effective_operation stringclasses 4
values | encoded_tokens int64 17 162 | internal_answer stringlengths 4 7 | natural_answer stringlengths 1 8 | operand_a int64 -999 999 | operand_b int64 -999 999 | operand_digits stringclasses 9
values | operation stringclasses 4
values | prompt stringlengths 4 10 | representation stringclasses 1
value | result_sign stringclasses 2
values | rounding stringclasses 1
value | scenario stringclasses 25
values | sign_pattern stringclasses 4
values | split stringclasses 3
values | state stringlengths 6 6 | steps listlengths 0 21 | text stringlengths 37 276 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mul | 119 | 434232 | -232434 | -349 | 666 | 3x3 | * | -349*666= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 943666 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 54,
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"serialized": "9654054",
"term_index": 0
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{
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"kind": "column",
... | -349*666=<mul><neg><state>943666<step>9654054<col>405<step>9654059<step>4624083<col>308<step>9654062<step>4624086<step>3618104<col>410<step>4624034<step>3618052<col>205<step>3618023<col>302<ans>434232 |
div | 160 | 012.214 | -12.214 | -342 | 28 | 3x2 | / | -342/28= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 342028 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
"divisor": 28,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -342/28=<div><neg><state>342028<step>00030003<qmul>00000<rem>003<step>00340034<qmul>10028<rem>006<step>00620062<qmul>20056<rem>006<step>00600060<qmul>20056<rem>004<step>00400040<qmul>10028<rem>012<step>01200120<qmul>40112<rem>008<step>00800080<qmul>20056<rem>024<ans>012.214 |
add | 43 | 0560 | -650 | -639 | -11 | 3x2 | + | -639+-11= | scratchpad-v3 | negative | null | single_carry | -- | train | 936110 | [
{
"a_digit": 9,
"b_digit": 1,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "91001"
},
{
"a_digit": 3,
"b_digit": 1,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 5,
"serialized": "31150"
},
{
"a_digit":... | -639+-11=<add><neg><state>936110<step>91001<step>31150<step>60060<ans>0560 |
sub | 44 | 0000 | 0 | -508 | -508 | 3x3 | - | -508--508= | scratchpad-v3 | positive | null | identity | -- | train | 805805 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 8,
"output_digit": 0,
"serialized": "88000",
"subtrahend_digit": 8
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 0,
"output_digit": 0,
"serialized": "00000",
"subtrahend... | -508--508=<sub><pos><state>805805<step>88000<step>00000<step>55000<ans>0000 |
div | 161 | 015.511 | 15.511 | -698 | -45 | 3x2 | / | -698/-45= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 698045 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 45,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -698/-45=<div><pos><state>698045<step>00060006<qmul>00000<rem>006<step>00690069<qmul>10045<rem>024<step>02480248<qmul>50225<rem>023<step>02300230<qmul>50225<rem>005<step>00500050<qmul>10045<rem>005<step>00500050<qmul>10045<rem>005<step>00500050<qmul>10045<rem>005<ans>015.511 |
mul | 118 | 948470 | -74849 | 841 | -89 | 3x2 | * | 841*-89= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 148980 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 9,
"running_total": 9,
"serialized": "1909009",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 9,
"kind": "column",
"o... | 841*-89=<mul><neg><state>148980<step>1909009<col>900<step>1808008<step>4936044<col>404<step>1000004<step>4832036<step>8972108<col>810<step>4000010<step>8864074<col>407<step>8000007<col>700<ans>948470 |
mul | 118 | 954659 | 956459 | 973 | 983 | 3x3 | * | 973*983= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 379389 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 3,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 9,
"running_total": 9,
"serialized": "3309009",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 9,
"kind": "column",
"o... | 973*983=<mul><pos><state>379389<step>3309009<col>900<step>3824024<step>7321045<col>504<step>3927031<step>7856087<step>9327114<col>411<step>7963074<step>9872146<col>614<step>9981095<col>509<ans>954659 |
mul | 117 | 653410 | 14356 | 388 | 37 | 3x2 | * | 388*37= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 883730 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 56,
"running_total": 56,
"serialized": "8756056",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 5,
"column": 0,
"column_sum": 56,
"kind": "column",
... | 388*37=<mul><pos><state>883730<step>8756056<col>605<step>8324029<step>8756085<col>508<step>8000008<step>8324032<step>3721053<col>305<step>8000005<step>3309014<col>401<step>3000001<col>100<ans>653410 |
mul | 118 | 537300 | 3735 | -45 | -83 | 2x2 | * | -45*-83= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 540380 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 3,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 15,
"running_total": 15,
"serialized": "5315015",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 15,
"kind": "column",
... | -45*-83=<mul><pos><state>540380<step>5315015<col>501<step>5840041<step>4312053<col>305<step>5000005<step>4832037<step>0300037<col>703<step>4000003<step>0800003<col>300<step>0000000<col>000<ans>537300 |
mul | 116 | 041400 | 4140 | 92 | 45 | 2x2 | * | 92*45= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 290540 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 10,
"running_total": 10,
"serialized": "2510010",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 10,
"kind": "column",
... | 92*45=<mul><pos><state>290540<step>2510010<col>001<step>2408009<step>9545054<col>405<step>2000005<step>9436041<step>0500041<col>104<step>9000004<step>0400004<col>400<step>0000000<col>000<ans>041400 |
div | 20 | <nan> | NAN | -883 | 0 | 3x1 | / | -883/0= | scratchpad-v3 | positive | round-half-up | nan | -+ | train | 883000 | [] | -883/0=<div><pos><state>883000<ans><nan> |
mul | 117 | 277200 | -2772 | -63 | 44 | 2x2 | * | -63*44= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 360440 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 12,
"running_total": 12,
"serialized": "3412012",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 12,
"kind": "column",
... | -63*44=<mul><neg><state>360440<step>3412012<col>201<step>3412013<step>6424037<col>703<step>3000003<step>6424027<step>0400027<col>702<step>6000002<step>0400002<col>200<step>0000000<col>000<ans>277200 |
mul | 118 | 324490 | 94423 | 287 | 329 | 3x3 | * | 287*329= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 782923 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 63,
"running_total": 63,
"serialized": "7963063",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 63,
"kind": "column",
... | 287*329=<mul><pos><state>782923<step>7963063<col>306<step>7214020<step>8972092<col>209<step>7321030<step>8216046<step>2918064<col>406<step>8324030<step>2204034<col>403<step>2306009<col>900<ans>324490 |
sub | 39 | 9500 | 59 | 67 | 8 | 2x1 | - | 67-8= | scratchpad-v3 | positive | null | single_borrow | ++ | val | 760800 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 7,
"output_digit": 9,
"serialized": "78091",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 5,
"serialized": "60150",
"subtrahend... | 67-8=<sub><pos><state>760800<step>78091<step>60150<step>00000<ans>9500 |
div | 160 | 000.888 | 0.888 | -71 | -80 | 2x2 | / | -71/-80= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 071080 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 80,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -71/-80=<div><pos><state>071080<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00710071<qmul>00000<rem>071<step>07100710<qmul>80640<rem>070<step>07000700<qmul>80640<rem>060<step>06000600<qmul>70560<rem>040<step>04000400<qmul>50400<rem>000<ans>000.888 |
mul | 117 | 415400 | -4514 | 74 | -61 | 2x2 | * | 74*-61= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 470160 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 4,
"running_total": 4,
"serialized": "4104004",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 4,
"kind": "column",
"o... | 74*-61=<mul><neg><state>470160<step>4104004<col>400<step>4624024<step>7107031<col>103<step>4000003<step>7642045<step>0100045<col>504<step>7000004<step>0600004<col>400<step>0000000<col>000<ans>415400 |
sub | 42 | 8210 | 128 | 613 | 485 | 3x3 | - | 613-485= | scratchpad-v3 | positive | null | multi_borrow | ++ | val | 316584 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 8,
"serialized": "35081",
"subtrahend_digit": 5
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 2,
"serialized": "18121",
"subtrahend... | 613-485=<sub><pos><state>316584<step>35081<step>18121<step>64110<ans>8210 |
add | 44 | 3270 | -723 | -124 | -599 | 3x3 | + | -124+-599= | scratchpad-v3 | negative | null | multi_carry | -- | train | 421995 | [
{
"a_digit": 4,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 3,
"serialized": "49031"
},
{
"a_digit": 2,
"b_digit": 9,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "29121"
},
{
"a_digit":... | -124+-599=<add><neg><state>421995<step>49031<step>29121<step>15170<ans>3270 |
add | 44 | 9850 | -589 | -248 | -341 | 3x3 | + | -248+-341= | scratchpad-v3 | negative | null | no_carry | -- | train | 842143 | [
{
"a_digit": 8,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "81090"
},
{
"a_digit": 4,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "44080"
},
{
"a_digit":... | -248+-341=<add><neg><state>842143<step>81090<step>44080<step>23050<ans>9850 |
mul | 119 | 245586 | -685542 | -858 | 799 | 3x3 | * | -858*799= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 858997 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 72,
"running_total": 72,
"serialized": "8972072",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 7,
"column": 0,
"column_sum": 72,
"kind": "column",
... | -858*799=<mul><neg><state>858997<step>8972072<col>207<step>8972079<step>5945124<col>412<step>8756068<step>5945113<step>8972185<col>518<step>5735053<step>8972125<col>512<step>8756068<col>806<ans>245586 |
div | 162 | 000.724 | 0.724 | -610 | -842 | 3x3 | / | -610/-842= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 610842 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 842,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -610/-842=<div><pos><state>610842<step>00060006<qmul>00000<rem>006<step>00610061<qmul>00000<rem>061<step>06100610<qmul>00000<rem>610<step>61006100<qmul>75894<rem>206<step>20602060<qmul>21684<rem>376<step>37603760<qmul>43368<rem>392<step>39203920<qmul>43368<rem>552<ans>000.724 |
add | 44 | 7211 | -1127 | -435 | -692 | 3x3 | + | -435+-692= | scratchpad-v3 | negative | null | overflow | -- | train | 534296 | [
{
"a_digit": 5,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "52070"
},
{
"a_digit": 3,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "39021"
},
{
"a_digit":... | -435+-692=<add><neg><state>534296<step>52070<step>39021<step>46111<ans>7211 |
div | 159 | 000.718 | -0.718 | 56 | -78 | 2x2 | / | 56/-78= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 056078 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 78,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 56/-78=<div><neg><state>056078<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00560056<qmul>00000<rem>056<step>05600560<qmul>70546<rem>014<step>01400140<qmul>10078<rem>062<step>06200620<qmul>70546<rem>074<step>07400740<qmul>90702<rem>038<ans>000.718 |
div | 160 | 000.718 | 0.718 | -51 | -71 | 2x2 | / | -51/-71= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 051071 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 71,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -51/-71=<div><pos><state>051071<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00510051<qmul>00000<rem>051<step>05100510<qmul>70497<rem>013<step>01300130<qmul>10071<rem>059<step>05900590<qmul>80568<rem>022<step>02200220<qmul>30213<rem>007<ans>000.718 |
add | 41 | 1820 | 281 | 237 | 44 | 3x2 | + | 237+44= | scratchpad-v3 | positive | null | single_carry | ++ | train | 732440 | [
{
"a_digit": 7,
"b_digit": 4,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "74011"
},
{
"a_digit": 3,
"b_digit": 4,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "34180"
},
{
"a_digit":... | 237+44=<add><pos><state>732440<step>74011<step>34180<step>20020<ans>1820 |
add | 42 | 2140 | 412 | 168 | 244 | 3x3 | + | 168+244= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 861442 | [
{
"a_digit": 8,
"b_digit": 4,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 2,
"serialized": "84021"
},
{
"a_digit": 6,
"b_digit": 4,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "64111"
},
{
"a_digit":... | 168+244=<add><pos><state>861442<step>84021<step>64111<step>12140<ans>2140 |
div | 160 | 013.528 | -13.528 | -974 | 72 | 3x2 | / | -974/72= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 974072 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 72,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -974/72=<div><neg><state>974072<step>00090009<qmul>00000<rem>009<step>00970097<qmul>10072<rem>025<step>02540254<qmul>30216<rem>038<step>03800380<qmul>50360<rem>020<step>02000200<qmul>20144<rem>056<step>05600560<qmul>70504<rem>056<step>05600560<qmul>70504<rem>056<ans>013.528 |
mul | 117 | 270270 | 72072 | 858 | 84 | 3x2 | * | 858*84= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 858480 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 32,
"running_total": 32,
"serialized": "8432032",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 32,
"kind": "column",
... | 858*84=<mul><pos><state>858480<step>8432032<col>203<step>8864067<step>5420087<col>708<step>8000008<step>5840048<step>8432080<col>008<step>5000008<step>8864072<col>207<step>8000007<col>700<ans>270270 |
sub | 42 | 7830 | 387 | 834 | 447 | 3x3 | - | 834-447= | scratchpad-v3 | positive | null | multi_borrow | ++ | test | 438744 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "47071",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 8,
"serialized": "34181",
"subtrahend... | 834-447=<sub><pos><state>438744<step>47071<step>34181<step>84130<ans>7830 |
add | 38 | 5000 | 5 | 2 | 3 | 1x1 | + | 2+3= | scratchpad-v3 | positive | null | no_carry | ++ | train | 200300 | [
{
"a_digit": 2,
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{
"a_digit":... | 2+3=<add><pos><state>200300<step>23050<step>00000<step>00000<ans>5000 |
mul | 120 | 065475 | 574560 | -864 | -665 | 3x3 | * | -864*-665= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 468566 | [
{
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... | -864*-665=<mul><pos><state>468566<step>4520020<col>002<step>4624026<step>6530056<col>605<step>4624029<step>6636065<step>8540105<col>510<step>6636046<step>8648094<col>409<step>8648057<col>705<ans>065475 |
mul | 118 | 588474 | 474885 | 549 | 865 | 3x3 | * | 549*865= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 945568 | [
{
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{
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... | 549*865=<mul><pos><state>945568<step>9545045<col>504<step>9654058<step>4520078<col>807<step>9872079<step>4624103<step>5525128<col>812<step>4832044<step>5630074<col>407<step>5840047<col>704<ans>588474 |
mul | 117 | 440550 | 55044 | 99 | 556 | 2x3 | * | 99*556= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 990655 | [
{
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{
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... | 99*556=<mul><pos><state>990655<step>9654054<col>405<step>9545050<step>9654104<col>410<step>9545055<step>9545100<step>0600100<col>010<step>9545055<step>0500055<col>505<step>0500005<col>500<ans>440550 |
div | 159 | 316.000 | -316 | 632 | -2 | 3x1 | / | 632/-2= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 632002 | [
{
"incoming_digit": 6,
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{
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{
"kind": ... | 632/-2=<div><neg><state>632002<step>00060006<qmul>30006<rem>000<step>00030003<qmul>10002<rem>001<step>00120012<qmul>60012<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>316.000 |
sub | 42 | 7000 | 7 | -37 | -44 | 2x2 | - | -37--44= | scratchpad-v3 | positive | null | single_borrow | -- | train | 440730 | [
{
"borrow_in": 0,
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{
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"serialized": "43100",
"subtrahend... | -37--44=<sub><pos><state>440730<step>47071<step>43100<step>00000<ans>7000 |
add | 40 | 8510 | 158 | 76 | 82 | 2x2 | + | 76+82= | scratchpad-v3 | positive | null | single_carry | ++ | train | 670280 | [
{
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{
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"serialized": "78051"
},
{
"a_digit":... | 76+82=<add><pos><state>670280<step>62080<step>78051<step>00110<ans>8510 |
add | 42 | 5350 | -535 | -63 | 472 | 2x3 | - | -63-472= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 360274 | [
{
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{
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"serialized": "67031"
},
{
"a_digit":... | -63-472=<add><neg><state>360274<step>32050<step>67031<step>04150<ans>5350 |
mul | 118 | 842487 | 784248 | 797 | 984 | 3x3 | * | 797*984= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 797489 | [
{
"a_digit": 7,
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},
{
"carry_in": 0,
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"kind": "column",
... | 797*984=<mul><pos><state>797489<step>7428028<col>802<step>7856058<step>9436094<col>409<step>7963072<step>9872144<step>7428172<col>217<step>9981098<step>7856154<col>415<step>7963078<col>807<ans>842487 |
div | 161 | 000.701 | -0.701 | 681 | -972 | 3x3 | / | 681/-972= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 681972 | [
{
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},
{
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"serialized": "00000"
},
{
"kind"... | 681/-972=<div><neg><state>681972<step>00060006<qmul>00000<rem>006<step>00680068<qmul>00000<rem>068<step>06810681<qmul>00000<rem>681<step>68106810<qmul>76804<rem>006<step>00600060<qmul>00000<rem>060<step>06000600<qmul>00000<rem>600<step>60006000<qmul>65832<rem>168<ans>000.701 |
div | 161 | 000.994 | -0.994 | -461 | 464 | 3x3 | / | -461/464= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | -+ | train | 461464 | [
{
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},
{
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{
"kind"... | -461/464=<div><neg><state>461464<step>00040004<qmul>00000<rem>004<step>00460046<qmul>00000<rem>046<step>04610461<qmul>00000<rem>461<step>46104610<qmul>94176<rem>434<step>43404340<qmul>94176<rem>164<step>16401640<qmul>31392<rem>248<step>24802480<qmul>52320<rem>160<ans>000.994 |
mul | 119 | 663640 | 46366 | -478 | -97 | 3x2 | * | -478*-97= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 874790 | [
{
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},
{
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"kind": "column",
... | -478*-97=<mul><pos><state>874790<step>8756056<col>605<step>8972077<step>7749126<col>612<step>8000012<step>7963075<step>4728103<col>310<step>7000010<step>4936046<col>604<step>4000004<col>400<ans>663640 |
div | 162 | 001.640 | 1.64 | -884 | -539 | 3x3 | / | -884/-539= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 884539 | [
{
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},
{
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"serialized": "00000"
},
{
"kind"... | -884/-539=<div><pos><state>884539<step>00080008<qmul>00000<rem>008<step>00880088<qmul>00000<rem>088<step>08840884<qmul>10539<rem>345<step>34503450<qmul>63234<rem>216<step>21602160<qmul>42156<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>00000<rem>400<ans>001.640 |
sub | 39 | 3800 | -83 | 2 | 85 | 1x2 | - | 2-85= | scratchpad-v3 | negative | null | negative_result | ++ | train | 580200 | [
{
"borrow_in": 0,
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"serialized": "52030",
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},
{
"borrow_in": 0,
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"column": 1,
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"output_digit": 8,
"serialized": "80080",
"subtrahend... | 2-85=<sub><neg><state>580200<step>52030<step>80080<step>00000<ans>3800 |
add | 41 | 7980 | 897 | 63 | 834 | 2x3 | + | 63+834= | scratchpad-v3 | positive | null | no_carry | ++ | train | 360438 | [
{
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},
{
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"column": 1,
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"serialized": "63090"
},
{
"a_digit":... | 63+834=<add><pos><state>360438<step>34070<step>63090<step>08080<ans>7980 |
add | 43 | 1640 | -461 | -404 | -57 | 3x2 | + | -404+-57= | scratchpad-v3 | negative | null | single_carry | -- | train | 404750 | [
{
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},
{
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"column": 1,
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"serialized": "05160"
},
{
"a_digit":... | -404+-57=<add><neg><state>404750<step>47011<step>05160<step>40040<ans>1640 |
add | 44 | 2051 | -1502 | -854 | -648 | 3x3 | + | -854+-648= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 458846 | [
{
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},
{
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"serialized": "54101"
},
{
"a_digit":... | -854+-648=<add><neg><state>458846<step>48021<step>54101<step>86151<ans>2051 |
sub | 43 | 3550 | 553 | -47 | -600 | 2x3 | - | -47--600= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 006740 | [
{
"borrow_in": 0,
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},
{
"borrow_in": 1,
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"column": 1,
"minuend_digit": 0,
"output_digit": 5,
"serialized": "04151",
"subtrahend... | -47--600=<sub><pos><state>006740<step>07031<step>04151<step>60150<ans>3550 |
sub | 42 | 0800 | -80 | -113 | 33 | 3x2 | + | -113+33= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 311330 | [
{
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},
{
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"column": 1,
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"output_digit": 8,
"serialized": "13081",
"subtrahend... | -113+33=<sub><neg><state>311330<step>33000<step>13081<step>10100<ans>0800 |
mul | 119 | 562927 | -729265 | -785 | 929 | 3x3 | * | -785*929= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 587929 | [
{
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},
{
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"kind": "column",
... | -785*929=<mul><neg><state>587929<step>5945045<col>504<step>5210014<step>8972086<col>608<step>5945053<step>8216069<step>7963132<col>213<step>8972085<step>7214099<col>909<step>7963072<col>207<ans>562927 |
add | 42 | 2080 | 802 | 328 | 474 | 3x3 | + | 328+474= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 823474 | [
{
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},
{
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"carry_in": 1,
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"column": 1,
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"serialized": "27101"
},
{
"a_digit":... | 328+474=<add><pos><state>823474<step>84021<step>27101<step>34180<ans>2080 |
sub | 41 | 2610 | 162 | 230 | 68 | 3x2 | - | 230-68= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 032860 | [
{
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"serialized": "08021",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 6,
"serialized": "36161",
"subtrahend... | 230-68=<sub><pos><state>032860<step>08021<step>36161<step>20110<ans>2610 |
div | 160 | 013.985 | -13.985 | -909 | 65 | 3x2 | / | -909/65= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 909065 | [
{
"incoming_digit": 9,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | -909/65=<div><neg><state>909065<step>00090009<qmul>00000<rem>009<step>00900090<qmul>10065<rem>025<step>02590259<qmul>30195<rem>064<step>06400640<qmul>90585<rem>055<step>05500550<qmul>80520<rem>030<step>03000300<qmul>40260<rem>040<step>04000400<qmul>60390<rem>010<ans>013.985 |
mul | 118 | 554896 | 698455 | 815 | 857 | 3x3 | * | 815*857= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 518758 | [
{
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},
{
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"column_sum": 35,
"kind": "column",
... | 815*857=<mul><pos><state>518758<step>5735035<col>503<step>5525028<step>1707035<col>503<step>5840043<step>1505048<step>8756104<col>410<step>1808018<step>8540058<col>805<step>8864069<col>906<ans>554896 |
mul | 120 | 033369 | 963330 | -985 | -978 | 3x3 | * | -985*-978= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 589879 | [
{
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},
{
"carry_in": 0,
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"column": 0,
"column_sum": 40,
"kind": "column",
... | -985*-978=<mul><pos><state>589879<step>5840040<col>004<step>5735039<step>8864103<col>310<step>5945055<step>8756111<step>9872183<col>318<step>8972090<step>9763153<col>315<step>9981096<col>609<ans>033369 |
sub | 42 | 1020 | 201 | 523 | 322 | 3x3 | - | 523-322= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 325223 | [
{
"borrow_in": 0,
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"output_digit": 1,
"serialized": "32010",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 0,
"serialized": "22000",
"subtrahend... | 523-322=<sub><pos><state>325223<step>32010<step>22000<step>53020<ans>1020 |
sub | 42 | 4360 | 634 | 655 | -21 | 3x2 | + | 655+-21= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 556120 | [
{
"borrow_in": 0,
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"serialized": "51040",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 5,
"output_digit": 3,
"serialized": "52030",
"subtrahend... | 655+-21=<sub><pos><state>556120<step>51040<step>52030<step>60060<ans>4360 |
mul | 117 | 977400 | -4779 | -81 | 59 | 2x2 | * | -81*59= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 180950 | [
{
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},
{
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"column_sum": 9,
"kind": "column",
"o... | -81*59=<mul><neg><state>180950<step>1909009<col>900<step>1505005<step>8972077<col>707<step>1000007<step>8540047<step>0900047<col>704<step>8000004<step>0500004<col>400<step>0000000<col>000<ans>977400 |
div | 159 | 004.854 | 4.854 | 233 | 48 | 3x2 | / | 233/48= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | val | 233048 | [
{
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},
{
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"serialized": "00000"
},
{
"kind":... | 233/48=<div><pos><state>233048<step>00020002<qmul>00000<rem>002<step>00230023<qmul>00000<rem>023<step>02330233<qmul>40192<rem>041<step>04100410<qmul>80384<rem>026<step>02600260<qmul>50240<rem>020<step>02000200<qmul>40192<rem>008<step>00800080<qmul>10048<rem>032<ans>004.854 |
mul | 119 | 561750 | -57165 | -111 | 515 | 3x3 | * | -111*515= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 111515 | [
{
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},
{
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"o... | -111*515=<mul><neg><state>111515<step>1505005<col>500<step>1101001<step>1505006<col>600<step>1505005<step>1101006<step>1505011<col>101<step>1505006<step>1101007<col>700<step>1505005<col>500<ans>561750 |
div | 160 | 000.082 | -0.082 | -41 | 503 | 2x3 | / | -41/503= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | -+ | train | 041503 | [
{
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},
{
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"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -41/503=<div><neg><state>041503<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00410041<qmul>00000<rem>041<step>04100410<qmul>00000<rem>410<step>41004100<qmul>84024<rem>076<step>07600760<qmul>10503<rem>257<step>25702570<qmul>52515<rem>055<ans>000.082 |
mul | 120 | 886576 | 675688 | -712 | -949 | 3x3 | * | -712*-949= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 217949 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 9,
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"column": 0,
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"serialized": "2918018",
"term_index": 0
},
{
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"kind": "column",
... | -712*-949=<mul><pos><state>217949<step>2918018<col>801<step>2408009<step>1909018<col>801<step>2918019<step>1404023<step>7963086<col>608<step>1909017<step>7428045<col>504<step>7963067<col>706<ans>886576 |
add | 42 | 9231 | 1329 | 441 | 888 | 3x3 | + | 441+888= | scratchpad-v3 | positive | null | overflow | ++ | train | 144888 | [
{
"a_digit": 1,
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"carry_in": 0,
"carry_out": 0,
"column": 0,
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},
{
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"carry_in": 0,
"carry_out": 1,
"column": 1,
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"serialized": "48021"
},
{
"a_digit":... | 441+888=<add><pos><state>144888<step>18090<step>48021<step>48131<ans>9231 |
div | 158 | 043.111 | 43.111 | 388 | 9 | 3x1 | / | 388/9= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 388009 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
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"serialized": "00030003"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 388/9=<div><pos><state>388009<step>00030003<qmul>00000<rem>003<step>00380038<qmul>40036<rem>002<step>00280028<qmul>30027<rem>001<step>00100010<qmul>10009<rem>001<step>00100010<qmul>10009<rem>001<step>00100010<qmul>10009<rem>001<step>00100010<qmul>10009<rem>001<ans>043.111 |
div | 159 | 013.053 | 13.053 | 248 | 19 | 3x2 | / | 248/19= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | train | 248019 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 248/19=<div><pos><state>248019<step>00020002<qmul>00000<rem>002<step>00240024<qmul>10019<rem>005<step>00580058<qmul>30057<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>50095<rem>005<step>00500050<qmul>20038<rem>012<step>01200120<qmul>60114<rem>006<ans>013.053 |
add | 41 | 6810 | 186 | 120 | 66 | 3x2 | + | 120+66= | scratchpad-v3 | positive | null | no_carry | ++ | train | 021660 | [
{
"a_digit": 0,
"b_digit": 6,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 6,
"serialized": "06060"
},
{
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"carry_out": 0,
"column": 1,
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"serialized": "26080"
},
{
"a_digit":... | 120+66=<add><pos><state>021660<step>06060<step>26080<step>10010<ans>6810 |
add | 42 | 6870 | 786 | 768 | -18 | 3x2 | - | 768--18= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 867810 | [
{
"a_digit": 8,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "88061"
},
{
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"carry_in": 1,
"carry_out": 0,
"column": 1,
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"serialized": "61180"
},
{
"a_digit":... | 768--18=<add><pos><state>867810<step>88061<step>61180<step>70070<ans>6870 |
add | 44 | 7101 | -1017 | -770 | -247 | 3x3 | + | -770+-247= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 077742 | [
{
"a_digit": 0,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "07070"
},
{
"a_digit": 7,
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"carry_in": 0,
"carry_out": 1,
"column": 1,
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"serialized": "74011"
},
{
"a_digit":... | -770+-247=<add><neg><state>077742<step>07070<step>74011<step>72101<ans>7101 |
sub | 41 | 9810 | -189 | 83 | 272 | 2x3 | - | 83-272= | scratchpad-v3 | negative | null | negative_result | ++ | train | 272380 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 9,
"serialized": "23091",
"subtrahend_digit": 3
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 7,
"output_digit": 8,
"serialized": "78181",
"subtrahend... | 83-272=<sub><neg><state>272380<step>23091<step>78181<step>20110<ans>9810 |
add | 40 | 9320 | 239 | 231 | 8 | 3x1 | + | 231+8= | scratchpad-v3 | positive | null | no_carry | ++ | val | 132800 | [
{
"a_digit": 1,
"b_digit": 8,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "18090"
},
{
"a_digit": 3,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
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"serialized": "30030"
},
{
"a_digit":... | 231+8=<add><pos><state>132800<step>18090<step>30030<step>20020<ans>9320 |
sub | 42 | 0720 | -270 | 336 | 606 | 3x3 | - | 336-606= | scratchpad-v3 | negative | null | negative_result | ++ | train | 606633 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
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"output_digit": 0,
"serialized": "66000",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 7,
"serialized": "03071",
"subtrahend... | 336-606=<sub><neg><state>606633<step>66000<step>03071<step>63120<ans>0720 |
div | 161 | 002.000 | -2 | -954 | 477 | 3x3 | / | -954/477= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 954477 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -954/477=<div><neg><state>954477<step>00090009<qmul>00000<rem>009<step>00950095<qmul>00000<rem>095<step>09540954<qmul>20954<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>002.000 |
div | 160 | 000.669 | 0.669 | 458 | 685 | 3x3 | / | 458/685= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 458685 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 685,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 458/685=<div><pos><state>458685<step>00040004<qmul>00000<rem>004<step>00450045<qmul>00000<rem>045<step>04580458<qmul>00000<rem>458<step>45804580<qmul>64110<rem>470<step>47004700<qmul>64110<rem>590<step>59005900<qmul>85480<rem>420<step>42004200<qmul>64110<rem>090<ans>000.669 |
mul | 118 | 294610 | -16492 | -589 | 28 | 3x2 | * | -589*28= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 985820 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 72,
"running_total": 72,
"serialized": "9872072",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 7,
"column": 0,
"column_sum": 72,
"kind": "column",
... | -589*28=<mul><neg><state>985820<step>9872072<col>207<step>9218025<step>8864089<col>908<step>9000008<step>8216024<step>5840064<col>406<step>8000006<step>5210016<col>601<step>5000001<col>100<ans>294610 |
add | 41 | 5270 | 725 | 84 | 641 | 2x3 | + | 84+641= | scratchpad-v3 | positive | null | single_carry | ++ | train | 480146 | [
{
"a_digit": 4,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "41050"
},
{
"a_digit": 8,
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"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "84021"
},
{
"a_digit":... | 84+641=<add><pos><state>480146<step>41050<step>84021<step>06170<ans>5270 |
mul | 120 | 568796 | 697865 | -889 | -785 | 3x3 | * | -889*-785= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 988587 | [
{
"a_digit": 9,
"a_index": 0,
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"column": 0,
"kind": "term",
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 45,
"kind": "column",
... | -889*-785=<mul><pos><state>988587<step>9545045<col>504<step>9872076<step>8540116<col>611<step>9763074<step>8864138<step>8540178<col>817<step>8756073<step>8864137<col>713<step>8756069<col>906<ans>568796 |
add | 43 | 0750 | -570 | -558 | -12 | 3x2 | + | -558+-12= | scratchpad-v3 | negative | null | single_carry | -- | train | 855210 | [
{
"a_digit": 8,
"b_digit": 2,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "82001"
},
{
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"carry_in": 1,
"carry_out": 0,
"column": 1,
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"serialized": "51170"
},
{
"a_digit":... | -558+-12=<add><neg><state>855210<step>82001<step>51170<step>50050<ans>0750 |
add | 42 | 4620 | 264 | 94 | -170 | 2x3 | - | 94--170= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 490071 | [
{
"a_digit": 4,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
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"serialized": "40040"
},
{
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"carry_in": 0,
"carry_out": 1,
"column": 1,
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"serialized": "97061"
},
{
"a_digit":... | 94--170=<add><pos><state>490071<step>40040<step>97061<step>01120<ans>4620 |
mul | 120 | 231096 | 690132 | -796 | -867 | 3x3 | * | -796*-867= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 697768 | [
{
"a_digit": 6,
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"column": 0,
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"serialized": "6742042",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 42,
"kind": "column",
... | -796*-867=<mul><pos><state>697768<step>6742042<col>204<step>6636040<step>9763103<col>310<step>6848058<step>9654112<step>7749161<col>116<step>9872088<step>7642130<col>013<step>7856069<col>906<ans>231096 |
mul | 119 | 167351 | -153761 | -859 | 179 | 3x3 | * | -859*179= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 958971 | [
{
"a_digit": 9,
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"column": 0,
"kind": "term",
"product": 81,
"running_total": 81,
"serialized": "9981081",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 8,
"column": 0,
"column_sum": 81,
"kind": "column",
... | -859*179=<mul><neg><state>958971<step>9981081<col>108<step>9763071<step>5945116<col>611<step>9109020<step>5735055<step>8972127<col>712<step>5105017<step>8756073<col>307<step>8108015<col>501<ans>167351 |
mul | 116 | 000000 | 0 | 0 | 739 | 1x3 | * | 0*739= | scratchpad-v3 | positive | null | identity | ++ | train | 000937 | [
{
"a_digit": 0,
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"column": 0,
"kind": "term",
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
"o... | 0*739=<mul><pos><state>000937<step>0900000<col>000<step>0300000<step>0900000<col>000<step>0700000<step>0300000<step>0900000<col>000<step>0700000<step>0300000<col>000<step>0700000<col>000<ans>000000 |
mul | 119 | 210792 | -297012 | 318 | -934 | 3x3 | * | 318*-934= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 813439 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 32,
"running_total": 32,
"serialized": "8432032",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 32,
"kind": "column",
... | 318*-934=<mul><neg><state>813439<step>8432032<col>203<step>8324027<step>1404031<col>103<step>8972075<step>1303078<step>3412090<col>009<step>1909018<step>3309027<col>702<step>3927029<col>902<ans>210792 |
add | 41 | 5810 | -185 | -2 | 183 | 1x3 | - | -2-183= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 200381 | [
{
"a_digit": 2,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "23050"
},
{
"a_digit": 0,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "08080"
},
{
"a_digit":... | -2-183=<add><neg><state>200381<step>23050<step>08080<step>01010<ans>5810 |
sub | 41 | 8170 | 718 | 725 | -7 | 3x1 | + | 725+-7= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 527700 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 5,
"output_digit": 8,
"serialized": "57081",
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 1,
"serialized": "20110",
"subtrahend... | 725+-7=<sub><pos><state>527700<step>57081<step>20110<step>70070<ans>8170 |
mul | 117 | 085410 | 14580 | 81 | 180 | 2x3 | * | 81*180= | scratchpad-v3 | positive | null | contains_zero_digit | ++ | train | 180081 | [
{
"a_digit": 1,
"a_index": 0,
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"column": 0,
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"serialized": "1000000",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 0,
"kind": "column",
"o... | 81*180=<mul><pos><state>180081<step>1000000<col>000<step>1808008<step>8000008<col>800<step>1101001<step>8864065<step>0000065<col>506<step>8108014<step>0800014<col>401<step>0100001<col>100<ans>085410 |
add | 43 | 8350 | 538 | 148 | -390 | 3x3 | - | 148--390= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 841093 | [
{
"a_digit": 8,
"b_digit": 0,
"carry_in": 0,
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"column": 0,
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"serialized": "80080"
},
{
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"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "49031"
},
{
"a_digit":... | 148--390=<add><pos><state>841093<step>80080<step>49031<step>13150<ans>8350 |
add | 43 | 3221 | 1223 | 672 | -551 | 3x3 | - | 672--551= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 276155 | [
{
"a_digit": 2,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "21030"
},
{
"a_digit": 7,
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"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "75021"
},
{
"a_digit":... | 672--551=<add><pos><state>276155<step>21030<step>75021<step>65121<ans>3221 |
sub | 40 | 5000 | -5 | -6 | -1 | 1x1 | - | -6--1= | scratchpad-v3 | negative | null | negative_result | -- | val | 600100 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 6,
"output_digit": 5,
"serialized": "61050",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 0,
"output_digit": 0,
"serialized": "00000",
"subtrahend... | -6--1=<sub><neg><state>600100<step>61050<step>00000<step>00000<ans>5000 |
div | 160 | 011.488 | -11.488 | -965 | 84 | 3x2 | / | -965/84= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 965084 | [
{
"incoming_digit": 9,
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"partial": 9,
"position": 0,
"remainder_in": 0,
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},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -965/84=<div><neg><state>965084<step>00090009<qmul>00000<rem>009<step>00960096<qmul>10084<rem>012<step>01250125<qmul>10084<rem>041<step>04100410<qmul>40336<rem>074<step>07400740<qmul>80672<rem>068<step>06800680<qmul>80672<rem>008<step>00800080<qmul>00000<rem>080<ans>011.488 |
div | 160 | 002.189 | -2.189 | 208 | -95 | 3x2 | / | 208/-95= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 208095 | [
{
"incoming_digit": 2,
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"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 208/-95=<div><neg><state>208095<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02080208<qmul>20190<rem>018<step>01800180<qmul>10095<rem>085<step>08500850<qmul>80760<rem>090<step>09000900<qmul>90855<rem>045<step>04500450<qmul>40380<rem>070<ans>002.189 |
add | 43 | 9621 | -1269 | -717 | 552 | 3x3 | - | -717-552= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 717255 | [
{
"a_digit": 7,
"b_digit": 2,
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},
{
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"output_digit": 6,
"serialized": "15060"
},
{
"a_digit":... | -717-552=<add><neg><state>717255<step>72090<step>15060<step>75021<ans>9621 |
sub | 40 | 6100 | 16 | 26 | 10 | 2x2 | - | 26-10= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 620010 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 6,
"output_digit": 6,
"serialized": "60060",
"subtrahend_digit": 0
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 1,
"serialized": "21010",
"subtrahend... | 26-10=<sub><pos><state>620010<step>60060<step>21010<step>00000<ans>6100 |
mul | 119 | 125250 | -52521 | -183 | 287 | 3x3 | * | -183*287= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 381782 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 21,
"running_total": 21,
"serialized": "3721021",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 21,
"kind": "column",
... | -183*287=<mul><neg><state>381782<step>3721021<col>102<step>3824026<step>8756082<col>208<step>3206014<step>8864078<step>1707085<col>508<step>8216024<step>1808032<col>203<step>1202005<col>500<ans>125250 |
sub | 42 | 3510 | 153 | 174 | -21 | 3x2 | + | 174+-21= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 471120 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 4,
"output_digit": 3,
"serialized": "41030",
"subtrahend_digit": 1
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 7,
"output_digit": 5,
"serialized": "72050",
"subtrahend... | 174+-21=<sub><pos><state>471120<step>41030<step>72050<step>10010<ans>3510 |
mul | 119 | 404603 | -306404 | -353 | 868 | 3x3 | * | -353*868= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 353868 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 24,
"running_total": 24,
"serialized": "3824024",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 24,
"kind": "column",
... | -353*868=<mul><neg><state>353868<step>3824024<col>402<step>3618020<step>5840060<col>006<step>3824030<step>5630060<step>3824084<col>408<step>5840048<step>3618066<col>606<step>3824030<col>003<ans>404603 |
div | 158 | 001.038 | 1.038 | 54 | 52 | 2x2 | / | 54/52= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 054052 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 52,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 54/52=<div><pos><state>054052<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00540054<qmul>10052<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>30156<rem>044<step>04400440<qmul>80416<rem>024<step>02400240<qmul>40208<rem>032<ans>001.038 |
mul | 117 | 063300 | -3360 | -70 | 48 | 2x2 | * | -70*48= | scratchpad-v3 | negative | null | contains_zero_digit | -+ | train | 070840 | [
{
"a_digit": 0,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 0,
"running_total": 0,
"serialized": "0800000",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | -70*48=<mul><neg><state>070840<step>0800000<col>000<step>0400000<step>7856056<col>605<step>0000005<step>7428033<step>0800033<col>303<step>7000003<step>0400003<col>300<step>0000000<col>000<ans>063300 |
add | 44 | 0470 | -740 | -281 | -459 | 3x3 | + | -281+-459= | scratchpad-v3 | negative | null | multi_carry | -- | train | 182954 | [
{
"a_digit": 1,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "19001"
},
{
"a_digit": 8,
"b_digit": 5,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 4,
"serialized": "85141"
},
{
"a_digit":... | -281+-459=<add><neg><state>182954<step>19001<step>85141<step>24170<ans>0470 |
div | 159 | 150.000 | -150 | -600 | 4 | 3x1 | / | -600/4= | scratchpad-v3 | negative | round-half-up | exact | -+ | test | 600004 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 4,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 1,
"quotient_product": 4,
"serialized": "10004"
},
{
"kind": ... | -600/4=<div><neg><state>600004<step>00060006<qmul>10004<rem>002<step>00200020<qmul>50020<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>150.000 |
sub | 42 | 7980 | 897 | -4 | -901 | 1x3 | - | -4--901= | scratchpad-v3 | positive | null | borrow_through_zero | -- | test | 109400 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 1,
"output_digit": 7,
"serialized": "14071",
"subtrahend_digit": 4
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 9,
"serialized": "00191",
"subtrahend... | -4--901=<sub><pos><state>109400<step>14071<step>00191<step>90180<ans>7980 |
mul | 116 | 091100 | 1190 | 35 | 34 | 2x2 | * | 35*34= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 530430 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 20,
"running_total": 20,
"serialized": "5420020",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 20,
"kind": "column",
... | 35*34=<mul><pos><state>530430<step>5420020<col>002<step>5315017<step>3412029<col>902<step>5000002<step>3309011<step>0400011<col>101<step>3000001<step>0300001<col>100<step>0000000<col>000<ans>091100 |
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