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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
sub | 42 | 2670 | 762 | 860 | -98 | 3x2 | + | 860+-98= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 068890 | [
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{
"borrow_in": 1,
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"minuend_digit": 6,
"output_digit": 6,
"serialized": "69161",
"subtrahend... | 860+-98=<sub><pos><state>068890<step>08021<step>69161<step>80170<ans>2670 |
div | 160 | 012.392 | -12.392 | -979 | 79 | 3x2 | / | -979/79= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 979079 | [
{
"incoming_digit": 9,
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"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | -979/79=<div><neg><state>979079<step>00090009<qmul>00000<rem>009<step>00970097<qmul>10079<rem>018<step>01890189<qmul>20158<rem>031<step>03100310<qmul>30237<rem>073<step>07300730<qmul>90711<rem>019<step>01900190<qmul>20158<rem>032<step>03200320<qmul>40316<rem>004<ans>012.392 |
mul | 118 | 275674 | 476572 | 842 | 566 | 3x3 | * | 842*566= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 248665 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 12,
"running_total": 12,
"serialized": "2612012",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 12,
"kind": "column",
... | 842*566=<mul><pos><state>248665<step>2612012<col>201<step>2612013<step>4624037<col>703<step>2510013<step>4624037<step>8648085<col>508<step>4520028<step>8648076<col>607<step>8540047<col>704<ans>275674 |
mul | 118 | 166348 | 843661 | 949 | 889 | 3x3 | * | 949*889= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 949988 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"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",
... | 949*889=<mul><pos><state>949988<step>9981081<col>108<step>9872080<step>4936116<col>611<step>9872083<step>4832115<step>9981196<col>619<step>4832051<step>9872123<col>312<step>9872084<col>408<ans>166348 |
add | 41 | 4900 | -94 | -3 | -91 | 1x2 | + | -3+-91= | scratchpad-v3 | negative | null | no_carry | -- | train | 300190 | [
{
"a_digit": 3,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 4,
"serialized": "31040"
},
{
"a_digit": 0,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "09090"
},
{
"a_digit":... | -3+-91=<add><neg><state>300190<step>31040<step>09090<step>00000<ans>4900 |
mul | 119 | 825476 | -674528 | -788 | 856 | 3x3 | * | -788*856= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 887658 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 48,
"running_total": 48,
"serialized": "8648048",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 48,
"kind": "column",
... | -788*856=<mul><neg><state>887658<step>8648048<col>804<step>8540044<step>8648092<col>209<step>8864073<step>8540113<step>7642155<col>515<step>8864079<step>7535114<col>411<step>7856067<col>706<ans>825476 |
mul | 117 | 278030 | 30872 | 908 | 34 | 3x2 | * | 908*34= | scratchpad-v3 | positive | null | contains_zero_digit | ++ | train | 809430 | [
{
"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",
... | 908*34=<mul><pos><state>809430<step>8432032<col>203<step>8324027<step>0400027<col>702<step>8000002<step>0300002<step>9436038<col>803<step>0000003<step>9327030<col>003<step>9000003<col>300<ans>278030 |
div | 160 | 008.750 | -8.75 | 350 | -40 | 3x2 | / | 350/-40= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 350040 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 350/-40=<div><neg><state>350040<step>00030003<qmul>00000<rem>003<step>00350035<qmul>00000<rem>035<step>03500350<qmul>80320<rem>030<step>03000300<qmul>70280<rem>020<step>02000200<qmul>50200<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>008.750 |
add | 40 | 0500 | -50 | -49 | 1 | 2x1 | - | -49-1= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 940100 | [
{
"a_digit": 9,
"b_digit": 1,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "91001"
},
{
"a_digit": 4,
"b_digit": 0,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 5,
"serialized": "40150"
},
{
"a_digit":... | -49-1=<add><neg><state>940100<step>91001<step>40150<step>00000<ans>0500 |
div | 159 | 000.944 | -0.944 | -34 | 36 | 2x2 | / | -34/36= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 034036 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 36,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -34/36=<div><neg><state>034036<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03400340<qmul>90324<rem>016<step>01600160<qmul>40144<rem>016<step>01600160<qmul>40144<rem>016<step>01600160<qmul>40144<rem>016<ans>000.944 |
div | 161 | 002.282 | 2.282 | -194 | -85 | 3x2 | / | -194/-85= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 194085 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 85,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -194/-85=<div><pos><state>194085<step>00010001<qmul>00000<rem>001<step>00190019<qmul>00000<rem>019<step>01940194<qmul>20170<rem>024<step>02400240<qmul>20170<rem>070<step>07000700<qmul>80680<rem>020<step>02000200<qmul>20170<rem>030<step>03000300<qmul>30255<rem>045<ans>002.282 |
mul | 117 | 719700 | -7917 | -87 | 91 | 2x2 | * | -87*91= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 780190 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 1,
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"column": 0,
"kind": "term",
"product": 7,
"running_total": 7,
"serialized": "7107007",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 7,
"kind": "column",
"o... | -87*91=<mul><neg><state>780190<step>7107007<col>700<step>7963063<step>8108071<col>107<step>7000007<step>8972079<step>0100079<col>907<step>8000007<step>0900007<col>700<step>0000000<col>000<ans>719700 |
mul | 118 | 464621 | 126464 | 494 | 256 | 3x3 | * | 494*256= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 494652 | [
{
"a_digit": 4,
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"kind": "term",
"product": 24,
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"serialized": "4624024",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 24,
"kind": "column",
... | 494*256=<mul><pos><state>494652<step>4624024<col>402<step>4520022<step>9654076<col>607<step>4208015<step>9545060<step>4624084<col>408<step>9218026<step>4520046<col>604<step>4208012<col>201<ans>464621 |
sub | 44 | 3530 | 353 | -244 | -597 | 3x3 | - | -244--597= | scratchpad-v3 | positive | null | no_borrow | -- | train | 795442 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 7,
"output_digit": 3,
"serialized": "74030",
"subtrahend_digit": 4
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 5,
"serialized": "94050",
"subtrahend... | -244--597=<sub><pos><state>795442<step>74030<step>94050<step>52030<ans>3530 |
add | 43 | 5930 | -395 | -357 | -38 | 3x2 | + | -357+-38= | scratchpad-v3 | negative | null | single_carry | -- | train | 753830 | [
{
"a_digit": 7,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 5,
"serialized": "78051"
},
{
"a_digit": 5,
"b_digit": 3,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "53190"
},
{
"a_digit":... | -357+-38=<add><neg><state>753830<step>78051<step>53190<step>30030<ans>5930 |
div | 159 | 239.000 | -239 | 956 | -4 | 3x1 | / | 956/-4= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 956004 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 4,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 2,
"quotient_product": 8,
"serialized": "20008"
},
{
"kind": ... | 956/-4=<div><neg><state>956004<step>00090009<qmul>20008<rem>001<step>00150015<qmul>30012<rem>003<step>00360036<qmul>90036<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>239.000 |
div | 160 | 000.645 | 0.645 | 519 | 805 | 3x3 | / | 519/805= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 519805 | [
{
"incoming_digit": 5,
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"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 519/805=<div><pos><state>519805<step>00050005<qmul>00000<rem>005<step>00510051<qmul>00000<rem>051<step>05190519<qmul>00000<rem>519<step>51905190<qmul>64830<rem>360<step>36003600<qmul>43220<rem>380<step>38003800<qmul>43220<rem>580<step>58005800<qmul>75635<rem>165<ans>000.645 |
sub | 40 | 6320 | 236 | 238 | 2 | 3x1 | - | 238-2= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 832200 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 8,
"output_digit": 6,
"serialized": "82060",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
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"column": 1,
"minuend_digit": 3,
"output_digit": 3,
"serialized": "30030",
"subtrahend... | 238-2=<sub><pos><state>832200<step>82060<step>30030<step>20020<ans>6320 |
sub | 42 | 1570 | -751 | 15 | -766 | 2x3 | + | 15+-766= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | train | 667510 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 6,
"output_digit": 1,
"serialized": "65010",
"subtrahend_digit": 5
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 5,
"serialized": "61050",
"subtrahend... | 15+-766=<sub><neg><state>667510<step>65010<step>61050<step>70070<ans>1570 |
div | 161 | 074.417 | 74.417 | -893 | -12 | 3x2 | / | -893/-12= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | val | 893012 | [
{
"incoming_digit": 8,
"kind": "partial",
"partial": 8,
"position": 0,
"remainder_in": 0,
"serialized": "00080008"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -893/-12=<div><pos><state>893012<step>00080008<qmul>00000<rem>008<step>00890089<qmul>70084<rem>005<step>00530053<qmul>40048<rem>005<step>00500050<qmul>40048<rem>002<step>00200020<qmul>10012<rem>008<step>00800080<qmul>60072<rem>008<step>00800080<qmul>60072<rem>008<ans>074.417 |
add | 44 | 5960 | -695 | -452 | -243 | 3x3 | + | -452+-243= | scratchpad-v3 | negative | null | no_carry | -- | train | 254342 | [
{
"a_digit": 2,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "23050"
},
{
"a_digit": 5,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "54090"
},
{
"a_digit":... | -452+-243=<add><neg><state>254342<step>23050<step>54090<step>42060<ans>5960 |
add | 40 | 0370 | 730 | 721 | 9 | 3x1 | + | 721+9= | scratchpad-v3 | positive | null | single_carry | ++ | train | 127900 | [
{
"a_digit": 1,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "19001"
},
{
"a_digit": 2,
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"carry_in": 1,
"carry_out": 0,
"column": 1,
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"serialized": "20130"
},
{
"a_digit":... | 721+9=<add><pos><state>127900<step>19001<step>20130<step>70070<ans>0370 |
sub | 44 | 5920 | 295 | -423 | -718 | 3x3 | - | -423--718= | scratchpad-v3 | positive | null | single_borrow | -- | train | 817324 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 8,
"output_digit": 5,
"serialized": "83050",
"subtrahend_digit": 3
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 9,
"serialized": "12091",
"subtrahend... | -423--718=<sub><pos><state>817324<step>83050<step>12091<step>74120<ans>5920 |
div | 159 | 000.000 | 0 | 0 | -188 | 1x3 | / | 0/-188= | scratchpad-v3 | negative | round-half-up | zero_numerator | +- | train | 000188 | [
{
"incoming_digit": 0,
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"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 188,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 0/-188=<div><neg><state>000188<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<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>000.000 |
mul | 118 | 258558 | 855852 | 977 | 876 | 3x3 | * | 977*876= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 779678 | [
{
"a_digit": 7,
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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": 42,
"kind": "column",
... | 977*876=<mul><pos><state>779678<step>7642042<col>204<step>7749053<step>7642095<col>509<step>7856065<step>7749114<step>9654168<col>816<step>7856072<step>9763135<col>513<step>9872085<col>508<ans>258558 |
div | 161 | 000.684 | -0.684 | -141 | 206 | 3x3 | / | -141/206= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 141206 | [
{
"incoming_digit": 1,
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},
{
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -141/206=<div><neg><state>141206<step>00010001<qmul>00000<rem>001<step>00140014<qmul>00000<rem>014<step>01410141<qmul>00000<rem>141<step>14101410<qmul>61236<rem>174<step>17401740<qmul>81648<rem>092<step>09200920<qmul>40824<rem>096<step>09600960<qmul>40824<rem>136<ans>000.684 |
add | 44 | 5161 | -1615 | -683 | -932 | 3x3 | + | -683+-932= | scratchpad-v3 | negative | null | overflow | -- | train | 386239 | [
{
"a_digit": 3,
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"column": 0,
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"serialized": "32050"
},
{
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"column": 1,
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"serialized": "83011"
},
{
"a_digit":... | -683+-932=<add><neg><state>386239<step>32050<step>83011<step>69161<ans>5161 |
div | 160 | 000.210 | 0.21 | -13 | -62 | 2x2 | / | -13/-62= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 013062 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind":... | -13/-62=<div><pos><state>013062<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00130013<qmul>00000<rem>013<step>01300130<qmul>20124<rem>006<step>00600060<qmul>00000<rem>060<step>06000600<qmul>90558<rem>042<step>04200420<qmul>60372<rem>048<ans>000.210 |
mul | 120 | 695102 | 201596 | -499 | -404 | 3x3 | * | -499*-404= | scratchpad-v3 | positive | null | contains_zero_digit | -- | train | 994404 | [
{
"a_digit": 9,
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},
{
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"kind": "column",
... | -499*-404=<mul><pos><state>994404<step>9436036<col>603<step>9000003<step>9436039<col>903<step>9436039<step>9000039<step>4416055<col>505<step>9436041<step>4000041<col>104<step>4416020<col>002<ans>695102 |
div | 160 | 007.145 | -7.145 | -443 | 62 | 3x2 | / | -443/62= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 443062 | [
{
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},
{
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"serialized": "00000"
},
{
"kind":... | -443/62=<div><neg><state>443062<step>00040004<qmul>00000<rem>004<step>00440044<qmul>00000<rem>044<step>04430443<qmul>70434<rem>009<step>00900090<qmul>10062<rem>028<step>02800280<qmul>40248<rem>032<step>03200320<qmul>50310<rem>010<step>01000100<qmul>10062<rem>038<ans>007.145 |
sub | 40 | 5400 | 45 | 68 | 23 | 2x2 | - | 68-23= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 860320 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
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"serialized": "83050",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 4,
"serialized": "62040",
"subtrahend... | 68-23=<sub><pos><state>860320<step>83050<step>62040<step>00000<ans>5400 |
mul | 116 | 274100 | 1472 | 92 | 16 | 2x2 | * | 92*16= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 290610 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 6,
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"column": 0,
"kind": "term",
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"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 12,
"kind": "column",
... | 92*16=<mul><pos><state>290610<step>2612012<col>201<step>2102003<step>9654057<col>705<step>2000005<step>9109014<step>0600014<col>401<step>9000001<step>0100001<col>100<step>0000000<col>000<ans>274100 |
div | 160 | 008.000 | -8 | 712 | -89 | 3x2 | / | 712/-89= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 712089 | [
{
"incoming_digit": 7,
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},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 712/-89=<div><neg><state>712089<step>00070007<qmul>00000<rem>007<step>00710071<qmul>00000<rem>071<step>07120712<qmul>80712<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>008.000 |
sub | 42 | 4500 | 54 | 325 | 271 | 3x3 | - | 325-271= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 523172 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 4,
"serialized": "51040",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 5,
"serialized": "27051",
"subtrahend... | 325-271=<sub><pos><state>523172<step>51040<step>27051<step>32100<ans>4500 |
sub | 44 | 0000 | 0 | -675 | -675 | 3x3 | - | -675--675= | scratchpad-v3 | positive | null | identity | -- | train | 576576 | [
{
"borrow_in": 0,
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"column": 0,
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"output_digit": 0,
"serialized": "55000",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 7,
"output_digit": 0,
"serialized": "77000",
"subtrahend... | -675--675=<sub><pos><state>576576<step>55000<step>77000<step>66000<ans>0000 |
mul | 120 | 173166 | 661371 | -849 | -779 | 3x3 | * | -849*-779= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 948977 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 9,
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"column": 0,
"kind": "term",
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"serialized": "9981081",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 8,
"column": 0,
"column_sum": 81,
"kind": "column",
... | -849*-779=<mul><pos><state>948977<step>9981081<col>108<step>9763071<step>4936107<col>710<step>9763073<step>4728101<step>8972173<col>317<step>4728045<step>8756101<col>110<step>8756066<col>606<ans>173166 |
div | 162 | 001.032 | 1.032 | -961 | -931 | 3x3 | / | -961/-931= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 961931 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
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"position": 0,
"quotient_digit": 0,
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"serialized": "00000"
},
{
"kind"... | -961/-931=<div><pos><state>961931<step>00090009<qmul>00000<rem>009<step>00960096<qmul>00000<rem>096<step>09610961<qmul>10931<rem>030<step>03000300<qmul>00000<rem>300<step>30003000<qmul>32793<rem>207<step>20702070<qmul>21862<rem>208<step>20802080<qmul>21862<rem>218<ans>001.032 |
div | 161 | 001.070 | -1.07 | 578 | -540 | 3x3 | / | 578/-540= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 578540 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 540,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 578/-540=<div><neg><state>578540<step>00050005<qmul>00000<rem>005<step>00570057<qmul>00000<rem>057<step>05780578<qmul>10540<rem>038<step>03800380<qmul>00000<rem>380<step>38003800<qmul>73780<rem>020<step>02000200<qmul>00000<rem>200<step>20002000<qmul>31620<rem>380<ans>001.070 |
sub | 42 | 1100 | 11 | 805 | 794 | 3x3 | - | 805-794= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 508497 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 1,
"serialized": "54010",
"subtrahend_digit": 4
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "09011",
"subtrahend... | 805-794=<sub><pos><state>508497<step>54010<step>09011<step>87100<ans>1100 |
sub | 44 | 8930 | 398 | -137 | -535 | 3x3 | - | -137--535= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 535731 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 5,
"output_digit": 8,
"serialized": "57081",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 9,
"serialized": "33191",
"subtrahend... | -137--535=<sub><pos><state>535731<step>57081<step>33191<step>51130<ans>8930 |
sub | 43 | 6800 | 86 | -71 | -157 | 2x3 | - | -71--157= | scratchpad-v3 | positive | null | single_borrow | -- | train | 751170 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 7,
"output_digit": 6,
"serialized": "71060",
"subtrahend_digit": 1
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 5,
"output_digit": 8,
"serialized": "57081",
"subtrahend... | -71--157=<sub><pos><state>751170<step>71060<step>57081<step>10100<ans>6800 |
sub | 44 | 8110 | -118 | -335 | -217 | 3x3 | - | -335--217= | scratchpad-v3 | negative | null | negative_result | -- | test | 533712 | [
{
"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": 3,
"output_digit": 1,
"serialized": "31110",
"subtrahend... | -335--217=<sub><neg><state>533712<step>57081<step>31110<step>32010<ans>8110 |
sub | 43 | 6950 | 596 | -64 | -660 | 2x3 | - | -64--660= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 066460 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
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"output_digit": 6,
"serialized": "04061",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 6,
"output_digit": 9,
"serialized": "66191",
"subtrahend... | -64--660=<sub><pos><state>066460<step>04061<step>66191<step>60150<ans>6950 |
add | 43 | 4901 | -1094 | -556 | 538 | 3x3 | - | -556-538= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 655835 | [
{
"a_digit": 6,
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"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "68041"
},
{
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"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "53190"
},
{
"a_digit":... | -556-538=<add><neg><state>655835<step>68041<step>53190<step>55001<ans>4901 |
sub | 43 | 3500 | 53 | -77 | -130 | 2x3 | - | -77--130= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 031770 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 3,
"serialized": "07031",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 5,
"serialized": "37151",
"subtrahend... | -77--130=<sub><pos><state>031770<step>07031<step>37151<step>10100<ans>3500 |
sub | 42 | 9360 | 639 | 943 | 304 | 3x3 | - | 943-304= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 349403 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 9,
"serialized": "34091",
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 4,
"output_digit": 3,
"serialized": "40130",
"subtrahend... | 943-304=<sub><pos><state>349403<step>34091<step>40130<step>93060<ans>9360 |
mul | 118 | 335709 | 907533 | 927 | 979 | 3x3 | * | 927*979= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 729979 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 9,
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"column": 0,
"kind": "term",
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"serialized": "7963063",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 63,
"kind": "column",
... | 927*979=<mul><pos><state>729979<step>7963063<col>306<step>7749055<step>2918073<col>307<step>7963070<step>2714084<step>9981165<col>516<step>2918034<step>9763097<col>709<step>9981090<col>009<ans>335709 |
div | 159 | 098.400 | -98.4 | -492 | 5 | 3x1 | / | -492/5= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 492005 | [
{
"incoming_digit": 4,
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"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -492/5=<div><neg><state>492005<step>00040004<qmul>00000<rem>004<step>00490049<qmul>90045<rem>004<step>00420042<qmul>80040<rem>002<step>00200020<qmul>40020<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>098.400 |
sub | 41 | 8520 | 258 | 306 | 48 | 3x2 | - | 306-48= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 603840 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 6,
"output_digit": 8,
"serialized": "68081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 5,
"serialized": "04151",
"subtrahend... | 306-48=<sub><pos><state>603840<step>68081<step>04151<step>30120<ans>8520 |
add | 41 | 9310 | -139 | -9 | 130 | 1x3 | - | -9-130= | scratchpad-v3 | negative | null | magnitude_addition | -+ | test | 900031 | [
{
"a_digit": 9,
"b_digit": 0,
"carry_in": 0,
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"column": 0,
"output_digit": 9,
"serialized": "90090"
},
{
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "03030"
},
{
"a_digit":... | -9-130=<add><neg><state>900031<step>90090<step>03030<step>01010<ans>9310 |
add | 42 | 4310 | -134 | -17 | 117 | 2x3 | - | -17-117= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 710711 | [
{
"a_digit": 7,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "77041"
},
{
"a_digit": 1,
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"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "11130"
},
{
"a_digit":... | -17-117=<add><neg><state>710711<step>77041<step>11130<step>01010<ans>4310 |
sub | 42 | 8800 | -88 | 241 | 329 | 3x3 | - | 241-329= | scratchpad-v3 | negative | null | negative_result | ++ | val | 923142 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 8,
"serialized": "91080",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 8,
"serialized": "24081",
"subtrahend... | 241-329=<sub><neg><state>923142<step>91080<step>24081<step>32100<ans>8800 |
mul | 119 | 984161 | -161489 | -967 | 167 | 3x3 | * | -967*167= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 769761 | [
{
"a_digit": 7,
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"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
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"serialized": "7749049",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 49,
"kind": "column",
... | -967*167=<mul><neg><state>769761<step>7749049<col>904<step>7642046<step>6742088<col>808<step>7107015<step>6636051<step>9763114<col>411<step>6106017<step>9654071<col>107<step>9109016<col>601<ans>984161 |
sub | 42 | 1410 | 141 | 735 | 594 | 3x3 | - | 735-594= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 537495 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 1,
"serialized": "54010",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 4,
"serialized": "39041",
"subtrahend... | 735-594=<sub><pos><state>537495<step>54010<step>39041<step>75110<ans>1410 |
add | 44 | 4490 | -944 | -375 | -569 | 3x3 | + | -375+-569= | scratchpad-v3 | negative | null | multi_carry | -- | train | 573965 | [
{
"a_digit": 5,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "59041"
},
{
"a_digit": 7,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 4,
"serialized": "76141"
},
{
"a_digit":... | -375+-569=<add><neg><state>573965<step>59041<step>76141<step>35190<ans>4490 |
add | 42 | 8141 | 1418 | 567 | 851 | 3x3 | + | 567+851= | scratchpad-v3 | positive | null | overflow | ++ | train | 765158 | [
{
"a_digit": 7,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 8,
"serialized": "71080"
},
{
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"b_digit": 5,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "65011"
},
{
"a_digit":... | 567+851=<add><pos><state>765158<step>71080<step>65011<step>58141<ans>8141 |
add | 42 | 9210 | -129 | -127 | -2 | 3x1 | + | -127+-2= | scratchpad-v3 | negative | null | no_carry | -- | train | 721200 | [
{
"a_digit": 7,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "72090"
},
{
"a_digit": 2,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 2,
"serialized": "20020"
},
{
"a_digit":... | -127+-2=<add><neg><state>721200<step>72090<step>20020<step>10010<ans>9210 |
div | 20 | <nan> | NAN | -403 | 0 | 3x1 | / | -403/0= | scratchpad-v3 | positive | round-half-up | nan | -+ | train | 403000 | [] | -403/0=<div><pos><state>403000<ans><nan> |
div | 162 | 001.050 | 1.05 | -796 | -758 | 3x3 | / | -796/-758= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 796758 | [
{
"incoming_digit": 7,
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"position": 0,
"remainder_in": 0,
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},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -796/-758=<div><pos><state>796758<step>00070007<qmul>00000<rem>007<step>00790079<qmul>00000<rem>079<step>07960796<qmul>10758<rem>038<step>03800380<qmul>00000<rem>380<step>38003800<qmul>53790<rem>010<step>01000100<qmul>00000<rem>100<step>10001000<qmul>10758<rem>242<ans>001.050 |
mul | 120 | 018056 | 650810 | -862 | -755 | 3x3 | * | -862*-755= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 268557 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 5,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 10,
"kind": "column",
... | -862*-755=<mul><pos><state>268557<step>2510010<col>001<step>2510011<step>6530041<col>104<step>2714018<step>6530048<step>8540088<col>808<step>6742050<step>8540090<col>009<step>8756065<col>506<ans>018056 |
add | 41 | 0550 | -550 | 0 | -550 | 1x3 | + | 0+-550= | scratchpad-v3 | negative | null | identity | +- | train | 000055 | [
{
"a_digit": 0,
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{
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{
"a_digit":... | 0+-550=<add><neg><state>000055<step>00000<step>05050<step>05050<ans>0550 |
mul | 117 | 516400 | -4615 | -65 | 71 | 2x2 | * | -65*71= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 560170 | [
{
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add | 40 | 2800 | -82 | -81 | 1 | 2x1 | - | -81-1= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 180100 | [
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{
"a_digit":... | -81-1=<add><neg><state>180100<step>11020<step>80080<step>00000<ans>2800 |
mul | 119 | 735986 | -689537 | 863 | -799 | 3x3 | * | 863*-799= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 368997 | [
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... | 863*-799=<mul><neg><state>368997<step>3927027<col>702<step>3927029<step>6954083<col>308<step>3721029<step>6954083<step>8972155<col>515<step>6742057<step>8972129<col>912<step>8756068<col>806<ans>735986 |
mul | 118 | 267300 | 3762 | -57 | -66 | 2x2 | * | -57*-66= | scratchpad-v3 | positive | null | repeated_digit | -- | train | 750660 | [
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... | -57*-66=<mul><pos><state>750660<step>7642042<col>204<step>7642046<step>5630076<col>607<step>7000007<step>5630037<step>0600037<col>703<step>5000003<step>0600003<col>300<step>0000000<col>000<ans>267300 |
mul | 116 | 065200 | 2560 | 64 | 40 | 2x2 | * | 64*40= | scratchpad-v3 | positive | null | contains_zero_digit | ++ | train | 460040 | [
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mul | 119 | 378843 | -348873 | -777 | 449 | 3x3 | * | -777*449= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 777944 | [
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... | -777*449=<mul><neg><state>777944<step>7963063<col>306<step>7428034<step>7963097<col>709<step>7428037<step>7428065<step>7963128<col>812<step>7428040<step>7428068<col>806<step>7428034<col>403<ans>378843 |
mul | 120 | 204797 | 797402 | -998 | -799 | 3x3 | * | -998*-799= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 899997 | [
{
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... | -998*-799=<mul><pos><state>899997<step>8972072<col>207<step>8972079<step>9981160<col>016<step>8756072<step>9981153<step>9981234<col>423<step>9763086<step>9981167<col>716<step>9763079<col>907<ans>204797 |
mul | 118 | 603349 | 943306 | 994 | 949 | 3x3 | * | 994*949= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 499949 | [
{
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{
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... | 994*949=<mul><pos><state>499949<step>4936036<col>603<step>4416019<step>9981100<col>010<step>4936046<step>9436082<step>9981163<col>316<step>9981097<step>9436133<col>313<step>9981094<col>409<ans>603349 |
sub | 39 | 8300 | -38 | 6 | 44 | 1x2 | - | 6-44= | scratchpad-v3 | negative | null | negative_result | ++ | val | 440600 | [
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"subtrahend... | 6-44=<sub><neg><state>440600<step>46081<step>40130<step>00000<ans>8300 |
mul | 119 | 401931 | -139104 | 368 | -378 | 3x3 | * | 368*-378= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 863873 | [
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... | 368*-378=<mul><neg><state>863873<step>8864064<col>406<step>8756062<step>6848110<col>011<step>8324035<step>6742077<step>3824101<col>110<step>6318028<step>3721049<col>904<step>3309013<col>301<ans>401931 |
sub | 42 | 7820 | 287 | 670 | 383 | 3x3 | - | 670-383= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 076383 | [
{
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"serialized": "78181",
"subtrahend... | 670-383=<sub><pos><state>076383<step>03071<step>78181<step>63120<ans>7820 |
add | 40 | 1710 | 171 | 2 | 169 | 1x3 | + | 2+169= | scratchpad-v3 | positive | null | single_carry | ++ | train | 200961 | [
{
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{
"a_digit":... | 2+169=<add><pos><state>200961<step>29011<step>06170<step>01010<ans>1710 |
mul | 119 | 043340 | 43340 | -55 | -788 | 2x3 | * | -55*-788= | scratchpad-v3 | positive | null | repeated_digit | -- | train | 550887 | [
{
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... | -55*-788=<mul><pos><state>550887<step>5840040<col>004<step>5840044<step>5840084<col>408<step>5735043<step>5840083<step>0800083<col>308<step>5735043<step>0800043<col>304<step>0700004<col>400<ans>043340 |
div | 19 | <nan> | NAN | -99 | 0 | 2x1 | / | -99/0= | scratchpad-v3 | positive | round-half-up | nan | -+ | train | 099000 | [] | -99/0=<div><pos><state>099000<ans><nan> |
mul | 118 | 194100 | 1491 | -71 | -21 | 2x2 | * | -71*-21= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 170120 | [
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mul | 120 | 938673 | 376839 | -821 | -459 | 3x3 | * | -821*-459= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 128954 | [
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{
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mul | 117 | 409300 | -3904 | 64 | -61 | 2x2 | * | 64*-61= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 460160 | [
{
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{
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"o... | 64*-61=<mul><neg><state>460160<step>4104004<col>400<step>4624024<step>6106030<col>003<step>4000003<step>6636039<step>0100039<col>903<step>6000003<step>0600003<col>300<step>0000000<col>000<ans>409300 |
div | 162 | 000.293 | 0.293 | -147 | -501 | 3x3 | / | -147/-501= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 147501 | [
{
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{
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div | 161 | 001.007 | -1.007 | 921 | -915 | 3x3 | / | 921/-915= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 921915 | [
{
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{
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div | 161 | 001.029 | -1.029 | 747 | -726 | 3x3 | / | 747/-726= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 747726 | [
{
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{
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div | 159 | 000.477 | -0.477 | -21 | 44 | 2x2 | / | -21/44= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 021044 | [
{
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{
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{
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mul | 118 | 476395 | 593674 | 919 | 646 | 3x3 | * | 919*646= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 919646 | [
{
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{
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... | 919*646=<mul><pos><state>919646<step>9654054<col>405<step>9436041<step>1606047<col>704<step>9654058<step>1404062<step>9654116<col>611<step>1606017<step>9436053<col>305<step>9654059<col>905<ans>476395 |
mul | 118 | 489609 | 906984 | 969 | 936 | 3x3 | * | 969*936= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 969639 | [
{
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{
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... | 969*936=<mul><pos><state>969639<step>9654054<col>405<step>9327032<step>6636068<col>806<step>9981087<step>6318105<step>9654159<col>915<step>6954069<step>9327096<col>609<step>9981090<col>009<ans>489609 |
mul | 119 | 860325 | -523068 | 958 | -546 | 3x3 | * | 958*-546= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 859645 | [
{
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{
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... | 958*-546=<mul><neg><state>859645<step>8648048<col>804<step>8432036<step>5630066<col>606<step>8540046<step>5420066<step>9654120<col>012<step>5525037<step>9436073<col>307<step>9545052<col>205<ans>860325 |
add | 42 | 6490 | -946 | -939 | -7 | 3x1 | + | -939+-7= | scratchpad-v3 | negative | null | single_carry | -- | train | 939700 | [
{
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{
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{
"a_digit":... | -939+-7=<add><neg><state>939700<step>97061<step>30140<step>90090<ans>6490 |
sub | 41 | 2810 | -182 | 2 | -184 | 1x3 | + | 2+-184= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | test | 481200 | [
{
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{
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"subtrahend... | 2+-184=<sub><neg><state>481200<step>42020<step>80080<step>10010<ans>2810 |
sub | 41 | 5500 | 55 | -29 | 84 | 2x2 | + | -29+84= | scratchpad-v3 | positive | null | magnitude_subtraction | -+ | train | 480920 | [
{
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"serialized": "82150",
"subtrahend... | -29+84=<sub><pos><state>480920<step>49051<step>82150<step>00000<ans>5500 |
div | 160 | 023.353 | -23.353 | -794 | 34 | 3x2 | / | -794/34= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 794034 | [
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{
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sub | 42 | 0020 | 200 | -62 | 262 | 2x3 | + | -62+262= | scratchpad-v3 | positive | null | magnitude_subtraction | -+ | test | 262260 | [
{
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{
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"subtrahend... | -62+262=<sub><pos><state>262260<step>22000<step>66000<step>20020<ans>0020 |
add | 42 | 6931 | 1396 | 485 | 911 | 3x3 | + | 485+911= | scratchpad-v3 | positive | null | overflow | ++ | train | 584119 | [
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"output_digit": 6,
"serialized": "51060"
},
{
"a_digit": 8,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "81090"
},
{
"a_digit":... | 485+911=<add><pos><state>584119<step>51060<step>81090<step>49031<ans>6931 |
mul | 117 | 465840 | 48564 | 852 | 57 | 3x2 | * | 852*57= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 258750 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 14,
"running_total": 14,
"serialized": "2714014",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 14,
"kind": "column",
... | 852*57=<mul><pos><state>258750<step>2714014<col>401<step>2510011<step>5735046<col>604<step>2000004<step>5525029<step>8756085<col>508<step>5000008<step>8540048<col>804<step>8000004<col>400<ans>465840 |
mul | 117 | 576400 | -4675 | 55 | -85 | 2x2 | * | 55*-85= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 550580 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 25,
"running_total": 25,
"serialized": "5525025",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 25,
"kind": "column",
... | 55*-85=<mul><neg><state>550580<step>5525025<col>502<step>5840042<step>5525067<col>706<step>5000006<step>5840046<step>0500046<col>604<step>5000004<step>0800004<col>400<step>0000000<col>000<ans>576400 |
sub | 44 | 8330 | 338 | -338 | -676 | 3x3 | - | -338--676= | scratchpad-v3 | positive | null | single_borrow | -- | train | 676833 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 6,
"output_digit": 8,
"serialized": "68081",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 7,
"output_digit": 3,
"serialized": "73130",
"subtrahend... | -338--676=<sub><pos><state>676833<step>68081<step>73130<step>63030<ans>8330 |
div | 162 | 000.382 | 0.382 | -293 | -767 | 3x3 | / | -293/-767= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 293767 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 767,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -293/-767=<div><pos><state>293767<step>00020002<qmul>00000<rem>002<step>00290029<qmul>00000<rem>029<step>02930293<qmul>00000<rem>293<step>29302930<qmul>32301<rem>629<step>62906290<qmul>86136<rem>154<step>15401540<qmul>21534<rem>006<step>00600060<qmul>00000<rem>060<ans>000.382 |
mul | 118 | 395620 | -26593 | -917 | 29 | 3x2 | * | -917*29= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 719920 | [
{
"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",
... | -917*29=<mul><neg><state>719920<step>7963063<col>306<step>7214020<step>1909029<col>902<step>7000002<step>1202004<step>9981085<col>508<step>1000008<step>9218026<col>602<step>9000002<col>200<ans>395620 |
mul | 120 | 297322 | 223792 | -568 | -394 | 3x3 | * | -568*-394= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 865493 | [
{
"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",
... | -568*-394=<mul><pos><state>865493<step>8432032<col>203<step>8972075<step>6424099<col>909<step>8324033<step>6954087<step>5420107<col>710<step>6318028<step>5945073<col>307<step>5315022<col>202<ans>297322 |
add | 42 | 6171 | 1716 | 898 | 818 | 3x3 | + | 898+818= | scratchpad-v3 | positive | null | overflow | ++ | train | 898818 | [
{
"a_digit": 8,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 6,
"serialized": "88061"
},
{
"a_digit": 9,
"b_digit": 1,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "91111"
},
{
"a_digit":... | 898+818=<add><pos><state>898818<step>88061<step>91111<step>88171<ans>6171 |
mul | 118 | 812020 | -20218 | 22 | -919 | 2x3 | * | 22*-919= | scratchpad-v3 | negative | null | repeated_digit | +- | val | 220919 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 18,
"running_total": 18,
"serialized": "2918018",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 18,
"kind": "column",
... | 22*-919=<mul><neg><state>220919<step>2918018<col>801<step>2102003<step>2918021<col>102<step>2918020<step>2102022<step>0900022<col>202<step>2918020<step>0100020<col>002<step>0900002<col>200<ans>812020 |
add | 44 | 8031 | -1308 | -631 | -677 | 3x3 | + | -631+-677= | scratchpad-v3 | negative | null | overflow | -- | train | 136776 | [
{
"a_digit": 1,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 8,
"serialized": "17080"
},
{
"a_digit": 3,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "37001"
},
{
"a_digit":... | -631+-677=<add><neg><state>136776<step>17080<step>37001<step>66131<ans>8031 |
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