family stringclasses 1 value | question_id int64 0 2 | signal_type stringclasses 2 values | amplitude_scale float64 0.5 2.5 | frequency_cycles float64 1 16 | phase_deg float64 0 240 ⌀ | time_step int64 0 255 | p_value float64 3.5 4.5 | prompt stringlengths 59 76 | ground_truth float64 0.52 2.33 | symbolic_baseline_answer float64 0.52 2.33 |
|---|---|---|---|---|---|---|---|---|---|---|
linear_system | 1 | sinusoid | 1 | 1 | 240 | 20 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 21 | 3.993456 | Solve this system for x:
3.9934561834356446x + 2y = 8
1x + 3y = 9
FINAL: | 0.60118 | 0.60118 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 22 | 4.013081 | Solve this system for x:
4.013080625846029x + 2y = 8
1x + 3y = 9
FINAL: | 0.597655 | 0.597655 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 23 | 4.032579 | Solve this system for x:
4.032579094678917x + 2y = 8
1x + 3y = 9
FINAL: | 0.594193 | 0.594193 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 24 | 4.051764 | Solve this system for x:
4.051763809020504x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 25 | 4.07045 | Solve this system for x:
4.070450009584246x + 2y = 8
1x + 3y = 9
FINAL: | 0.587581 | 0.587581 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 26 | 4.088458 | Solve this system for x:
4.0884577380438x + 2y = 8
1x + 3y = 9
FINAL: | 0.584489 | 0.584489 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 27 | 4.105614 | Solve this system for x:
4.105613570130074x + 2y = 8
1x + 3y = 9
FINAL: | 0.581573 | 0.581573 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 28 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 29 | 4.136718 | Solve this system for x:
4.136718460404574x + 2y = 8
1x + 3y = 9
FINAL: | 0.57636 | 0.57636 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 30 | 4.150368 | Solve this system for x:
4.150367961495795x + 2y = 8
1x + 3y = 9
FINAL: | 0.574102 | 0.574102 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 31 | 4.162569 | Solve this system for x:
4.162569336918323x + 2y = 8
1x + 3y = 9
FINAL: | 0.572098 | 0.572098 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 32 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 33 | 4.182173 | Solve this system for x:
4.1821727649842355x + 2y = 8
1x + 3y = 9
FINAL: | 0.568908 | 0.568908 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 34 | 4.189386 | Solve this system for x:
4.189386025899021x + 2y = 8
1x + 3y = 9
FINAL: | 0.567743 | 0.567743 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 35 | 4.194775 | Solve this system for x:
4.1947753958554665x + 2y = 8
1x + 3y = 9
FINAL: | 0.566876 | 0.566876 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 36 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 37 | 4.199893 | Solve this system for x:
4.199892917495273x + 2y = 8
1x + 3y = 9
FINAL: | 0.566055 | 0.566055 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 38 | 4.199572 | Solve this system for x:
4.199571784647721x + 2y = 8
1x + 3y = 9
FINAL: | 0.566106 | 0.566106 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 39 | 4.197329 | Solve this system for x:
4.1973286664169756x + 2y = 8
1x + 3y = 9
FINAL: | 0.566466 | 0.566466 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 40 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 41 | 4.187181 | Solve this system for x:
4.1871811853514656x + 2y = 8
1x + 3y = 9
FINAL: | 0.568099 | 0.568099 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 42 | 4.179375 | Solve this system for x:
4.179374548306538x + 2y = 8
1x + 3y = 9
FINAL: | 0.569361 | 0.569361 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 43 | 4.16984 | Solve this system for x:
4.169840436305316x + 2y = 8
1x + 3y = 9
FINAL: | 0.570911 | 0.570911 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 44 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 45 | 4.145973 | Solve this system for x:
4.145972814539567x + 2y = 8
1x + 3y = 9
FINAL: | 0.574827 | 0.574827 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 46 | 4.131869 | Solve this system for x:
4.1318691630200135x + 2y = 8
1x + 3y = 9
FINAL: | 0.577167 | 0.577167 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 47 | 4.116496 | Solve this system for x:
4.1164955393735605x + 2y = 8
1x + 3y = 9
FINAL: | 0.579739 | 0.579739 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 48 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 49 | 4.082541 | Solve this system for x:
4.082541405960879x + 2y = 8
1x + 3y = 9
FINAL: | 0.585502 | 0.585502 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 50 | 4.064288 | Solve this system for x:
4.064287893060633x + 2y = 8
1x + 3y = 9
FINAL: | 0.588647 | 0.588647 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 51 | 4.045415 | Solve this system for x:
4.045415252606875x + 2y = 8
1x + 3y = 9
FINAL: | 0.591935 | 0.591935 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 52 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 53 | 4.006544 | Solve this system for x:
4.006543816564355x + 2y = 8
1x + 3y = 9
FINAL: | 0.598824 | 0.598824 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 54 | 3.986919 | Solve this system for x:
3.9869193741539717x + 2y = 8
1x + 3y = 9
FINAL: | 0.602364 | 0.602364 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 55 | 3.967421 | Solve this system for x:
3.9674209053210823x + 2y = 8
1x + 3y = 9
FINAL: | 0.605922 | 0.605922 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 56 | 3.948236 | Solve this system for x:
3.948236190979496x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 57 | 3.92955 | Solve this system for x:
3.9295499904157536x + 2y = 8
1x + 3y = 9
FINAL: | 0.612955 | 0.612955 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 58 | 3.911542 | Solve this system for x:
3.9115422619561997x + 2y = 8
1x + 3y = 9
FINAL: | 0.616356 | 0.616356 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 59 | 3.894386 | Solve this system for x:
3.8943864298699262x + 2y = 8
1x + 3y = 9
FINAL: | 0.619632 | 0.619632 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 60 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 61 | 3.863282 | Solve this system for x:
3.863281539595426x + 2y = 8
1x + 3y = 9
FINAL: | 0.625662 | 0.625662 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 62 | 3.849632 | Solve this system for x:
3.8496320385042044x + 2y = 8
1x + 3y = 9
FINAL: | 0.628345 | 0.628345 |
linear_system | 1 | sinusoid | 1 | 1 | 240 | 63 | 3.837431 | Solve this system for x:
3.837430663081677x + 2y = 8
1x + 3y = 9
FINAL: | 0.630763 | 0.630763 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 0 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 1 | 3.810614 | Solve this system for x:
3.810613974100979x + 2y = 8
1x + 3y = 9
FINAL: | 0.636143 | 0.636143 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 2 | 3.801711 | Solve this system for x:
3.801711027725238x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 3 | 3.800428 | Solve this system for x:
3.8004282153522793x + 2y = 8
1x + 3y = 9
FINAL: | 0.638211 | 0.638211 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 4 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 5 | 3.820625 | Solve this system for x:
3.8206254516934623x + 2y = 8
1x + 3y = 9
FINAL: | 0.634124 | 0.634124 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 6 | 3.841329 | Solve this system for x:
3.841329331941753x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 7 | 3.868131 | Solve this system for x:
3.868130836979986x + 2y = 8
1x + 3y = 9
FINAL: | 0.624714 | 0.624714 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 8 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 9 | 3.935712 | Solve this system for x:
3.9357121069393677x + 2y = 8
1x + 3y = 9
FINAL: | 0.611799 | 0.611799 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 10 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 11 | 4.013081 | Solve this system for x:
4.013080625846029x + 2y = 8
1x + 3y = 9
FINAL: | 0.597655 | 0.597655 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 12 | 4.051764 | Solve this system for x:
4.051763809020504x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 13 | 4.088458 | Solve this system for x:
4.0884577380438x + 2y = 8
1x + 3y = 9
FINAL: | 0.584489 | 0.584489 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 14 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 15 | 4.150368 | Solve this system for x:
4.150367961495795x + 2y = 8
1x + 3y = 9
FINAL: | 0.574102 | 0.574102 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 16 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 17 | 4.189386 | Solve this system for x:
4.189386025899021x + 2y = 8
1x + 3y = 9
FINAL: | 0.567743 | 0.567743 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 18 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 19 | 4.199572 | Solve this system for x:
4.199571784647721x + 2y = 8
1x + 3y = 9
FINAL: | 0.566106 | 0.566106 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 20 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 21 | 4.179375 | Solve this system for x:
4.179374548306538x + 2y = 8
1x + 3y = 9
FINAL: | 0.569361 | 0.569361 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 22 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 23 | 4.131869 | Solve this system for x:
4.1318691630200135x + 2y = 8
1x + 3y = 9
FINAL: | 0.577167 | 0.577167 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 24 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 25 | 4.064288 | Solve this system for x:
4.064287893060633x + 2y = 8
1x + 3y = 9
FINAL: | 0.588647 | 0.588647 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 26 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 27 | 3.986919 | Solve this system for x:
3.9869193741539717x + 2y = 8
1x + 3y = 9
FINAL: | 0.602364 | 0.602364 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 28 | 3.948236 | Solve this system for x:
3.948236190979496x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 29 | 3.911542 | Solve this system for x:
3.9115422619561997x + 2y = 8
1x + 3y = 9
FINAL: | 0.616356 | 0.616356 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 30 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 31 | 3.849632 | Solve this system for x:
3.8496320385042044x + 2y = 8
1x + 3y = 9
FINAL: | 0.628345 | 0.628345 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 32 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 33 | 3.810614 | Solve this system for x:
3.810613974100979x + 2y = 8
1x + 3y = 9
FINAL: | 0.636143 | 0.636143 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 34 | 3.801711 | Solve this system for x:
3.8017110277252377x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 35 | 3.800428 | Solve this system for x:
3.8004282153522793x + 2y = 8
1x + 3y = 9
FINAL: | 0.638211 | 0.638211 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 36 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 37 | 3.820625 | Solve this system for x:
3.8206254516934623x + 2y = 8
1x + 3y = 9
FINAL: | 0.634124 | 0.634124 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 38 | 3.841329 | Solve this system for x:
3.8413293319417527x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 39 | 3.868131 | Solve this system for x:
3.868130836979986x + 2y = 8
1x + 3y = 9
FINAL: | 0.624714 | 0.624714 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 40 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 41 | 3.935712 | Solve this system for x:
3.9357121069393677x + 2y = 8
1x + 3y = 9
FINAL: | 0.611799 | 0.611799 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 42 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 43 | 4.013081 | Solve this system for x:
4.013080625846028x + 2y = 8
1x + 3y = 9
FINAL: | 0.597655 | 0.597655 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 44 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 45 | 4.088458 | Solve this system for x:
4.0884577380438x + 2y = 8
1x + 3y = 9
FINAL: | 0.584489 | 0.584489 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 46 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 47 | 4.150368 | Solve this system for x:
4.150367961495795x + 2y = 8
1x + 3y = 9
FINAL: | 0.574102 | 0.574102 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 48 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 49 | 4.189386 | Solve this system for x:
4.1893860258990205x + 2y = 8
1x + 3y = 9
FINAL: | 0.567743 | 0.567743 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 50 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 51 | 4.199572 | Solve this system for x:
4.199571784647721x + 2y = 8
1x + 3y = 9
FINAL: | 0.566106 | 0.566106 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 52 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 53 | 4.179375 | Solve this system for x:
4.179374548306538x + 2y = 8
1x + 3y = 9
FINAL: | 0.569361 | 0.569361 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 54 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 55 | 4.131869 | Solve this system for x:
4.1318691630200135x + 2y = 8
1x + 3y = 9
FINAL: | 0.577167 | 0.577167 |
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