697113, 0.17172212898731232, 0.24398775398731232, 0.006846491247415543, 0.009077601134777069 ], [ 0.24736689031124115, 0.04598561301827431, 0.08284678310155869, 0.003959689289331436, 0.1353512406349182, 0.01827099919319153, 0.13408198952674866, 0.05052405223250389, 0.2897617220878601, 0.03317733854055405, 0.21487660706043243, 0.016115624457597733, 0.36852821707725525, 0.060407429933547974, 0.08496066927909851, 0.15679220855236053, 0.0034544868394732475, 0.042566344141960144, 0.006605373229831457 ], [ 0.21438150107860565, 0.0018505140906199813, 0.10748440027236938, 0.0003072848485317081, 0.12464304268360138, 0.0008480747346766293, 0.17555491626262665, 0.0025245852302759886, 0.5386441946029663, 0.004816611763089895 ], [ 0.21438303589820862, 0.002961935941129923, 0.0019916309975087643, 0.04721583053469658, 0.05122528225183487, 0.002207700628787279, 0.10105521231889725, 0.02962399646639824, 0.09775771200656891, 0.09824927896261215, 0.0013840885367244482, 0.000898935308214277, 0.9243984222412109, 0.06394850462675095, 0.01759619452059269, 0.09958337247371674, 0.005060523748397827, 0.05964592471718788, 0.059357259422540665, 0.04360680282115936, 0.0231232438236475, 0.05046015605330467, 0.036748699843883514, 0.02679094299674034, 0.09070827066898346, 0.027342988178133965, 0.022981824353337288, 0.02542450837790966, 0.012244388461112976 ] ] }, { "q_id": "9091_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8407686948776245, 0.13761092722415924, 0.15021492540836334, 0.1342717707157135, 0.2053036093711853, 0.2812177240848541, 0.2559899389743805, 0.28423118591308594, 0.0013903818326070905, 0.10073111206293106, 0.27327239513397217, 0.09381306916475296, 0.03329302743077278, 0.1024942621588707 ], [ 0.900191068649292, 0.34243956208229065, 0.10341058671474457, 0.06830409914255142, 0.06555473059415817, 0.08686397224664688, 0.15489467978477478, 0.03485984727740288, 0.000976576004177332 ], [ 0.9001917839050293, 0.18257321417331696, 0.2092798501253128, 0.30667179822921753, 0.48388707637786865, 0.1092052310705185, 0.13605725765228271, 0.22106096148490906, 0.4209330081939697, 0.7443960905075073, 0.9071038365364075, 0.14783358573913574 ], [ 0.7808292508125305, 0.1180386021733284, 0.0776771828532219, 0.11516115069389343, 0.13772501051425934, 0.35943156480789185, 0.08142708241939545, 0.21593952178955078, 0.04256179556250572, 0.030403682962059975, 0.0016397200524806976 ], [ 0.12624888122081757, 0.003053294960409403, 0.004380801226943731, 0.007790806703269482, 0.0860578790307045, 0.38804540038108826, 0.05690022557973862, 0.1061275526881218, 0.009885762818157673, 0.36141735315322876, 0.26654908061027527, 0.013195996172726154, 0.013075682334601879, 0.016781099140644073, 0.06353205442428589, 0.0017876031342893839, 0.018877916038036346, 0.015071381814777851, 0.012581713497638702, 0.0012296201894059777 ], [ 0.2216545194387436, 0.16344322264194489, 0.1773720532655716, 0.10100589692592621, 0.06100686267018318, 0.7198227047920227, 0.2077767699956894, 0.19428978860378265, 0.20562709867954254, 0.20521079003810883, 0.1602543443441391, 0.10878776758909225, 0.17749063670635223, 0.18271344900131226 ], [ 0.5157007575035095, 0.2051558941602707, 0.2481539249420166, 0.254975825548172, 0.0441599078476429, 0.1377606838941574, 0.25749728083610535, 0.39926677942276, 0.10699889063835144 ], [ 0.9001904129981995, 0.17155446112155914, 0.08403518050909042, 0.09776636213064194, 0.1271899938583374, 0.10484617203474045, 0.14573141932487488, 0.33146896958351135, 0.0015120527241379023 ], [ 0.9001896381378174, 0.16479159891605377, 0.12109875679016113, 0.7640294432640076, 0.18946273624897003, 0.22714363038539886, 0.2836120128631592, 0.08660180866718292, 0.1266479343175888, 0.7356107831001282, 0.9434279203414917, 0.32159408926963806 ], [ 0.12624873220920563, 0.03370819613337517, 0.03609243407845497, 0.0006367265013977885, 0.0037977914325892925, 0.0013612740440294147, 0.0324413888156414, 0.0014677841681987047, 0.0025138752534985542, 0.15992645919322968, 0.044009700417518616, 0.10234794020652771, 0.05198723077774048, 0.005073955748230219, 0.04299434646964073, 0.0335686132311821, 0.6007938385009766, 0.18425852060317993 ], [ 0.12624888122081757, 0.0033106852788478136, 0.12045003473758698, 0.0009388152393512428, 0.011919334530830383, 0.02494528517127037, 0.2057371735572815, 0.008339080959558487, 0.0732443705201149, 0.02808254584670067, 0.005148374009877443, 0.06092618778347969, 0.07914517819881439, 0.014688623137772083, 0.26484790444374084, 0.881682813167572 ], [ 0.12624868750572205, 0.003053306369110942, 0.1229935809969902, 0.008157661184668541, 0.22552569210529327, 0.0075837913900613785, 0.043072912842035294, 0.004757520277053118, 0.02087266743183136, 0.05464421585202217, 0.16150915622711182 ], [ 0.2914174497127533, 0.14917467534542084, 0.18318594992160797, 0.024672307074069977, 0.4795522093772888, 0.1807243824005127, 0.042480435222387314, 0.2614526152610779, 0.34724482893943787, 0.15508748590946198, 0.24377654492855072, 0.15055939555168152, 0.13661092519760132, 0.5216729640960693, 0.00040577142499387264, 0.047833312302827835, 0.009027255699038506, 0.14409150183200836, 0.7199927568435669, 0.0031054604332894087 ], [ 0.12624715268611908, 0.004275368060916662, 0.38984593749046326, 0.00043574205483309925, 0.06977493315935135, 0.0006079498562030494, 0.2809179425239563, 0.20628957450389862, 0.019257867708802223, 0.7173930406570435, 0.15873727202415466 ], [ 0.12624947726726532, 0.003310669446364045, 0.05893820896744728, 0.0005611178348772228, 0.2671128809452057, 0.0007915390888229012, 0.0799131840467453, 0.0007363551412709057, 0.139241561293602, 0.01525523979216814, 0.08649851381778717, 0.021509582176804543, 0.5524208545684814, 0.16004636883735657 ] ] }, { "q_id": "9290_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.7769394516944885, 0.1298459768295288, 0.5011129379272461, 0.712522566318512, 0.9962499737739563, 0.9995654225349426 ], [ 0.8445120453834534, 0.37854331731796265, 0.5530351400375366, 0.9993582367897034, 0.9999220371246338 ], [ 0.8183788061141968, 0.36663493514060974, 0.695214569568634, 0.5300009250640869, 0.3228609561920166, 0.9992181062698364, 0.999940037727356 ], [ 0.6108677387237549, 0.10468026995658875, 0.16376946866512299, 0.35683462023735046, 0.5345259308815002, 0.09605318307876587, 0.12503468990325928, 0.9984608888626099, 0.9998753070831299 ], [ 0.7731796503067017, 0.3949994444847107, 0.2727927267551422, 0.025797098875045776, 0.9960165619850159, 0.9995416402816772 ], [ 0.5909987688064575, 0.1985902488231659, 0.5309716463088989, 0.12360509485006332, 0.9988588094711304, 0.9998792409896851 ], [ 0.6108641028404236, 0.04420056566596031, 0.049248453229665756, 0.05035325139760971, 0.1324748694896698, 0.6221036314964294, 0.024977900087833405, 0.5873470306396484, 0.03302863985300064, 0.1442626714706421, 0.9980981945991516, 0.9999182224273682 ], [ 0.8286370635032654, 0.3659980893135071, 0.5588922500610352, 0.9994297623634338, 0.9999226331710815 ], [ 0.6108683943748474, 0.2670961022377014, 0.9994891881942749, 0.9999703168869019 ], [ 0.6108648777008057, 0.04958080127835274, 0.10581948608160019, 0.15899017453193665, 0.46563106775283813, 0.28342896699905396, 0.6108282804489136, 0.05696361884474754, 0.9993385672569275, 0.9999643564224243 ], [ 0.87007075548172, 0.4046499729156494, 0.41635578870773315, 0.41723692417144775, 0.9995137453079224, 0.9999316930770874 ], [ 0.8109570741653442, 0.35664236545562744, 0.3743910789489746, 0.4944084882736206, 0.999599039554596, 0.9999357461929321 ], [ 0.8165838718414307, 0.322747141122818, 0.03278296813368797, 0.9958855509757996, 0.9995237588882446 ], [ 0.8322851657867432, 0.8041079044342041, 0.5693949460983276, 0.8330535292625427, 0.9978558421134949, 0.9996140599250793 ], [ 0.8165849447250366, 0.38108953833580017, 0.7965450882911682, 0.5149503350257874, 0.8686259984970093, 0.9977245926856995, 0.9995569586753845 ], [ 0.5555329322814941, 0.08660075068473816, 0.10733011364936829, 0.6132782697677612, 0.4846207797527313, 0.08750253170728683, 0.20479761064052582, 0.9985489249229431, 0.9998818635940552 ] ] }, { "q_id": "9154_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.27245235443115234, 0.027082592248916626, 0.04936360940337181, 0.036568887531757355, 0.03521280735731125, 0.040769752115011215, 0.019284527748823166 ], [ 0.10240424424409866, 0.08561302721500397, 0.0007178738596849144, 0.025036074221134186, 0.07841116935014725, 0.03294069692492485, 0.28521519899368286, 0.5460386276245117, 0.055045705288648605, 0.33342161774635315, 0.02657383494079113, 0.0036354290787130594 ], [ 0.08984968811273575, 0.05411924794316292, 0.062202103435993195, 0.033932458609342575, 0.29717355966567993, 0.12673671543598175, 0.11006485670804977, 0.07487309724092484, 0.028283406049013138, 0.0031030774116516113 ], [ 0.08875058591365814, 0.13488683104515076, 0.00029903906397521496, 0.01910492405295372, 0.007664170581847429, 0.045394424349069595, 0.019362062215805054, 0.37828078866004944, 0.6957423686981201, 0.0040588341653347015 ], [ 0.3563727140426636, 0.16497911512851715, 0.5541273951530457, 0.5369551777839661, 0.03691333532333374, 0.23517648875713348, 0.013195996172726154, 0.08073397725820541, 0.004032248165458441 ], [ 0.30164915323257446, 0.06680415570735931, 0.0005137934349477291, 0.1998874843120575, 0.032675694674253464, 0.23062452673912048, 0.030428942292928696, 0.07762923091650009, 0.39853066205978394, 0.005903692916035652 ], [ 0.09960123896598816, 0.06676845252513885, 0.0008639123407192528, 0.03457184135913849, 0.05031062290072441, 0.027635928243398666, 0.19252854585647583, 0.08828325569629669, 0.3450366258621216, 0.020068956539034843, 0.0022324901074171066 ], [ 0.0900857225060463, 0.08333601802587509, 0.3097820580005646, 0.016497548669576645, 0.4955075979232788, 0.02279398962855339, 0.0032851803116500378 ], [ 0.20920142531394958, 0.007019868120551109, 0.032200269401073456, 0.047214116901159286, 0.12364658713340759, 0.021641336381435394, 0.21313276886940002, 0.06410782039165497, 0.009239104576408863, 0.19742466509342194, 0.4101589024066925, 0.004898855462670326 ], [ 0.10501770675182343, 0.02419077605009079, 0.046273887157440186, 0.010451480746269226, 0.0694962739944458, 0.1884407103061676, 0.0130483228713274, 0.43720322847366333, 0.5685374736785889, 0.0018970518140122294 ], [ 0.07044254243373871, 0.047373440116643906, 0.17752349376678467, 0.020084207877516747, 0.08825965225696564, 0.16589343547821045, 0.02723502367734909, 0.3471972644329071, 0.02766440249979496, 0.21436014771461487, 0.217329740524292, 0.0018511005910113454 ], [ 0.08875127881765366, 0.10650400817394257, 0.09566178172826767, 0.09047161787748337, 0.05339494347572327, 0.033356837928295135, 0.02843816950917244 ], [ 0.1439024806022644, 0.08580651134252548, 0.07598429918289185, 0.11649279296398163, 0.021136606112122536, 0.17206457257270813, 0.08913698047399521, 0.0051374249160289764 ], [ 0.10240280628204346, 0.2577681839466095, 0.01976204290986061, 0.260490745306015, 0.8000338077545166, 0.004339733626693487 ], [ 0.060091063380241394, 0.023743361234664917, 0.00043575806193985045, 0.12391583621501923, 0.25700658559799194, 0.4162907898426056, 0.0013554667821153998 ], [ 0.27591821551322937, 0.1943328082561493, 0.2751741409301758, 0.03196217492222786, 0.2486426681280136, 0.0498572513461113, 0.004161155316978693 ] ] }, { "q_id": "9570_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.06944384425878525, 0.11277899146080017, 0.03480163961648941, 0.002736880676820874 ], [ 0.09344737231731415, 0.044791437685489655, 0.05766511708498001, 0.08703955262899399, 0.06783769279718399, 0.0014244003687053919 ], [ 0.06361877173185349, 0.044347427785396576, 0.060498785227537155, 0.03403347358107567, 0.0026578812394291162 ], [ 0.10651484876871109, 0.042889874428510666, 0.0464785061776638, 0.0404176339507103, 0.002854694612324238 ], [ 0.1826379895210266, 0.05520585551857948, 0.069426529109478, 0.09020555764436722, 0.0014331990387290716 ], [ 0.07799047976732254, 0.06645186245441437, 0.09995777159929276, 0.0022813156247138977 ], [ 0.06458380073308945, 0.03660115599632263, 0.04855779930949211, 0.003030248684808612 ], [ 0.7072107195854187, 0.5817182660102844, 0.0022861547768115997 ], [ 0.10075046122074127, 0.03851859271526337, 0.07731188833713531, 0.05114169046282768, 0.0014222899917513132 ], [ 0.07968323677778244, 0.3385898172855377, 0.09834085404872894, 0.001407778006978333 ], [ 0.057492971420288086, 0.10067103803157806, 0.002348260721191764 ], [ 0.6810709834098816, 0.5391125082969666, 0.001703136833384633 ], [ 0.041588861495256424, 0.04580371454358101, 0.03311809152364731, 0.0020484006963670254 ], [ 0.07799078524112701, 0.3780362010002136, 0.0023733116686344147 ], [ 0.07798975706100464, 0.1329101026058197, 0.038414373993873596, 0.007987435907125473, 0.0024481825530529022 ], [ 0.13851793110370636, 0.2038532942533493, 0.1709212213754654, 0.0152159184217453 ] ] }, { "q_id": "9327_mmlu_physics", "cot_ids": [ 4, 5, 6, 9, 13, 15 ], "rewards": [ [ 0.2175643891096115, 0.0024176156148314476, 0.08181673288345337, 0.06975927203893661, 0.0769970566034317, 0.011690756306052208, 0.13566985726356506, 0.17288459837436676, 0.16983364522457123, 0.029521208256483078, 0.20024828612804413, 0.015155640430748463, 0.17544761300086975, 0.136033833026886, 0.3878636658191681, 0.5141096711158752 ], [ 0.19450896978378296, 0.20396289229393005, 0.0004186118603684008, 0.38856738805770874, 0.002514164661988616, 0.19150449335575104, 0.1922195851802826, 0.1152510792016983, 0.3263165056705475, 0.1772918403148651, 0.016668502241373062 ], [ 0.2339891493320465, 0.0037204837426543236, 0.01835707016289234, 0.1480381190776825, 0.5736696720123291, 0.05100766941905022, 0.07857152074575424, 0.18037454783916473, 0.13779938220977783, 0.0529240258038044, 0.12138823419809341, 0.27705830335617065, 0.2775992155075073, 0.1003994271159172, 0.02837769128382206, 0.08122540265321732, 0.03569476306438446, 0.0023769200779497623 ], [ 0.23398451507091522, 0.001968377735465765, 0.008845485746860504, 0.02863595448434353, 0.00037943251663818955, 0.18399614095687866, 0.49307844042778015, 0.025078430771827698, 0.03927118331193924, 0.20646293461322784, 0.2841915488243103, 0.049341775476932526, 0.1437181830406189, 0.2895166575908661, 0.2222093939781189, 0.11398106813430786, 0.03706268593668938, 0.12560810148715973, 0.049549173563718796, 0.0026807994581758976 ], [ 0.23398733139038086, 0.008294673636555672, 0.020897286012768745, 0.025121694430708885, 0.03196246922016144, 0.3808925449848175, 0.020362455397844315, 0.044895973056554794, 0.21296890079975128, 0.1656002253293991, 0.03741985186934471, 0.13426771759986877, 0.23601838946342468, 0.2217712551355362, 0.1985839605331421, 0.05262789502739906, 0.1096198782324791, 0.034369684755802155, 0.0037519079633057117 ], [ 0.5954297184944153, 0.29034900665283203, 0.05263238772749901, 0.16366226971149445, 0.05852364003658295, 0.3252468407154083, 0.08494476228952408, 0.10123499482870102, 0.016756469383835793, 0.001050436869263649 ] ] }, { "q_id": "9978_mmlu_physics", "cot_ids": [ 7 ], "rewards": [ [ 0.22301967442035675, 0.004324318375438452, 0.008218612521886826, 0.04973584786057472, 0.0004884866648353636, 0.000693199341185391, 0.011860864236950874, 0.05692973732948303, 0.008640173822641373, 0.0019823177717626095, 0.017700837925076485, 0.007839160040020943, 0.07788819074630737, 0.05319371819496155, 0.9931132197380066 ] ] }, { "q_id": "9936_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9954332709312439, 0.9944196343421936, 0.20496197044849396, 0.9969390630722046 ], [ 0.9970128536224365, 0.11864672601222992, 0.009867236949503422 ], [ 0.9966700673103333, 0.6852959990501404, 0.007115777116268873 ], [ 0.99676114320755, 0.05431017279624939, 0.6291044354438782, 0.007679689675569534 ], [ 0.9962055683135986, 0.9946699738502502, 0.9982618689537048 ], [ 0.9932076334953308, 0.4385726749897003, 0.009043470956385136 ], [ 0.052351512014865875, 0.7955650091171265, 0.007916416972875595, 0.01288506668061018, 0.03521421551704407, 0.024692751467227936, 0.0461355485022068, 0.08879350870847702, 0.995519757270813 ], [ 0.9977394342422485, 0.051079243421554565, 0.7807573080062866, 0.00786618236452341 ], [ 0.9945409893989563, 0.9946830868721008, 0.6383362412452698, 0.7552729249000549, 0.0075747850351035595 ], [ 0.03371066600084305, 0.6526150107383728, 0.9940910935401917, 0.9992349147796631 ], [ 0.9941248297691345, 0.6052398085594177, 0.12802334129810333, 0.6989297866821289, 0.99735426902771 ], [ 0.9954332709312439, 0.9966598749160767, 0.2146424502134323, 0.9972917437553406 ], [ 0.9956855773925781, 0.9941639304161072, 0.5119783282279968, 0.04669013246893883, 0.07772635668516159, 0.009542714804410934 ], [ 0.032288145273923874, 0.4402405619621277, 0.15202081203460693, 0.009092126972973347 ], [ 0.9954332113265991, 0.9966597557067871, 0.9984670281410217 ], [ 0.99676114320755, 0.847134530544281, 0.0074205887503921986 ] ] }, { "q_id": "9611_mmlu_physics", "cot_ids": [ 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.2610955238342285, 0.08955051004886627, 0.4561443030834198, 0.026623008772730827, 0.39451664686203003, 0.12636102735996246, 0.029143018648028374, 0.06662619113922119, 0.0618591271340847, 0.05771786719560623, 0.09390135109424591, 0.07406611740589142 ], [ 0.08050216734409332, 0.0700184628367424, 0.018584629520773888, 0.0003103171766269952, 0.23382891714572906, 0.005452234763652086, 0.2024623602628708, 0.23654130101203918, 0.00026697528664954007, 0.4696250259876251, 0.07327952980995178, 0.0669577419757843, 0.4424307644367218, 0.0008639103034511209 ], [ 0.08050153404474258, 0.0669386088848114, 0.018213631585240364, 0.00029920757515355945, 0.246130108833313, 0.005910469219088554, 0.1958290934562683, 0.0027584536001086235, 0.10882031172513962, 0.00047540615196339786, 0.28210848569869995, 0.012804996222257614, 0.03386674448847771, 0.2441602200269699, 0.6253674626350403, 0.8479019999504089 ], [ 0.08050189167261124, 0.06630370020866394, 0.016527045518159866, 0.0002950080088339746, 0.29036492109298706, 0.04166841506958008, 0.020389238372445107, 0.20094254612922668, 0.3098423182964325, 0.4725106954574585, 0.0015479192370548844, 0.05990440398454666, 0.009247750043869019, 0.1238282099366188, 0.00810785312205553, 0.030188580974936485, 0.2228243052959442, 0.24894505739212036, 0.1040828749537468, 0.17301541566848755, 0.006964438129216433, 0.044532548636198044, 0.0035805951338261366 ], [ 0.053740013390779495, 0.018214209005236626, 0.03797050938010216, 0.09504947066307068, 0.28159260749816895, 0.11421560496091843, 0.26883700489997864, 0.015524403192102909, 0.040070462971925735, 0.05779865011572838, 0.08357065171003342, 0.11679966747760773, 0.146650031208992, 0.07322274893522263, 0.0776783749461174, 0.06341687589883804, 0.015924926847219467, 0.012494882568717003 ], [ 0.3799159526824951, 0.04386276379227638, 0.0009480095468461514, 0.29202741384506226, 0.040622279047966, 0.22352468967437744, 0.07733267545700073, 0.17910173535346985, 0.004376604687422514, 0.018759917467832565, 0.019774721935391426, 0.003594695357605815, 0.0065351310186088085 ], [ 0.34270331263542175, 0.1064145490527153, 0.27157163619995117, 0.16104276478290558, 0.0648118332028389, 0.03596557676792145, 0.08445341140031815, 0.07443200051784515, 0.0112448213621974, 0.0031075295992195606 ], [ 0.44689199328422546, 0.13539862632751465, 0.25638410449028015, 0.16677060723304749, 0.23454077541828156, 0.06939954310655594, 0.07978099584579468, 0.0027999375015497208, 0.9335207343101501, 0.9818674325942993 ], [ 0.08050230890512466, 0.06693805009126663, 0.020672839134931564, 0.00017871567979454994, 0.2794158458709717, 0.057300519198179245, 0.7969090342521667, 0.2796134948730469, 0.0933273434638977, 0.14642424881458282, 0.0012407994363456964, 0.3284550607204437, 0.08349614590406418, 0.2994860112667084, 0.8608486652374268 ], [ 0.3115819990634918, 0.0812763050198555, 0.1763976514339447, 0.023316606879234314, 0.13487374782562256, 0.1086098924279213, 0.002768955659121275, 0.030387379229068756, 0.05100695416331291, 0.07499000430107117, 0.016647614538669586, 0.023688998073339462, 0.030669843778014183, 0.05866403877735138, 0.007046601269394159, 0.004092947579920292 ], [ 0.2590799629688263, 0.09199971705675125, 0.43841591477394104, 0.19517174363136292, 0.05167407914996147, 0.14716389775276184, 0.024872610345482826, 0.044372983276844025, 0.12195243686437607, 0.0010231276974081993, 0.15854105353355408, 0.13851144909858704, 0.08425460010766983, 0.007473945617675781, 0.003348266240209341 ], [ 0.0805014967918396, 0.07001908123493195, 0.02297944761812687, 0.00020847280393354595, 0.2747862935066223, 0.006208417005836964, 0.18301235139369965, 0.13352899253368378, 0.0198622178286314, 0.012614077888429165, 0.18813760578632355, 0.09515878558158875, 0.023758096620440483, 0.857839047908783, 0.982568085193634 ] ] }, { "q_id": "9690_mmlu_physics", "cot_ids": [ 1, 2, 3, 6, 7, 10, 11, 12, 13, 15 ], "rewards": [ [ 0.3003959059715271, 0.05026480183005333, 0.09195777028799057, 0.04546566307544708, 0.07485569268465042, 0.0021444426383823156, 0.04490451514720917, 0.02431260608136654, 0.31502795219421387, 0.08788955211639404, 0.18900497257709503, 0.0005207700887694955 ], [ 0.4734823703765869, 0.0024703284725546837, 0.054315317422151566, 0.0007262362632900476, 0.04333939775824547, 0.033705540001392365, 0.04797353968024254, 0.001277132541872561, 0.014615870080888271, 0.009044179692864418, 0.9095907807350159, 0.00047816665028221905 ], [ 0.4734835624694824, 0.00247026514261961, 0.054387398064136505, 0.0007714509265497327, 0.049024373292922974, 0.03840849548578262, 0.04533285275101662, 0.004154912196099758, 0.12158020585775375, 0.010936254635453224, 0.014697528444230556, 0.0070627350360155106 ], [ 0.4333984851837158, 0.002331384224817157, 0.10722667723894119, 0.005564504768699408, 0.014977142214775085, 0.004228696692734957, 0.005472893826663494, 0.0007034796290099621 ], [ 0.4734894931316376, 0.0024703212548047304, 0.11515280604362488, 0.0017010512528941035, 0.25198209285736084, 0.04999261721968651, 0.024937182664871216, 0.0051590874791145325, 0.014450126327574253, 0.0006954494747333229 ], [ 0.47348734736442566, 0.002470320323482156, 0.0200662724673748, 0.0028733655344694853, 0.09994400292634964, 0.024488570168614388, 0.043560691177845, 0.02049941010773182, 0.1619354784488678, 0.0006584168295376003 ], [ 0.4734853506088257, 0.0024703212548047304, 0.011106820777058601, 0.0009243926033377647, 0.049149349331855774, 0.0005110825295560062, 0.02155701443552971, 0.10069702565670013, 0.04413196071982384, 0.08251586556434631, 0.0012022360460832715, 0.017840590327978134, 0.017926542088389397, 0.005551882553845644, 0.01102273166179657, 0.011255614459514618, 0.015272090211510658, 0.0006936758873052895 ], [ 0.4734909236431122, 0.0032583987340331078, 0.012845505028963089, 0.015169467777013779, 0.0285616647452116, 0.0013309050118550658, 0.015311859548091888, 0.10918941348791122, 0.08528351038694382, 0.06267751008272171, 0.0026802069041877985, 0.007361358031630516, 0.06010168418288231, 0.031525854021310806, 0.0007503447704948485 ], [ 0.47348809242248535, 0.002470266306772828, 0.054301485419273376, 0.0010927146067842841, 0.04434617608785629, 0.04388528689742088, 0.04939798638224602, 0.0019460486946627498, 0.024691348895430565, 0.011647749692201614, 0.014324872754514217, 0.004313581623136997, 0.004922826308757067, 0.000762990559451282 ], [ 0.47349411249160767, 0.0024703131057322025, 0.028640544041991234, 0.0019810579251497984, 0.12462525814771652, 0.046826671808958054, 0.05446695536375046, 0.02766524814069271, 0.2897946834564209, 0.0007456299499608576 ] ] }, { "q_id": "9925_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.18111330270767212, 0.1570887267589569, 0.05210698023438454, 0.01118565909564495 ], [ 0.11732511222362518, 0.22454552352428436, 0.7900417447090149, 0.19526314735412598, 0.07034328579902649, 0.10955343395471573 ], [ 0.17811767756938934, 0.20044317841529846, 0.9132763743400574, 0.9800850749015808 ], [ 0.14789515733718872, 0.011850978247821331, 0.2972060441970825, 0.16884444653987885, 0.0528666228055954, 0.04165857285261154, 0.00421562185510993 ], [ 0.27545735239982605, 0.13611416518688202, 0.036380793899297714, 0.013889147900044918 ], [ 0.14212022721767426, 0.27071505784988403, 0.5294711589813232, 0.9661556482315063 ], [ 0.36568373441696167, 0.2977101802825928, 0.7836271524429321, 0.22051066160202026, 0.0015518241561949253 ], [ 0.42015784978866577, 0.05425514653325081, 0.8718745112419128, 0.312455415725708, 0.046044837683439255, 0.07094889134168625, 0.9600222110748291 ], [ 0.17152546346187592, 0.21497035026550293, 0.06976030021905899, 0.023052681237459183 ], [ 0.5652251243591309, 0.4080654978752136, 0.9217494130134583, 0.9838390350341797 ], [ 0.20397908985614777, 0.25896573066711426, 0.3420398235321045, 0.9603325128555298, 0.9855519533157349 ], [ 0.15190890431404114, 0.005515770521014929, 0.1081414446234703, 0.14436505734920502, 0.051052555441856384, 0.0004313655663281679, 0.9321871995925903, 9.25932326936163e-05, 0.047386057674884796, 0.04875006154179573 ], [ 0.30559006333351135, 0.04018871486186981, 0.005227205343544483, 0.5307058691978455, 0.0005843206308782101, 0.21019577980041504, 0.04140996187925339, 0.0012054144171997905 ], [ 0.16912782192230225, 0.30947282910346985, 0.8985774517059326, 0.9775698184967041 ], [ 0.29657813906669617, 0.19018417596817017, 0.08484116196632385, 0.008163828402757645 ], [ 0.1582721471786499, 0.31432807445526123, 0.6864200234413147, 0.9625713229179382, 0.9749358296394348 ] ] }, { "q_id": "9237_mmlu_physics", "cot_ids": [ 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.23798999190330505, 0.1527187079191208, 0.14055995643138885, 0.009597810916602612, 0.06158764287829399, 0.03381732106208801 ], [ 0.28741455078125, 0.07030033320188522, 0.08707988262176514, 0.3508642613887787, 0.0064335837960243225, 0.054761532694101334, 0.18031814694404602, 0.3752341568470001, 0.0018924454925581813 ], [ 0.32770559191703796, 0.07517202198505402, 0.07161342352628708, 0.39971575140953064, 0.04715432599186897, 0.05472780019044876, 0.0027111319359391928, 0.0031598571222275496 ], [ 0.4485108256340027, 0.060095857828855515, 0.05648871511220932, 0.0862651988863945, 0.10318422317504883, 0.03356293961405754, 0.018690522760152817, 0.0017018984071910381 ], [ 0.28741443157196045, 0.09065660089254379, 0.10644257068634033, 0.41836896538734436, 0.010992291383445263, 0.036028604954481125, 0.003931700251996517 ], [ 0.23799145221710205, 0.16448040306568146, 0.791499674320221, 0.12272626906633377, 0.1887621432542801, 0.9429935812950134, 0.9897088408470154 ], [ 0.47210779786109924, 0.07286089658737183, 0.09910621494054794, 0.1743016093969345, 0.042281147092580795, 0.08301606774330139, 0.28669923543930054, 0.17346931993961334, 0.9787620306015015 ], [ 0.2874148190021515, 0.1753864288330078, 0.2591405510902405, 0.028389697894454002, 0.0668092593550682, 0.02229674533009529, 0.025051644071936607, 0.001867452054284513 ], [ 0.20990191400051117, 0.06268865615129471, 0.08800183981657028, 0.04007237032055855, 0.03780703991651535, 0.0016072295838966966 ], [ 0.3669624328613281, 0.16374576091766357, 0.0010561785893514752, 0.06496503949165344, 0.0325150266289711, 0.06710373610258102, 0.1762298047542572, 0.0017497434746474028 ], [ 0.4051455557346344, 0.09393365681171417, 0.07802868634462357, 0.004341066814959049, 0.08657292276620865, 0.0837719514966011, 0.04570245370268822, 0.0027286536060273647, 0.0028451611287891865 ], [ 0.3664088547229767, 0.1053226888179779, 0.0726531445980072, 0.07901418954133987, 0.06833524256944656, 0.10273638367652893, 0.10496797412633896, 0.12875711917877197, 0.0023572531063109636, 0.002810725010931492 ], [ 0.3804057538509369, 0.4202159345149994, 0.0912974551320076, 0.054990097880363464, 0.12685726583003998, 0.00041862064972519875, 0.13283532857894897, 0.14621561765670776, 0.08784517645835876, 0.7211788892745972, 0.09122875332832336, 0.16582448780536652, 0.8529504537582397, 0.010844412259757519 ], [ 0.2954731285572052, 0.04689493030309677, 0.07151356339454651, 0.035000141710042953, 0.044938825070858, 0.024773163720965385, 0.036173176020383835, 0.0024001491256058216 ], [ 0.35765594244003296, 0.0939851626753807, 0.10257746279239655, 0.19931896030902863, 0.05972471088171005, 0.03953886777162552, 0.004753421992063522, 0.003766791196539998 ] ] }, { "q_id": "10128_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.087137371301651, 0.03439211845397949, 0.033007584512233734, 0.9520233273506165, 0.007107490673661232, 0.009194827638566494, 0.017337385565042496, 0.026886530220508575, 0.025845207273960114, 0.011990092694759369, 0.01000955794006586, 0.015619127079844475, 0.9981169700622559 ], [ 0.12808585166931152, 0.04868770018219948, 0.9667734503746033, 0.05882210657000542, 0.03391995653510094, 0.013832430355250835, 0.02535320818424225, 0.08205493539571762, 0.007194090634584427, 0.08020951598882675, 0.05057629942893982, 0.06697909533977509, 0.9984571933746338 ], [ 0.12238617986440659, 0.0034487154334783554, 0.1621709167957306, 0.016093291342258453, 0.10291800647974014, 0.00839473120868206, 0.6907917857170105, 0.002578536281362176, 0.01464096363633871, 0.04114920273423195, 0.004085656721144915, 0.0556783527135849, 0.09030332416296005, 0.349284827709198, 0.9992419481277466 ], [ 0.12315058708190918, 0.009942673146724701, 0.004671754315495491, 0.013762997463345528, 0.013891787268221378, 0.9519910216331482, 0.003952094353735447, 0.27547621726989746, 0.7007010579109192, 0.9993840456008911 ], [ 0.1280859410762787, 0.043015968054533005, 0.03158530592918396, 0.001905418117530644, 0.016774963587522507, 0.02499295398592949, 0.039633285254240036, 0.059105608612298965, 0.0832255408167839, 0.02788255177438259, 0.0013853440759703517, 0.001336537068709731 ], [ 0.12315034121274948, 0.009942377917468548, 0.007344199810177088, 0.9571533799171448, 0.007870463654398918, 0.016082527115941048, 0.033147022128105164, 0.04555487632751465, 0.06233883649110794, 0.9989445805549622 ], [ 0.12315116822719574, 0.004260522313416004, 0.0092162461951375, 0.007277996279299259, 0.05269264057278633, 0.029520554468035698, 0.9457815885543823, 0.005389143247157335, 0.01847901940345764, 0.009859510697424412, 0.03792237490415573, 0.028574129566550255, 0.07070589810609818, 0.8629764914512634, 0.9993613362312317 ], [ 0.12314992398023605, 0.00793986115604639, 0.004616885911673307, 0.003351316787302494, 0.05581911653280258, 0.32633695006370544, 0.008649082854390144 ], [ 0.08199005573987961, 0.002887589391320944, 0.08059898018836975, 0.004024194087833166, 0.9592189788818359, 0.0020398295018821955, 0.016014069318771362, 0.06461016088724136, 0.005012662149965763, 0.09292479604482651, 0.4487023949623108, 0.9993652701377869 ], [ 0.12314826995134354, 0.015546195209026337, 0.007165862247347832, 0.006936345249414444, 0.0030237785540521145, 0.011691709980368614, 0.025913028046488762, 0.0853184163570404, 0.006439832039177418, 0.08884723484516144, 0.9989485144615173 ], [ 0.10070406645536423, 0.010087772272527218, 0.9815216064453125, 0.0038393985014408827, 0.023052765056490898, 0.9989848732948303 ], [ 0.12314970791339874, 0.009602662175893784, 0.014566237106919289, 0.038716331124305725, 0.03846830874681473, 0.00271705468185246, 0.0376596674323082, 0.14818087220191956, 0.7314046621322632, 0.600378155708313 ], [ 0.1129201129078865, 0.03564922884106636, 0.08269506692886353, 0.942523717880249, 0.06875387579202652, 0.14532840251922607, 0.01586366444826126, 0.0431700274348259, 0.009524240158498287, 0.010430064052343369, 0.0009817049140110612 ], [ 0.04866179823875427, 0.01654115691781044, 0.02409016340970993, 0.048656463623046875, 0.05933747813105583, 0.16016075015068054, 0.09166915714740753, 0.000901442370377481, 0.1089935228228569, 0.0921512320637703, 0.20357531309127808, 0.03684929758310318, 0.05344675853848457, 0.03761310502886772, 0.0008714881842024624, 0.12829315662384033, 0.1999155730009079, 0.7396845817565918, 0.04623657092452049 ] ] }, { "q_id": "10302_mmlu_physics", "cot_ids": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8343146443367004, 0.016720594838261604, 0.029668040573596954, 0.12903928756713867, 0.2146003544330597, 0.005955166183412075, 0.038651805371046066, 0.002352238865569234, 0.010793905705213547, 0.0119472099468112, 0.0017319319304078817, 0.0007166946888901293 ], [ 0.03093988448381424, 0.08995378762483597, 0.439826637506485, 0.00840426329523325, 0.02937670610845089, 0.0008883000118657947, 0.027527283877134323, 0.011096769012510777, 0.04537432640790939, 0.9997095465660095 ], [ 0.8343157768249512, 0.002759320894256234, 0.07834802567958832, 0.0006197518086992204, 0.16005821526050568, 0.0033161465544253588, 0.043776191771030426, 0.0044217417016625404, 0.021038025617599487, 0.03023459017276764, 0.01221493724733591, 0.09130429476499557, 0.006492869462817907, 0.0005149630014784634 ], [ 0.15164531767368317, 0.21400436758995056, 0.5385527014732361, 0.008775168098509312, 0.04293501377105713, 0.03555532172322273, 0.1815159022808075, 0.06203000620007515, 0.023484790697693825, 0.03737053647637367, 0.023843184113502502, 0.040414392948150635, 0.018951447680592537, 0.9930465817451477, 0.9998339414596558 ], [ 0.8343141078948975, 0.002759314374998212, 0.04423300549387932, 0.12603968381881714, 0.0031868142541497946, 0.054801881313323975, 0.002149012638255954, 0.022176844999194145, 0.02836107835173607, 0.003353910753503442, 0.000632534094620496 ], [ 0.8343150615692139, 0.022255118936300278, 0.030524568632245064, 0.13391372561454773, 0.2703862488269806, 0.0060530537739396095, 0.04668769985437393, 0.0024515639524906874, 0.033660996705293655, 0.013196133077144623, 0.019107112661004066, 0.0011466405121609569 ], [ 0.8343148827552795, 0.02367035672068596, 0.012344893999397755, 0.024217331781983376, 0.00047372831613756716, 0.03741311654448509, 0.003954024985432625, 0.03475912660360336, 0.00692132068797946, 0.0033111826051026583, 0.0007249452755786479 ], [ 0.70159512758255, 0.0032640176359564066, 0.044718336313962936, 0.0011153691448271275, 0.022779421880841255, 0.03604636341333389, 0.005116990767419338, 0.00044470815919339657 ], [ 0.030939768999814987, 0.12911292910575867, 0.315338134765625, 0.008969172835350037, 0.04033368080854416, 0.08509975671768188, 0.056082092225551605, 0.0033561671152710915, 0.04032956808805466, 0.0377233512699604, 0.018815912306308746, 0.9459126591682434, 0.9998072981834412 ], [ 0.8343154788017273, 0.0033399814274162054, 0.03981131687760353, 0.045275017619132996, 0.0055755795910954475, 0.0442798025906086, 0.04005879908800125, 0.005816175136715174, 0.04568469151854515, 0.020455386489629745, 0.022921152412891388, 0.014069698750972748, 0.0006762699922546744 ], [ 0.83431476354599, 0.015502302907407284, 0.02687872014939785, 0.08659645915031433, 0.28337424993515015, 0.0014998235274106264, 0.05637570098042488, 0.0023430988658219576, 0.03567851707339287, 0.013918357901275158, 0.017748849466443062, 0.0005587506457231939 ], [ 0.118228018283844, 0.21291318535804749, 0.6171914935112, 0.004070014227181673, 0.016452381387352943, 0.024055995047092438, 0.12125886231660843, 0.0632239431142807, 0.015330859459936619, 0.03519725799560547, 0.03298409283161163, 0.03712484985589981, 0.013731861487030983, 0.003532776376232505, 0.002408125903457403, 0.0006077688885852695 ], [ 0.030939869582653046, 0.10340426862239838, 0.4806317389011383, 0.012666005641222, 0.04924539476633072, 0.03730218857526779, 0.1931622475385666, 0.04343497380614281, 0.041194889694452286, 0.01500262413173914, 0.004311824683099985, 0.00046705640852451324 ], [ 0.8343144655227661, 0.004745593760162592, 0.046097565442323685, 0.14749197661876678, 0.009371764957904816, 0.023416008800268173, 0.0015898523852229118, 0.02220383659005165, 0.017396435141563416, 0.009923592209815979, 0.0005080247647128999, 0.00044482984230853617 ], [ 0.17117542028427124, 0.03598403558135033, 0.2582854926586151, 0.545529842376709, 0.009603827260434628, 0.02962971106171608, 0.06709591299295425, 0.05340559780597687, 0.003062907373532653, 0.03893440589308739, 0.040287841111421585, 0.008124339394271374, 0.0006722083198837936 ] ] }, { "q_id": "9771_mmlu_physics", "cot_ids": [ 0, 2, 3, 4, 5, 6, 9, 10, 11, 12, 14, 15 ], "rewards": [ [ 0.8645720481872559, 0.013411247171461582, 0.11829312145709991, 0.13499659299850464, 0.029497012495994568, 0.24876338243484497, 0.011234036646783352, 0.303153395652771, 0.0013009060639888048, 0.09462523460388184, 0.9043624401092529, 0.0006218179478310049 ], [ 0.29893994331359863, 0.04229290410876274, 0.04668077826499939, 0.9998165965080261 ], [ 0.1746264547109604, 0.011333988048136234, 0.1050867959856987, 0.00586949335411191, 0.09187252819538116, 0.0030244803056120872, 0.03986464440822601, 0.99755859375, 0.999842643737793 ], [ 0.7647980451583862, 0.13312923908233643, 0.03822831064462662, 0.25221890211105347, 0.9417092204093933, 0.9998939037322998, 0.9996689558029175 ], [ 0.2800533175468445, 0.10158313065767288, 0.034925349056720734, 0.17232827842235565, 0.12265630811452866, 0.9780332446098328, 0.9998795986175537 ], [ 0.38296470046043396, 0.0726294219493866, 0.04056654870510101, 0.26758867502212524, 0.42399200797080994, 0.2247842401266098, 0.14636990427970886, 0.00863345805555582 ], [ 0.007642452139407396, 0.05237990990281105, 0.031846899539232254, 0.17185483872890472, 0.0537361279129982, 0.1613854020833969, 0.0508190281689167, 0.9952918291091919, 0.9998369216918945 ], [ 0.010129322297871113, 0.054566916078329086, 0.10839560627937317, 0.045478109270334244, 0.04607313871383667, 0.024750476703047752, 0.031854283064603806, 0.04645201191306114, 0.007507998030632734, 0.05349843204021454, 0.997054934501648, 0.9998482465744019 ], [ 0.47715872526168823, 0.06861796975135803, 0.036927223205566406, 0.2896358072757721, 0.0003088164667133242, 0.01749047078192234, 0.3088870048522949, 0.9981008172035217, 0.9998064637184143 ], [ 0.10086682438850403, 0.07729992270469666, 0.03405911102890968, 0.042889323085546494, 0.060884278267621994, 0.13709960877895355, 0.12100047618150711, 0.23803728818893433, 0.10560892522335052, 0.013187726959586143, 0.09340827912092209, 0.022499321028590202, 0.06285105645656586, 0.0004126981657464057, 0.17720937728881836, 0.03208767622709274, 0.0004064215754624456 ], [ 0.4189014434814453, 0.058009739965200424, 0.012009046971797943, 0.12936244904994965, 0.0034607993438839912, 0.6093474626541138, 0.9965081810951233, 0.9998323917388916 ], [ 0.5425180792808533, 0.07787644863128662, 0.31787317991256714, 0.11000148952007294, 0.9136802554130554, 0.0002783853269647807 ] ] }, { "q_id": "10087_mmlu_physics", "cot_ids": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.2958965003490448, 0.06680242717266083, 0.06035832688212395, 0.016070231795310974, 0.002575294580310583 ], [ 0.716071605682373, 0.15734443068504333, 0.11901815980672836, 0.0023636084515601397 ], [ 0.28975504636764526, 0.056920699775218964, 0.02301918715238571, 0.05810145288705826, 0.024914825335144997, 0.0072257379069924355 ], [ 0.2523389756679535, 0.022873731330037117, 0.04515634477138519, 0.28467920422554016, 0.029985064640641212, 0.014402229338884354, 0.0028944723308086395 ], [ 0.2035149335861206, 0.03014848195016384, 0.03445645421743393, 0.02152370475232601, 0.002997261704877019 ], [ 0.4557960629463196, 0.05248011648654938, 0.07451541721820831, 0.039046432822942734, 0.04695634916424751, 0.012778905220329762, 0.006433206144720316 ], [ 0.046365831047296524, 0.05229131504893303, 0.08152364194393158, 0.007638005539774895, 0.006845932453870773 ], [ 0.3075873851776123, 0.026822837069630623, 0.002326454035937786 ], [ 0.420244038105011, 0.04664578288793564, 0.013671571388840675, 0.002730055246502161 ], [ 0.14356224238872528, 0.05565842613577843, 0.04398699849843979, 0.05686497688293457, 0.09161533415317535, 0.03139331564307213 ], [ 0.05066725239157677, 0.03649161756038666, 0.046432141214609146, 0.09985974431037903, 0.11826909333467484, 0.09520593285560608, 0.035789936780929565 ], [ 0.3057776987552643, 0.2234642654657364, 0.20316816866397858, 0.002368534915149212 ], [ 0.25505030155181885, 0.030758796259760857, 0.03109482303261757, 0.013155943714082241, 0.004982749465852976 ], [ 0.11181703954935074, 0.02896823175251484, 0.039058420807123184, 0.10269010066986084, 0.043066900223493576, 0.012073294259607792, 0.0065030865371227264 ], [ 0.09814700484275818, 0.036017708480358124, 0.21812792122364044, 0.06252844631671906, 0.06432890146970749, 0.04655870422720909, 0.004505868535488844 ] ] }, { "q_id": "9639_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9859748482704163, 0.96769118309021, 0.004331045784056187 ], [ 0.976318895816803, 0.9526513814926147, 0.004199732560664415 ], [ 0.9903062582015991, 0.8193346858024597, 0.0047861626371741295 ], [ 0.9881702661514282, 0.003897198475897312 ], [ 0.9891684055328369, 0.9187700152397156, 0.004307887516915798 ], [ 0.9932004809379578, 0.9832325577735901, 0.005200689192861319 ], [ 0.9950487017631531, 0.7133556008338928, 0.004558308981359005 ], [ 0.9888829588890076, 0.9588305354118347, 0.8475872874259949, 0.004976571537554264 ], [ 0.9846919178962708, 0.7169867753982544, 0.004954732954502106 ], [ 0.9912453293800354, 0.972145676612854, 0.005163624417036772 ], [ 0.9859545826911926, 0.9759052395820618, 0.004476962145417929 ], [ 0.9935300946235657, 0.9560654163360596, 0.003913415130227804 ], [ 0.9640002846717834, 0.00033436971716582775, 0.4016875922679901, 0.005453695543110371 ], [ 0.9906501770019531, 0.8610854744911194, 0.004096636548638344 ], [ 0.9903061389923096, 0.9871783256530762, 0.004296623170375824 ], [ 0.983144998550415, 0.9817824959754944, 0.00441514328122139 ] ] }, { "q_id": "10133_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15 ], "rewards": [ [ 0.14243313670158386, 0.12994207441806793, 0.07362670451402664, 0.9035906195640564, 0.36907678842544556, 0.2534383535385132, 0.15183693170547485, 0.13694602251052856, 0.03990708291530609 ], [ 0.1390250325202942, 0.11778458952903748, 0.15689612925052643, 0.042029861360788345, 0.1704341024160385, 0.06730832159519196, 0.11334643512964249 ], [ 0.086842380464077, 0.09158506244421005, 0.03619729354977608, 0.052185602486133575, 0.06449996680021286 ], [ 0.42142707109451294, 0.07143747806549072, 0.4416709840297699, 0.0714901015162468, 0.2733018696308136, 0.13825219869613647, 0.275538831949234, 0.048804447054862976, 0.12638677656650543, 0.13196168839931488, 0.1577599197626114, 0.0730685219168663, 0.019019613042473793 ], [ 0.20119138062000275, 0.1995733380317688, 0.15166261792182922, 0.20125454664230347, 0.058173224329948425, 0.11287493258714676, 0.05199199914932251, 0.18933379650115967, 0.046982184052467346, 0.06276510655879974, 0.03744048252701759 ], [ 0.21756716072559357, 0.05738557502627373, 0.15194258093833923, 0.5013405084609985, 0.03408919647336006, 0.12247948348522186, 0.13607913255691528, 0.29773688316345215, 0.14388181269168854, 0.11047443747520447, 0.2083253264427185, 0.3043840229511261, 0.25827300548553467, 0.030582573264837265, 0.0011471359757706523 ], [ 0.17066991329193115, 0.27948689460754395, 0.08972140401601791, 0.25411081314086914, 0.05843104049563408, 0.07386617362499237, 0.2621738612651825, 0.031468044966459274, 0.0011037277290597558 ], [ 0.21756666898727417, 0.21363140642642975, 0.0773148462176323, 0.1864837259054184, 0.06440872699022293, 0.11113046109676361, 0.12547989189624786 ], [ 0.1747405230998993, 0.21262356638908386, 0.19402039051055908, 0.0834723636507988, 0.17112042009830475, 0.03075866959989071, 0.07606831192970276, 0.03988451138138771 ], [ 0.16987597942352295, 0.02369450032711029, 0.1033768579363823, 0.4902382493019104, 0.056661929935216904, 0.09271969646215439, 0.0907449722290039, 0.038527313619852066, 0.10919220000505447, 0.40091702342033386, 0.08647553622722626, 0.16983437538146973, 0.05979863554239273, 0.13502226769924164, 0.11776801943778992, 0.10654180496931076, 0.03490319103002548 ], [ 0.07855277508497238, 0.004349846858531237, 0.5883648991584778, 0.004427308216691017, 0.17624226212501526, 0.005549201276153326, 0.04605335742235184, 0.009341534227132797, 0.10927970707416534, 0.07832032442092896, 0.03673508018255234, 0.03547308221459389 ], [ 0.13493074476718903, 0.15518353879451752, 0.21299326419830322, 0.036891646683216095, 0.08344566076993942, 0.1071188673377037, 0.12740007042884827, 0.026213044300675392 ], [ 0.07855431735515594, 0.014107882045209408, 0.08049048483371735, 0.257821261882782, 0.12754248082637787, 0.05447034537792206, 0.06725741922855377, 0.1162637397646904, 0.10715571790933609, 0.062001653015613556, 0.03392486274242401 ], [ 0.07855349779129028, 0.011814824305474758, 0.24397967755794525, 0.08257501572370529, 0.14622266590595245, 0.0388416089117527, 0.05233091488480568, 0.10316123068332672, 0.1561543196439743, 0.07067732512950897, 0.033274829387664795, 0.03920750692486763 ] ] }, { "q_id": "9885_mmlu_physics", "cot_ids": [ 0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 ], "rewards": [ [ 0.5247176885604858, 0.11268865317106247, 0.32772356271743774, 0.9735960960388184, 0.014436742290854454, 0.026456687599420547, 0.19337011873722076, 0.011784881353378296, 0.05670556053519249, 0.039413440972566605, 0.002845549723133445 ], [ 0.5247162580490112, 0.11269093304872513, 0.10710375756025314, 0.04442296922206879, 0.35648253560066223, 0.06315278261899948, 0.9586790204048157, 0.015208560973405838, 0.03062407672405243, 0.015267551876604557, 0.02659441903233528, 0.05660535395145416, 0.08079749345779419, 0.04201419651508331, 0.10379962623119354, 0.1331949084997177, 0.0032974600326269865 ], [ 0.524717390537262, 0.11268950998783112, 0.09337525069713593, 0.017058953642845154, 0.42321380972862244, 0.0702720358967781, 0.9581153988838196, 0.015998244285583496, 0.014802519232034683, 0.014189665205776691, 0.0255343709141016, 0.11304832249879837, 0.6582114100456238, 0.15102963149547577 ], [ 0.5247176885604858, 0.11268837004899979, 0.1616886854171753, 0.016017645597457886, 0.37397897243499756, 0.08120786398649216, 0.9547138810157776, 0.015000044368207455, 0.008091533556580544, 0.01827361062169075, 0.04573692008852959, 0.004695485346019268, 0.22487522661685944, 0.0031822097953408957 ], [ 0.5247182846069336, 0.11268969625234604, 0.31940388679504395, 0.9723095893859863, 0.014367465861141682, 0.03256666287779808, 0.025613533332943916, 0.053908515721559525, 0.20518724620342255, 0.003907764330506325 ], [ 0.5247164964675903, 0.11268962174654007, 0.27666497230529785, 0.9736073613166809, 0.014448300935328007, 0.04372299090027809, 0.09880425781011581, 0.1638934463262558, 0.004494525026530027 ], [ 0.5247189998626709, 0.11268950998783112, 0.2547893524169922, 0.9489755630493164, 0.014113355427980423, 0.02523978427052498, 0.1122056245803833, 0.003345783334225416 ], [ 0.524718165397644, 0.11268702894449234, 0.40924593806266785, 0.969397783279419, 0.014918350614607334, 0.029221156612038612, 0.029730064794421196, 0.05666973441839218, 0.6112241148948669, 0.002854185411706567 ], [ 0.5247162580490112, 0.11269093304872513, 0.04426680505275726, 0.04359474033117294, 0.47098228335380554, 0.9676129221916199, 0.01859758235514164, 0.025984665378928185, 0.01919364184141159, 0.027967244386672974, 0.02887549065053463, 0.12259192019701004, 0.003930705599486828 ], [ 0.5247169733047485, 0.11268962174654007, 0.043521247804164886, 0.015752265229821205, 0.5104876756668091, 0.08299331367015839, 0.9592050909996033, 0.016942007467150688, 0.0325116291642189, 0.011397812515497208, 0.04220319166779518, 0.05991474166512489, 0.06131546199321747, 0.01031128317117691, 0.20445667207241058, 0.08015419542789459 ], [ 0.5247162580490112, 0.11269093304872513, 0.1465572565793991, 0.015589798800647259, 0.43545109033584595, 0.07275857031345367, 0.9623351097106934, 0.015797091647982597, 0.011709045618772507, 0.024859869852662086, 0.03142675757408142, 0.025757521390914917, 0.012461178004741669, 0.03231896832585335, 0.09371647238731384, 0.14722423255443573, 0.003030280349776149 ], [ 0.5247164964675903, 0.11268818378448486, 0.05837618187069893, 0.05322634056210518, 0.023962581530213356, 0.034181371331214905, 0.1672116369009018, 0.007665612734854221, 0.04109835997223854, 0.9565045237541199, 0.016374921426177025, 0.0312623456120491, 0.02440001629292965, 0.04458172991871834, 0.05318915471434593, 0.1548900008201599, 0.18844683468341827, 0.003365392331033945 ], [ 0.5247151851654053, 0.11268751323223114, 0.36177071928977966, 0.9642841815948486, 0.0355863980948925, 0.025714144110679626, 0.034115977585315704, 0.05304703116416931, 0.2130027711391449, 0.0028068881947547197 ] ] }, { "q_id": "9307_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.37374112010002136, 0.6368063688278198, 0.003472269279882312 ], [ 0.4633654057979584, 0.3966214954853058, 0.18483439087867737, 0.994890570640564, 0.9996302127838135 ], [ 0.0733279287815094, 0.8400061726570129, 0.19904202222824097, 0.12078768759965897, 0.9959858059883118, 0.9992967844009399 ], [ 0.9822758436203003, 0.6634621024131775, 0.4472520053386688, 0.16900642216205597, 0.9851829409599304, 0.9993334412574768 ], [ 0.2747603952884674, 0.029836272820830345, 0.4881792664527893, 0.005190959200263023 ], [ 0.915480375289917, 0.015367081388831139, 0.7678925395011902, 0.01579234004020691, 0.0036399790551513433 ], [ 0.9938306212425232, 0.49594447016716003, 0.44706693291664124, 0.9053652882575989, 0.0037367921322584152 ], [ 0.5110074281692505, 0.501082181930542, 0.16424398124217987, 0.9892026782035828, 0.9994989633560181 ], [ 0.543442964553833, 0.3122117817401886, 0.6553062200546265, 0.6350072026252747, 0.004289453849196434 ], [ 0.3614658713340759, 0.29209092259407043, 0.8526854515075684, 0.002810150384902954 ], [ 0.8572036027908325, 0.525706946849823, 0.9942135214805603, 0.999640941619873 ], [ 0.6654536724090576, 0.5104193687438965, 0.993945300579071, 0.9996527433395386 ], [ 0.7435063123703003, 0.3430204689502716, 0.6798843741416931, 0.8954960703849792, 0.9974762797355652, 0.999664306640625 ], [ 0.9727725982666016, 0.3007763624191284, 0.9945275187492371, 0.9994753003120422 ], [ 0.9250627756118774, 0.9956653714179993, 0.9479098916053772, 0.0021144472993910313 ], [ 0.5223818421363831, 0.30163538455963135, 0.05875972658395767, 0.9526045322418213, 0.0022029904648661613 ] ] }, { "q_id": "10293_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.10519649088382721, 0.1442272961139679, 0.006455511320382357, 0.17858977615833282, 0.747468113899231, 0.26444879174232483, 0.23611117899417877, 0.09283922612667084, 0.03658483177423477, 0.016038816422224045 ], [ 0.04955489933490753, 0.10371878743171692, 0.08399093151092529, 0.445383757352829, 0.0900106281042099, 0.1228470653295517, 0.057815033942461014, 0.022817568853497505 ], [ 0.061412304639816284, 0.129742830991745, 0.1118297353386879, 0.025428231805562973, 0.15528564155101776, 0.04906833916902542, 0.065793976187706 ], [ 0.04955584183335304, 0.0988212376832962, 0.12010654807090759, 0.49087437987327576, 0.0910564661026001, 0.1866973638534546, 0.07219136506319046, 0.09777498990297318, 0.01832759566605091 ], [ 0.12350156903266907, 0.06612523645162582, 0.13257996737957, 0.13732066750526428, 0.5317813158035278, 0.10149643570184708, 0.06123606115579605, 0.05662352964282036, 0.024810075759887695 ], [ 0.10559109598398209, 0.291846364736557, 0.1969565749168396, 0.5407904982566833, 0.12758924067020416, 0.0708402469754219, 0.06699522584676743, 0.014132688753306866 ], [ 0.22613760828971863, 0.12367676943540573, 0.45096898078918457, 0.1401536464691162, 0.04526115208864212, 0.023121928796172142 ], [ 0.090357705950737, 0.2861708998680115, 0.5817561149597168, 0.17363755404949188, 0.17413318157196045, 0.15837839245796204, 0.029571250081062317 ], [ 0.1293027400970459, 0.1486329883337021, 0.1415967047214508, 0.546772301197052, 0.045503899455070496, 0.036194998770952225, 0.01181595865637064, 0.009119103662669659 ], [ 0.12350039184093475, 0.03025994449853897, 0.15642458200454712, 0.16482007503509521, 0.5466669201850891, 0.12273027747869492, 0.194721981883049, 0.153383269906044, 0.061255693435668945, 0.05065702274441719, 0.011832652613520622 ], [ 0.10169734060764313, 0.16199465095996857, 0.1181393712759018, 0.5781049132347107, 0.16154538094997406, 0.05355248972773552, 0.12468107789754868, 0.047759223729372025 ], [ 0.03916054591536522, 0.10897870361804962, 0.10872744768857956, 0.5196481943130493, 0.15386539697647095, 0.1454392522573471, 0.06058036535978317, 0.02037854492664337 ], [ 0.09030068665742874, 0.1607079654932022, 0.28605014085769653, 0.45424163341522217, 0.1041237935423851, 0.06660925596952438, 0.07644571363925934, 0.028958575800061226 ], [ 0.12350095063447952, 0.04881841689348221, 0.20421035587787628, 0.19977937638759613, 0.41031432151794434, 0.022186100482940674, 0.4921559691429138, 0.171634241938591, 0.20014560222625732, 0.07122316211462021, 0.17707453668117523, 0.04996361583471298, 0.02654232643544674 ], [ 0.11310413479804993, 0.17118799686431885, 0.13960282504558563, 0.3657497763633728, 0.09627602994441986, 0.1355687975883484, 0.1607160121202469, 0.9687834978103638, 0.005232958123087883 ], [ 0.12350095063447952, 0.060525838285684586, 0.12330380827188492, 0.19512267410755157, 0.0029877324122935534, 0.6321911811828613, 0.24593311548233032, 0.2233765572309494, 0.013509202748537064, 0.986376941204071, 0.015562278218567371 ] ] }, { "q_id": "9187_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15 ], "rewards": [ [ 0.11696864664554596, 0.2518255412578583, 0.9773331880569458, 0.06156807392835617 ], [ 0.10923399031162262, 0.01470300555229187, 0.02162526734173298, 0.15618103742599487, 0.031037548556923866, 0.05866191163659096, 0.02519785612821579, 0.03580908849835396, 0.039375368505716324 ], [ 0.13112150132656097, 0.14508460462093353, 0.06842357665300369, 0.027848269790410995, 0.06706100702285767, 0.018056385219097137, 0.33848071098327637, 0.9531892538070679 ], [ 0.11697115749120712, 0.08162625133991241, 0.046951357275247574, 0.04587525129318237, 0.07016029953956604, 0.137693852186203, 0.05982357636094093, 0.0400075800716877, 0.048142846673727036, 0.10620352625846863, 0.003113390412181616, 0.0021493174135684967 ], [ 0.4507755935192108, 0.03651414066553116, 0.04995517432689667, 0.2038528174161911, 0.040394872426986694, 0.011999739333987236, 0.0028162288945168257 ], [ 0.26783227920532227, 0.07935046404600143, 0.06513270735740662, 0.08888708055019379, 0.06980323046445847 ], [ 0.10387177765369415, 0.044847168028354645, 0.04695470631122589, 0.20887582004070282, 0.11340104043483734, 0.01792202703654766, 0.002569120144471526 ], [ 0.10920806229114532, 0.029235877096652985, 0.0724298357963562, 0.16837279498577118, 0.011727915145456791, 0.03197929635643959, 0.016634546220302582, 0.02793186530470848, 0.0030300584621727467 ], [ 0.09248907119035721, 0.05084468051791191, 0.05295180529356003, 0.2712130546569824, 0.0529424324631691, 0.03797313570976257, 0.05598551407456398 ], [ 0.19148419797420502, 0.055501788854599, 0.1135699450969696, 0.0966683104634285, 0.038382597267627716, 0.03816574066877365, 0.047817397862672806, 0.08389514684677124, 0.002680392935872078 ], [ 0.20419053733348846, 0.2224433720111847, 0.1077047660946846, 0.04659656807780266, 0.006321489345282316, 0.0037697628140449524 ], [ 0.11343056708574295, 0.01854836940765381, 0.19759085774421692, 0.06676533073186874, 0.05851336196064949, 0.0233162809163332, 0.07140183448791504, 0.025189310312271118, 0.01131821982562542, 0.002033533528447151 ], [ 0.07166355848312378, 0.0029561161063611507, 0.2071920931339264, 0.09438513964414597, 0.018574045971035957, 0.060031957924366, 0.02015945129096508, 0.0404965803027153, 0.12987975776195526, 0.1041550263762474, 0.07442313432693481, 0.04757443442940712 ], [ 0.11697273701429367, 0.07849881052970886, 0.17977413535118103, 0.0966145247220993, 0.03896987438201904, 0.050184737890958786 ] ] }, { "q_id": "9328_mmlu_physics", "cot_ids": [ 3, 6, 7, 11, 12, 14, 15 ], "rewards": [ [ 0.24366328120231628, 0.000532564998138696, 0.05152588337659836, 0.0008191621745936573, 0.016004424542188644, 0.005075074732303619, 0.003726113587617874, 0.013166532851755619, 0.00961065012961626, 0.023087071254849434, 0.002577501116320491, 0.027611592784523964, 0.035732071846723557, 0.09090834110975266, 0.06024438142776489, 0.05714816600084305, 0.02519282139837742, 0.001833367976360023, 0.006935241632163525, 0.0015270718140527606 ], [ 0.24366502463817596, 0.0007569370209239423, 3.85095045203343e-05, 0.042046625167131424, 0.06090470030903816, 0.0008014720515348017, 0.002700239885598421, 0.01260610856115818, 0.008990699425339699, 0.0010384381748735905, 0.018978675827383995, 0.0038394236471503973, 0.03232207149267197, 0.0010909847915172577, 0.006544803269207478, 0.001453898148611188 ], [ 0.24366424977779388, 0.0007569422596134245, 0.0001910733408294618, 0.05724022537469864, 0.0009297794895246625, 0.00025770897627808154, 0.03172997385263443, 0.0044680447317659855, 0.4725169837474823, 0.6814585328102112, 0.6701346635818481 ], [ 0.2436615228652954, 0.0003072151157539338, 0.0482884980738163, 0.00031742671853862703, 0.02861102670431137, 0.00045347740524448454, 0.015159313566982746, 0.0026389043778181076, 0.03177502751350403, 0.0006504121702164412, 0.07110335677862167, 0.0046159434132277966, 0.0013009085087105632 ], [ 0.24366168677806854, 0.0005325571401044726, 6.0641341406153515e-05, 0.09498001635074615, 0.0004965286934748292, 0.01955641247332096, 0.004923402797430754, 0.0028691361658275127, 0.0028044639620929956, 0.02226378582417965, 0.014115503989160061, 0.027020355686545372, 0.010325325652956963, 0.028263425454497337, 0.0012814861256629229, 0.05170150101184845, 0.01524428278207779, 0.005436289124190807, 0.0012909576762467623 ], [ 0.1746681034564972, 0.00030699995113536716, 0.07312754541635513, 0.0002886802249122411, 0.02230837009847164, 0.0003267901483923197, 0.02919570729136467, 0.001927172765135765, 0.019205981865525246, 0.0003677130735013634, 0.03808183968067169, 0.061419013887643814, 0.0932818055152893 ], [ 0.2436639815568924, 0.0007569340523332357, 4.005081791547127e-05, 0.057522326707839966, 0.0004977341741323471, 0.0002104557934217155, 0.05909006670117378, 0.0002835092891473323, 0.0003161121567245573, 0.06788215786218643, 0.010031789541244507, 0.00815743301063776, 0.02431585267186165, 0.010131913237273693, 0.04132796451449394, 0.0012706128181889653, 0.011947468854486942, 0.0850522443652153 ] ] }, { "q_id": "10040_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.5449598431587219, 0.33611512184143066, 0.0489344596862793, 0.04479086771607399, 0.052301619201898575, 0.14063818752765656, 0.9955698847770691, 0.9844948649406433 ], [ 0.5448492765426636, 0.3816823959350586, 0.9892404675483704, 0.9737304449081421 ], [ 0.08530349284410477, 0.3544059693813324, 0.38127467036247253, 0.0639185979962349, 0.1519595980644226, 0.3691350519657135, 0.014149626716971397, 0.07333913445472717, 0.017773637548089027, 0.9874691963195801, 0.9942381381988525 ], [ 0.514647364616394, 0.37399759888648987, 0.07387498766183853, 0.04085565358400345, 0.07972510159015656, 0.02280852384865284, 0.06983170658349991, 0.9922841191291809, 0.9639766812324524 ], [ 0.8142785429954529, 0.3753933608531952, 0.07472962141036987, 0.057840295135974884, 0.06814360618591309, 0.1250712275505066, 0.995453953742981, 0.26157668232917786 ], [ 0.2196127027273178, 0.4300801455974579, 0.35246172547340393, 0.0003333483764436096, 0.29974567890167236, 0.13356149196624756, 0.1327640563249588, 0.014585869386792183, 0.052046388387680054, 0.0014751434791833162, 0.9834186434745789, 0.9942675828933716 ], [ 0.35408052802085876, 0.3919420838356018, 0.32186245918273926, 0.490629106760025, 0.048817288130521774, 0.1102994829416275, 0.09424615651369095, 0.9945242404937744, 0.9804161190986633 ], [ 0.4367992877960205, 0.36005285382270813, 0.3916919231414795, 0.41420888900756836, 0.9945706725120544, 0.9717939496040344 ], [ 0.3780921697616577, 0.3908792734146118, 0.0049729435704648495, 0.2574128210544586, 0.30930155515670776, 0.17518013715744019, 0.016272330656647682, 0.003859453136101365, 0.9849181771278381, 0.9941684007644653 ], [ 0.49570760130882263, 0.2988867163658142, 0.33588799834251404, 0.2028712034225464, 0.8575087189674377 ], [ 0.6068311333656311, 0.42542022466659546, 0.24639873206615448, 0.9958668947219849, 0.9764734506607056 ], [ 0.6328763961791992, 0.5246990919113159, 0.33401235938072205, 0.07535206526517868, 0.45934930443763733, 0.3107510507106781, 0.0963325947523117, 0.9841232895851135, 0.9899317026138306 ], [ 0.5361785888671875, 0.3583928346633911, 0.15798839926719666, 0.07212739437818527, 0.24222034215927124, 7.071685104165226e-05, 0.04495592042803764, 0.9924212098121643, 0.9837712049484253 ], [ 0.4653751254081726, 0.3072587549686432, 0.3757683336734772, 0.1295023113489151, 0.516356348991394, 0.00264001009054482, 0.9340144395828247, 0.9838936924934387 ], [ 0.31554511189460754, 0.4547412395477295, 0.32701826095581055, 0.1720338612794876, 0.9935358762741089, 0.9907998442649841 ], [ 0.775689423084259, 0.24609418213367462, 0.4897793233394623, 0.42918381094932556, 0.4637629985809326, 0.14451704919338226, 0.9414281845092773, 0.968519389629364 ] ] }, { "q_id": "9700_mmlu_physics", "cot_ids": [ 0, 1, 2, 4, 6, 9, 11, 15 ], "rewards": [ [ 0.2526615262031555, 0.0028948942199349403, 0.01780945248901844, 0.0043050930835306644, 0.00014558274415321648, 0.03424474224448204, 0.0041940947994589806, 0.011879007332026958, 0.10062067210674286, 0.016177626326680183, 0.05240064486861229, 0.01074367854744196, 0.03668631613254547, 0.03234848007559776, 0.020570794120430946, 0.2433454841375351, 0.025912340730428696, 0.009160309098660946, 0.09758968651294708, 0.011606285348534584, 0.013006678782403469, 0.0026491107419133186, 0.03164796903729439, 0.033433523029088974, 0.0012117207515984774 ], [ 0.25265955924987793, 0.00362563319504261, 0.1243295669555664, 0.12345166504383087, 0.004622503649443388, 0.21510881185531616, 0.019247449934482574, 0.01820174604654312, 0.0038860859349370003, 0.6971794366836548, 0.011007917113602161, 0.9671863317489624, 0.9981557726860046 ], [ 0.2526584565639496, 0.002430690685287118, 0.018140137195587158, 0.003085200907662511, 0.00011371177970431745, 0.026230357587337494, 0.033629801124334335, 0.13283021748065948, 0.005773815326392651, 0.011410810984671116, 0.07934509217739105, 0.0014417129568755627, 0.13141252100467682, 0.02592710219323635, 0.11044439673423767, 0.015538526698946953, 0.06492301821708679, 0.007340838201344013, 0.024653827771544456, 0.02500453032553196, 0.17256632447242737, 0.8553087115287781, 0.004253851715475321, 0.001370595651678741, 0.11555210500955582, 0.027797721326351166, 0.9903184175491333 ], [ 0.25265955924987793, 0.0028948793187737465, 0.01617824099957943, 0.04627670347690582, 0.001925970078445971, 0.06732017546892166, 0.007338091265410185, 0.03134269639849663, 0.013041562400758266, 0.04617803916335106, 0.0054270303808152676, 0.015016242861747742, 0.008842965587973595, 0.025024252012372017, 0.022525310516357422 ], [ 0.2526613473892212, 0.0028948928229510784, 0.03116030804812908, 0.0060783205553889275, 0.00021904089953750372, 0.038156986236572266, 0.04114355519413948, 0.00340207084082067, 0.018190816044807434, 0.12641319632530212, 0.18353016674518585, 0.039620399475097656, 0.08022584766149521, 0.043488528579473495, 0.1891523003578186, 0.01967483200132847, 0.30493882298469543, 0.02775399573147297, 0.0115496926009655, 0.1108325645327568, 0.8210157155990601, 0.005296800751239061, 0.0013432493433356285, 0.9849464893341064, 0.9991762042045593 ], [ 0.3535235524177551, 0.10392145067453384, 0.4352436363697052, 0.48781028389930725, 0.98843914270401 ], [ 0.23213832080364227, 0.09530723094940186, 0.00016352004604414105, 0.4519912600517273, 0.033465463668107986, 0.12189910560846329, 0.021158624440431595, 0.024341287091374397, 0.004416306037455797, 0.029746783897280693, 0.9926015734672546 ], [ 0.25266334414482117, 0.004088796209543943, 0.028971292078495026, 0.008777955546975136, 0.019840693101286888, 0.0019512204453349113, 0.01514047384262085, 0.007691922597587109, 0.02852250263094902, 0.98602294921875 ] ] }, { "q_id": "10076_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.9442298412322998, 0.9793160557746887, 0.17315101623535156, 0.9858419299125671, 0.010575870983302593 ], [ 0.9501904249191284, 0.980012059211731, 0.14926095306873322, 0.9769639372825623, 0.018402183428406715 ], [ 0.9487947821617126, 0.9748201370239258, 0.16074547171592712, 0.013251697644591331, 0.9823019504547119, 0.02197660692036152 ], [ 0.13568048179149628, 0.6246781945228577, 0.8729786276817322, 0.12481341511011124, 0.9689540266990662, 0.004702999256551266, 0.04882928729057312, 0.09461270272731781, 0.03729287534952164, 0.16181249916553497, 0.052571505308151245, 0.9771087765693665, 0.017650868743658066 ], [ 0.9547156095504761, 0.9772072434425354, 0.19243454933166504, 0.10666914284229279, 0.9836379289627075, 0.007655971217900515 ], [ 0.9290663599967957, 0.978303849697113, 0.19964814186096191, 0.9742648005485535, 0.012798993848264217 ], [ 0.14611008763313293, 0.5393834710121155, 0.8872361183166504, 0.10853929072618484, 0.9688360691070557, 0.018865177407860756, 0.05343826860189438, 0.15702560544013977, 0.026930391788482666, 0.9779493808746338, 0.017258694395422935 ], [ 0.9562265276908875, 0.9735136032104492, 0.2347152829170227, 0.9863937497138977, 0.010591895319521427 ], [ 0.949263334274292, 0.061675313860177994, 0.9808696508407593, 0.0970178097486496, 0.025123028084635735, 0.9826835989952087, 0.02099839597940445 ], [ 0.9568711519241333, 0.9805262684822083, 0.17046524584293365, 0.9880237579345703, 0.019489042460918427 ], [ 0.9296302795410156, 0.11751732230186462, 0.9507272839546204, 0.002469758503139019, 0.08999486267566681, 0.014452905394136906, 0.9815592765808105, 0.016419680789113045 ], [ 0.13567793369293213, 0.5459751486778259, 0.8545305132865906, 0.12501925230026245, 0.9776713848114014, 0.014028780162334442, 0.04332020878791809, 0.1562396138906479, 0.03608648106455803, 0.980134904384613, 0.02100086398422718 ], [ 0.2700389623641968, 0.6062832474708557, 0.7849037051200867, 0.09199904650449753, 0.9696556925773621, 0.005560772959142923, 0.045023608952760696, 0.07048686593770981, 0.01129700243473053, 0.14492706954479218, 0.0090596042573452, 0.9809067845344543, 0.014696912840008736 ], [ 0.9562264084815979, 0.9749721884727478, 0.16553995013237, 0.987459659576416, 0.011391703970730305 ], [ 0.9635769724845886, 0.11841315776109695, 0.9756940007209778, 0.013232295401394367, 0.09408558160066605, 0.026961885392665863, 0.16048292815685272, 0.0481143444776535, 0.9732196927070618, 0.008433137089014053 ], [ 0.9569551944732666, 0.9796523451805115, 0.18327800929546356, 0.02375381998717785, 0.9812498688697815, 0.023100323975086212 ] ] }, { "q_id": "10176_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.25999799370765686, 0.06512972712516785, 0.055946145206689835, 0.1335304230451584, 0.06284712255001068, 0.9907496571540833, 0.9941976070404053 ], [ 0.03478024899959564, 0.1222362220287323, 0.15719863772392273, 0.9955001473426819, 0.9928148984909058 ], [ 0.35294976830482483, 0.023061208426952362, 0.031616710126399994, 0.2702919840812683, 0.07179252058267593, 0.007429645396769047 ], [ 0.21988698840141296, 0.025868050754070282, 0.03770807385444641, 0.00358276697807014, 0.23326677083969116, 0.026319243013858795, 0.04867080971598625, 0.27970069646835327, 0.9883164763450623, 0.992924690246582 ], [ 0.03428502753376961, 0.04089657589793205, 0.13341085612773895, 0.01811879873275757, 0.9934387803077698, 0.9928239583969116 ], [ 0.21988920867443085, 0.056292757391929626, 0.06443421542644501, 0.20188972353935242, 0.03609943762421608, 0.033169277012348175, 0.0883730798959732, 0.04367068409919739, 0.034755557775497437, 0.0015680992510169744 ], [ 0.21988454461097717, 0.027627652511000633, 0.03754445165395737, 0.20129486918449402, 0.08772570639848709, 0.21840529143810272, 0.048502448946237564, 0.017061742022633553, 0.12110688537359238, 0.20372731983661652, 0.06787992268800735, 0.16968020796775818, 0.9652171730995178, 0.9827658534049988 ], [ 0.2198897749185562, 0.028775524348020554, 0.041979510337114334, 0.32392874360084534, 0.280853807926178, 0.07282280176877975, 0.9936715364456177, 0.9951903820037842 ], [ 0.21988733112812042, 0.029329968616366386, 0.05089816451072693, 0.12616212666034698, 0.02779983915388584, 0.03067934699356556, 0.12947367131710052, 0.037782471626996994, 0.9839122891426086, 0.9895732998847961 ], [ 0.35295000672340393, 0.019865097478032112, 0.037631403654813766, 0.004193020984530449, 0.047057218849658966, 0.04482625797390938, 0.14282457530498505, 0.038040466606616974, 0.10596323758363724, 0.052871543914079666, 0.9961808919906616, 0.9939380884170532 ], [ 0.21988897025585175, 0.025310197845101357, 0.03558481112122536, 0.10656730830669403, 0.05227907747030258, 0.989546000957489, 0.9936018586158752 ], [ 0.21988733112812042, 0.025868063792586327, 0.03581707552075386, 0.06384032964706421, 0.1542966514825821, 0.10549895465373993, 0.04977232217788696, 0.9924759268760681, 0.9962571859359741 ], [ 0.28334954380989075, 0.029711995273828506, 0.042222391813993454, 0.2758551239967346, 0.02783723548054695, 0.054810527712106705, 0.23075570166110992, 0.9894715547561646, 0.993224024772644 ], [ 0.21988578140735626, 0.05559442192316055, 0.07324349135160446, 0.06779253482818604, 0.09501706808805466, 0.22101916372776031, 0.02999686822295189, 0.05864666774868965, 0.12197715044021606, 0.1943695992231369, 0.04824048653244972, 0.1194712296128273, 0.9813284873962402, 0.9920200705528259 ], [ 0.2685111463069916, 0.04328218102455139, 0.058492980897426605, 0.15708109736442566, 0.417313814163208, 0.051931463181972504, 0.9921365976333618, 0.9926038384437561 ], [ 0.5431857109069824, 0.0245048888027668, 0.04401478171348572, 0.06907372921705246, 0.08921466767787933, 0.026664188131690025, 0.03470371663570404, 0.9923374056816101, 0.9921127557754517 ] ] }, { "q_id": "9790_mmlu_physics", "cot_ids": [ 0, 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.17408129572868347, 0.05092655494809151, 0.05621865764260292, 0.05526144430041313, 0.048663217574357986, 0.03594093769788742, 0.04218460991978645, 0.06363130360841751, 0.01122316811233759, 0.03107995167374611, 0.01054236851632595, 0.005837128963321447, 0.003183965105563402 ], [ 0.1740819215774536, 0.002716858172789216, 0.023635778576135635, 0.006281169597059488, 0.013878519646823406, 0.0003817720280494541, 0.02102244272828102, 0.02572372555732727, 0.0006300611421465874, 0.08006958663463593, 0.003707529278472066, 0.016943329945206642, 0.07433386892080307, 0.008271856233477592, 0.06438878923654556, 0.43834421038627625, 0.9913271069526672 ], [ 0.17408135533332825, 0.002716873772442341, 0.022614851593971252, 0.004796118009835482, 0.0444970540702343, 0.00015298844664357603, 0.024691786617040634, 0.000537573010660708, 0.002004955429583788, 0.062369201332330704, 0.009263724088668823, 0.04057534411549568, 0.011876892298460007, 0.04971795529127121, 0.09176826477050781, 0.1592516154050827, 0.9909964799880981 ], [ 0.1740819215774536, 0.002716858172789216, 0.023635778576135635, 0.007714951876550913, 0.042809609323740005, 0.00022815531701780856, 0.03520626574754715, 0.0005717852618545294, 0.03317082300782204, 0.055207543075084686, 0.04963291063904762, 0.0034933635033667088, 0.4206702411174774, 0.0016925603849813342, 0.30945029854774475, 0.0015416648238897324 ], [ 0.17408129572868347, 0.05092655494809151, 0.05621865764260292, 0.05526144430041313, 0.011185412295162678, 0.03484842926263809, 0.06928596645593643, 0.0468863844871521, 0.04682771861553192, 0.01808532141149044, 0.06207377463579178, 0.9884737133979797, 0.9972032308578491 ], [ 0.17652182281017303, 0.026668742299079895, 0.00405552051961422, 0.009770100004971027, 0.00747432466596365, 0.03757423907518387, 0.04533827304840088, 0.0353049673140049, 0.023892344906926155, 0.008243552409112453 ], [ 0.1740839034318924, 0.004004788585007191, 0.027846798300743103, 0.007262152153998613, 0.0004968640860170126, 0.08337613940238953, 0.0009009792120195925, 0.014789505861699581, 0.021282393485307693, 0.001457786071114242, 0.0169075895100832, 0.03144504874944687, 0.03690486401319504, 0.053762272000312805, 0.03317485749721527, 0.007302488200366497, 0.017193671315908432, 0.16104348003864288, 0.6244720220565796, 0.00408270163461566 ], [ 0.174080953001976, 0.012989471666514874, 0.012068279087543488, 0.0006185686797834933, 0.015986783429980278, 0.011577090248465538, 0.0066572753712534904, 0.06393027305603027, 0.08286602050065994, 0.9365168213844299, 0.002981869038194418 ], [ 0.17408211529254913, 0.003838935401290655, 0.025704383850097656, 0.007868479005992413, 0.04710879549384117, 0.0005797175108455122, 0.018643468618392944, 0.0007324509788304567, 0.03895237296819687, 0.00404472416266799, 0.0472337007522583, 0.06816552579402924, 0.010939235799014568, 0.06671485304832458, 0.12213069945573807, 0.09272684156894684, 0.9905235171318054 ], [ 0.17652273178100586, 0.04489562287926674, 0.05809967592358589, 0.060857776552438736, 0.05496970936655998, 0.06191984564065933, 0.07372570782899857, 0.03427250310778618, 0.09845757484436035, 0.1264147311449051, 0.027191447094082832, 0.06628574430942535, 0.022437749430537224, 0.9591619372367859, 0.9906209707260132 ], [ 0.17652219533920288, 0.00282285432331264, 0.02444107085466385, 0.003998425789177418, 0.015073506161570549, 0.00025717387325130403, 0.01873968541622162, 0.0006260861991904676, 0.06497830897569656, 0.09568121284246445, 0.017328117042779922, 0.026809075847268105, 0.05417541041970253, 0.012637468054890633, 0.0010163610568270087, 0.12266436219215393, 0.013939105905592442, 0.03412476181983948, 0.01825321838259697, 0.9698987603187561, 0.9909419417381287 ], [ 0.17652204632759094, 0.051642708480358124, 0.040628451853990555, 0.04422154277563095, 0.09522038698196411, 0.004547095857560635, 0.060744721442461014, 0.020266247913241386, 0.012293072417378426, 0.026869406923651695, 0.03975309804081917, 0.020038483664393425, 0.4934953451156616, 0.07130502164363861, 0.01548272930085659, 0.005651956424117088 ], [ 0.2234957069158554, 0.23893699049949646, 0.12119182199239731, 0.0040323552675545216, 0.05785253271460533, 0.06776273250579834, 0.025935037061572075, 0.09212657809257507, 0.03390422463417053, 0.9732660055160522, 0.9931426048278809 ], [ 0.17652231454849243, 0.026668455451726913, 0.00405558617785573, 0.00977012887597084, 0.006888058502227068, 0.015749139711260796, 0.02028876356780529, 0.010707513429224491, 0.019145945087075233, 0.029377097263932228, 0.24254922568798065, 0.003618056420236826 ] ] }, { "q_id": "9090_mmlu_physics", "cot_ids": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.8550746440887451, 0.031081490218639374, 0.7549638748168945, 0.0537731908261776, 0.9730720520019531, 0.0021214494481682777 ], [ 0.8340891599655151, 0.7752222418785095, 0.9668045043945312, 0.0027558787260204554 ], [ 0.5542104244232178, 0.04133503511548042, 0.5959997177124023, 0.664755642414093, 0.9672407507896423, 0.0019630463793873787 ], [ 0.5342217087745667, 0.7174567580223083, 0.9051993489265442, 0.9809807538986206, 0.9967239499092102 ], [ 0.5542119741439819, 0.03915625810623169, 0.7098002433776855, 0.05060194805264473, 0.6217836737632751, 0.03631607070565224, 0.9447118043899536, 0.002879493637010455 ], [ 0.5946192145347595, 0.04821901023387909, 0.5957116484642029, 0.028820466250181198, 0.8765799403190613, 0.034155186265707016, 0.9815461039543152, 0.996639609336853 ], [ 0.8665419816970825, 0.8181772828102112, 0.9795315265655518, 0.001950486097484827 ], [ 0.8054459691047668, 0.9069061279296875, 0.9844478368759155, 0.9975559711456299 ], [ 0.5718445777893066, 0.7391722202301025, 0.7144021987915039, 0.9327430725097656, 0.9944191575050354 ], [ 0.8221679925918579, 0.8077308535575867, 0.9721882343292236, 0.0022603708785027266 ], [ 0.866204023361206, 0.7338604927062988, 0.9361476898193359, 0.9946411848068237 ], [ 0.8009731769561768, 0.7498985528945923, 0.9639313817024231, 0.9961094260215759 ], [ 0.8086415529251099, 0.032759491354227066, 0.7230033874511719, 0.049768801778554916, 0.9660230278968811, 0.002301896922290325 ], [ 0.8234907388687134, 0.8154098391532898, 0.9698582887649536, 0.0022504827938973904 ], [ 0.8428027629852295, 0.7945296764373779, 0.975864589214325, 0.001991561846807599 ], [ 0.8304629921913147, 0.8084791898727417, 0.9727858901023865, 0.0023384287487715483 ] ] }, { "q_id": "9335_mmlu_physics", "cot_ids": [ 0, 1, 2, 6, 8, 9, 10, 13, 14, 15 ], "rewards": [ [ 0.4018079340457916, 0.12062618136405945, 0.49015066027641296, 0.01532721146941185, 0.48373880982398987, 0.06598532944917679, 0.2506610155105591, 0.002292035613209009, 0.004533669445663691 ], [ 0.7684919238090515, 0.06928686052560806, 0.0004462556098587811, 0.24326612055301666, 0.5793244242668152, 0.31253597140312195, 0.061693113297224045, 0.16404420137405396, 0.07892339676618576, 0.0030924018938094378, 0.003266214858740568 ], [ 0.7139213681221008, 0.12233129888772964, 0.040407683700323105, 0.22615738213062286, 0.04259960725903511, 0.0002735255111474544 ], [ 0.6511660814285278, 0.1090688481926918, 0.12077189236879349, 0.00024711646256037056, 0.8521575331687927, 0.9795006513595581, 0.0003151877026539296 ], [ 0.6495306491851807, 0.052731551229953766, 0.10537976026535034, 0.0001600858522579074, 0.21813540160655975, 0.4198927879333496, 0.09012892097234726, 0.16829648613929749, 0.003599573392421007, 0.0034001218155026436 ], [ 0.49813175201416016, 0.0670730248093605, 0.13130800426006317, 0.42798495292663574, 0.18760760128498077, 0.07240244746208191, 0.00039892568020150065 ], [ 0.6971254348754883, 0.019532790407538414, 0.05625596269965172, 0.00020956635125912726, 0.2201501727104187, 0.2484823614358902, 0.7138908505439758, 0.0959593653678894, 0.21540232002735138, 0.002891906537115574, 0.0023838437628000975 ], [ 0.0886986181139946, 0.03048121929168701, 0.12560239434242249, 0.00030536961276084185, 0.050893764942884445, 0.02792220748960972, 0.02546907775104046, 0.3793383240699768, 0.8631102442741394, 0.00023547638556919992 ], [ 0.40597426891326904, 0.006277185864746571, 0.06437043845653534, 0.006629521027207375, 0.02204720862209797, 0.002658562734723091, 0.00020509681780822575, 0.27850142121315, 0.009865676052868366, 0.39566606283187866, 0.03172909840941429, 0.025145811960101128, 0.0028068653773516417, 0.006372870411723852, 0.0006710750167258084, 0.0006787281599827111 ], [ 0.5475825667381287, 0.05344342812895775, 0.11360762268304825, 0.00021784953423775733, 0.21543146669864655, 0.027037611231207848, 0.34999537467956543, 0.9443829655647278, 0.000246886134846136 ] ] }, { "q_id": "9272_mmlu_physics", "cot_ids": [ 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], "rewards": [ [ 0.891586184501648, 0.013594395481050014, 0.06689615547657013, 0.0003475997073110193, 0.07925660163164139, 0.06689433753490448, 0.0017256800783798099, 0.0067612347193062305, 0.028974030166864395, 0.40913066267967224, 0.00038459611823782325 ], [ 0.8915855884552002, 0.055135954171419144, 0.011566770263016224, 0.05249078944325447, 0.0002039675018750131, 0.08220749348402023, 0.07551335543394089, 0.14013125002384186, 0.01577162556350231, 0.05253138393163681, 0.05569485202431679, 0.00036832777550444007 ], [ 0.8915873169898987, 0.05634704604744911, 0.1060108169913292, 0.010495551861822605, 0.03814731165766716, 0.00012711489398498088, 0.07172493636608124, 0.12920425832271576, 0.08272799104452133, 0.005268061067909002, 0.08887896686792374, 0.011955549009144306, 0.0562981478869915, 0.09919100254774094, 0.9999048709869385 ], [ 0.969228982925415, 0.13128820061683655, 0.03979925066232681, 0.14328555762767792, 0.9998939037322998 ], [ 0.9823136925697327, 0.08078300952911377, 0.02537355199456215, 0.0004849931283388287, 0.06983435153961182, 0.040136728435754776, 0.10262337327003479, 0.002844688016921282, 0.006377944257110357, 0.001084075658582151, 0.020595401525497437, 0.03134354576468468, 0.3314295709133148, 0.03468797355890274, 0.10507598519325256, 0.007146874442696571, 0.06890115141868591, 0.039869993925094604, 0.00041522906394675374 ], [ 0.4846816658973694, 0.020131422206759453, 0.04756522178649902, 0.0003319997922517359, 0.05667730048298836, 0.05943237617611885, 0.07876681536436081, 0.020061418414115906, 0.05593578889966011, 0.0005358390044420958, 0.011449377983808517, 0.008898253552615643, 0.08806339651346207, 0.013325962238013744, 0.001509966212324798, 0.0005152797093614936 ], [ 0.9745054244995117, 0.009289605543017387, 0.05174785107374191, 0.00041671787039376795, 0.08982851356267929, 0.14445403218269348, 0.03612260892987251, 0.09224916994571686, 0.01243891753256321, 0.06508085131645203, 0.2102520912885666, 0.9999297857284546 ], [ 0.02832024358212948, 0.04529445618391037, 0.0003263066755607724, 0.06516455113887787, 0.008653425611555576, 0.10978861153125763, 0.0015952233225107193, 0.18874409794807434, 0.9098809361457825, 0.00034892643452621996 ], [ 0.9709439277648926, 0.010737031698226929, 0.0559641495347023, 0.00030861777486279607, 0.0845278650522232, 0.0012055471306666732, 0.003469996154308319, 0.024972859770059586, 0.7802385687828064, 0.9999099969863892 ], [ 0.8915860652923584, 0.007437076419591904, 0.06391777098178864, 0.0001509035937488079, 0.06181259825825691, 0.11226481199264526, 0.015810353681445122, 0.06521089375019073, 0.011579692363739014, 0.062217094004154205, 0.006502301432192326, 0.001899417140521109, 0.000481429451610893 ], [ 0.9209674596786499, 0.014116798527538776, 0.047625429928302765, 0.00010523802484385669, 0.0809527114033699, 0.16908790171146393, 0.0016453452408313751, 0.004395290277898312, 0.0009111354011110961, 0.030786944553256035, 0.3676415681838989, 0.9998788833618164 ], [ 0.9633383750915527, 0.018376540392637253, 0.04606953635811806, 0.0003607643593568355, 0.04769223928451538, 0.038337282836437225, 0.08685878664255142, 0.9562309980392456, 0.9999175071716309 ], [ 0.8544458746910095, 0.020001644268631935, 0.05252786725759506, 0.06575649976730347, 0.0015461848815903068, 0.011092426255345345, 0.02385268732905388, 0.015843607485294342, 0.02450062893331051, 0.07041516900062561, 0.044303879141807556, 0.084873266518116, 0.02474134974181652, 0.04630079120397568, 0.030035726726055145, 0.07940062880516052, 0.05146043747663498, 0.0015664024977013469, 0.0005044676945544779 ], [ 0.9709445238113403, 0.013224913738667965, 0.06903611868619919, 0.0002702404744923115, 0.06364402920007706, 0.18259620666503906, 0.0037245580460876226, 0.05914974585175514, 0.0011983646545559168, 0.08988062292337418, 0.01810469478368759, 0.026273569092154503, 0.04227367043495178, 0.019312573596835136, 0.06728652864694595, 0.006695999298244715, 0.9997298121452332 ], [ 0.9709433913230896, 0.009212395176291466, 0.053809721022844315, 0.08403301984071732, 0.040494006127119064, 0.10435433685779572, 0.0052640121430158615, 0.030196944251656532, 0.0005516940727829933, 0.002911070827394724, 0.0023638929706066847, 0.0531512051820755, 0.046910256147384644, 0.9998754262924194 ] ] } ]