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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
div | 161 | 000.573 | -0.573 | 430 | -750 | 3x3 | / | 430/-750= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 430750 | [
{
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{
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{
"kind"... | 430/-750=<div><neg><state>430750<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04300430<qmul>00000<rem>430<step>43004300<qmul>53750<rem>550<step>55005500<qmul>75250<rem>250<step>25002500<qmul>32250<rem>250<step>25002500<qmul>32250<rem>250<ans>000.573 |
div | 159 | 000.261 | -0.261 | 18 | -69 | 2x2 | / | 18/-69= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 018069 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 18/-69=<div><neg><state>018069<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00180018<qmul>00000<rem>018<step>01800180<qmul>20138<rem>042<step>04200420<qmul>60414<rem>006<step>00600060<qmul>00000<rem>060<step>06000600<qmul>80552<rem>048<ans>000.261 |
mul | 120 | 386450 | 54683 | -367 | -149 | 3x3 | * | -367*-149= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 763941 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 63,
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"serialized": "7963063",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 63,
"kind": "column",
... | -367*-149=<mul><pos><state>763941<step>7963063<col>306<step>7428034<step>6954088<col>808<step>7107015<step>6424039<step>3927066<col>606<step>6106012<step>3412024<col>402<step>3103005<col>500<ans>386450 |
sub | 42 | 7010 | -107 | 817 | 924 | 3x3 | - | 817-924= | scratchpad-v3 | negative | null | negative_result | ++ | train | 429718 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "47071",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 0,
"serialized": "21100",
"subtrahend... | 817-924=<sub><neg><state>429718<step>47071<step>21100<step>98010<ans>7010 |
mul | 118 | 280797 | 797082 | 929 | 858 | 3x3 | * | 929*858= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 929858 | [
{
"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,
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"column": 0,
"column_sum": 72,
"kind": "column",
... | 929*858=<mul><pos><state>929858<step>9872072<col>207<step>9545052<step>2816068<col>806<step>9872078<step>2510088<step>9872160<col>016<step>2816032<step>9545077<col>707<step>9872079<col>907<ans>280797 |
sub | 44 | 1100 | 11 | -118 | -129 | 3x3 | - | -118--129= | scratchpad-v3 | positive | null | no_borrow | -- | train | 921811 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 1,
"serialized": "98010",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 1,
"serialized": "21010",
"subtrahend... | -118--129=<sub><pos><state>921811<step>98010<step>21010<step>11000<ans>1100 |
mul | 120 | 626787 | 787626 | -798 | -987 | 3x3 | * | -798*-987= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 897789 | [
{
"a_digit": 8,
"a_index": 0,
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"column": 0,
"kind": "term",
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"serialized": "8756056",
"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 56,
"kind": "column",
... | -798*-987=<mul><pos><state>897789<step>8756056<col>605<step>8864069<step>9763132<col>213<step>8972085<step>9872157<step>7749206<col>620<step>9981101<step>7856157<col>715<step>7963078<col>807<ans>626787 |
div | 161 | 000.369 | -0.369 | 257 | -697 | 3x3 | / | 257/-697= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | test | 257697 | [
{
"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"... | 257/-697=<div><neg><state>257697<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02570257<qmul>00000<rem>257<step>25702570<qmul>32091<rem>479<step>47904790<qmul>64182<rem>608<step>60806080<qmul>85576<rem>504<step>50405040<qmul>74879<rem>161<ans>000.369 |
sub | 42 | 7220 | -227 | 402 | 629 | 3x3 | - | 402-629= | scratchpad-v3 | negative | null | negative_result | ++ | train | 926204 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 7,
"serialized": "92070",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 2,
"serialized": "20020",
"subtrahend... | 402-629=<sub><neg><state>926204<step>92070<step>20020<step>64020<ans>7220 |
add | 44 | 4290 | -924 | -596 | -328 | 3x3 | + | -596+-328= | scratchpad-v3 | negative | null | multi_carry | -- | train | 695823 | [
{
"a_digit": 6,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 4,
"serialized": "68041"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "92121"
},
{
"a_digit":... | -596+-328=<add><neg><state>695823<step>68041<step>92121<step>53190<ans>4290 |
mul | 118 | 932584 | 485239 | 769 | 631 | 3x3 | * | 769*631= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 967136 | [
{
"a_digit": 9,
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"b_digit": 1,
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"column": 0,
"kind": "term",
"product": 9,
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"serialized": "9109009",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 9,
"kind": "column",
"o... | 769*631=<mul><pos><state>967136<step>9109009<col>900<step>9327027<step>6106033<col>303<step>9654057<step>6318075<step>7107082<col>208<step>6636044<step>7321065<col>506<step>7642048<col>804<ans>932584 |
sub | 43 | 5110 | 115 | -88 | -203 | 2x3 | - | -88--203= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 302880 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 3,
"output_digit": 5,
"serialized": "38051",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | -88--203=<sub><pos><state>302880<step>38051<step>08111<step>20110<ans>5110 |
div | 160 | 005.000 | 5 | 770 | 154 | 3x3 | / | 770/154= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 770154 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 770/154=<div><pos><state>770154<step>00070007<qmul>00000<rem>007<step>00770077<qmul>00000<rem>077<step>07700770<qmul>50770<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>005.000 |
sub | 44 | 5710 | -175 | -601 | -426 | 3x3 | - | -601--426= | scratchpad-v3 | negative | null | negative_result | -- | train | 106624 | [
{
"borrow_in": 0,
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"serialized": "16051",
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},
{
"borrow_in": 1,
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"column": 1,
"minuend_digit": 0,
"output_digit": 7,
"serialized": "02171",
"subtrahend... | -601--426=<sub><neg><state>106624<step>16051<step>02171<step>64110<ans>5710 |
add | 43 | 2560 | 652 | 253 | -399 | 3x3 | - | 253--399= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 352993 | [
{
"a_digit": 3,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 2,
"serialized": "39021"
},
{
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"carry_out": 1,
"column": 1,
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"serialized": "59151"
},
{
"a_digit":... | 253--399=<add><pos><state>352993<step>39021<step>59151<step>23160<ans>2560 |
mul | 119 | 092087 | -780290 | -994 | 785 | 3x3 | * | -994*785= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 499587 | [
{
"a_digit": 4,
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"column": 0,
"kind": "term",
"product": 20,
"running_total": 20,
"serialized": "4520020",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 20,
"kind": "column",
... | -994*785=<mul><neg><state>499587<step>4520020<col>002<step>4832034<step>9545079<col>907<step>4728035<step>9872107<step>9545152<col>215<step>9763078<step>9872150<col>015<step>9763078<col>807<ans>092087 |
div | 161 | 017.036 | 17.036 | -477 | -28 | 3x2 | / | -477/-28= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 477028 | [
{
"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":... | -477/-28=<div><pos><state>477028<step>00040004<qmul>00000<rem>004<step>00470047<qmul>10028<rem>019<step>01970197<qmul>70196<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>30084<rem>016<step>01600160<qmul>50140<rem>020<step>02000200<qmul>70196<rem>004<ans>017.036 |
div | 158 | 000.216 | 0.216 | 19 | 88 | 2x2 | / | 19/88= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 019088 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind":... | 19/88=<div><pos><state>019088<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00190019<qmul>00000<rem>019<step>01900190<qmul>20176<rem>014<step>01400140<qmul>10088<rem>052<step>05200520<qmul>50440<rem>080<step>08000800<qmul>90792<rem>008<ans>000.216 |
sub | 42 | 5350 | 535 | 958 | 423 | 3x3 | - | 958-423= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 859324 | [
{
"borrow_in": 0,
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"serialized": "83050",
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},
{
"borrow_in": 0,
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"column": 1,
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"output_digit": 3,
"serialized": "52030",
"subtrahend... | 958-423=<sub><pos><state>859324<step>83050<step>52030<step>94050<ans>5350 |
mul | 118 | 422400 | -4224 | 192 | -22 | 3x2 | * | 192*-22= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 291220 | [
{
"a_digit": 2,
"a_index": 0,
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},
{
"carry_in": 0,
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"column_sum": 4,
"kind": "column",
"o... | 192*-22=<mul><neg><state>291220<step>2204004<col>400<step>2204004<step>9218022<col>202<step>2000002<step>9218020<step>1202022<col>202<step>9000002<step>1202004<col>400<step>1000000<col>000<ans>422400 |
div | 161 | 018.000 | 18 | -810 | -45 | 3x2 | / | -810/-45= | scratchpad-v3 | positive | round-half-up | exact | -- | train | 810045 | [
{
"incoming_digit": 8,
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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":... | -810/-45=<div><pos><state>810045<step>00080008<qmul>00000<rem>008<step>00810081<qmul>10045<rem>036<step>03600360<qmul>80360<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>018.000 |
mul | 119 | 174537 | -735471 | -759 | 969 | 3x3 | * | -759*969= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 957969 | [
{
"a_digit": 9,
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"column": 0,
"kind": "term",
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"serialized": "9981081",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 81,
"kind": "column",
... | -759*969=<mul><neg><state>957969<step>9981081<col>108<step>9654062<step>5945107<col>710<step>9981091<step>5630121<step>7963184<col>418<step>5945063<step>7642105<col>510<step>7963073<col>307<ans>174537 |
mul | 119 | 831114 | -411138 | 546 | -753 | 3x3 | * | 546*-753= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 645357 | [
{
"a_digit": 6,
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"serialized": "6318018",
"term_index": 0
},
{
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"column_sum": 18,
"kind": "column",
... | 546*-753=<mul><neg><state>645357<step>6318018<col>801<step>6530031<step>4312043<col>304<step>6742046<step>4520066<step>5315081<col>108<step>4728036<step>5525061<col>106<step>5735041<col>104<ans>831114 |
sub | 43 | 3520 | 253 | 727 | -474 | 3x3 | + | 727+-474= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 727474 | [
{
"borrow_in": 0,
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"output_digit": 3,
"serialized": "74030",
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},
{
"borrow_in": 0,
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"column": 1,
"minuend_digit": 2,
"output_digit": 5,
"serialized": "27051",
"subtrahend... | 727+-474=<sub><pos><state>727474<step>74030<step>27051<step>74120<ans>3520 |
mul | 119 | 094600 | 6490 | -22 | -295 | 2x3 | * | -22*-295= | scratchpad-v3 | positive | null | repeated_digit | -- | train | 220592 | [
{
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{
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"kind": "column",
... | -22*-295=<mul><pos><state>220592<step>2510010<col>001<step>2918019<step>2510029<col>902<step>2204006<step>2918024<step>0500024<col>402<step>2204006<step>0900006<col>600<step>0200000<col>000<ans>094600 |
add | 41 | 3850 | -583 | -583 | 0 | 3x1 | + | -583+0= | scratchpad-v3 | negative | null | identity | -+ | train | 385000 | [
{
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},
{
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"column": 1,
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"serialized": "80080"
},
{
"a_digit":... | -583+0=<add><neg><state>385000<step>30030<step>80080<step>50050<ans>3850 |
mul | 120 | 678558 | 855876 | -966 | -886 | 3x3 | * | -966*-886= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 669688 | [
{
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},
{
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"kind": "column",
... | -966*-886=<mul><pos><state>669688<step>6636036<col>603<step>6848051<step>6636087<col>708<step>6848056<step>6848104<step>9654158<col>815<step>6848063<step>9872135<col>513<step>9872085<col>508<ans>678558 |
mul | 120 | 499048 | 840994 | -946 | -889 | 3x3 | * | -946*-889= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 649988 | [
{
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},
{
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"kind": "column",
... | -946*-889=<mul><pos><state>649988<step>6954054<col>405<step>6848053<step>4936089<col>908<step>6848056<step>4832088<step>9981169<col>916<step>4832048<step>9872120<col>012<step>9872084<col>408<ans>499048 |
sub | 41 | 9520 | 259 | 305 | 46 | 3x2 | - | 305-46= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 503640 | [
{
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},
{
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"serialized": "04151",
"subtrahend... | 305-46=<sub><pos><state>503640<step>56091<step>04151<step>30120<ans>9520 |
div | 160 | 015.370 | -15.37 | 707 | -46 | 3x2 | / | 707/-46= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 707046 | [
{
"incoming_digit": 7,
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},
{
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"serialized": "00000"
},
{
"kind":... | 707/-46=<div><neg><state>707046<step>00070007<qmul>00000<rem>007<step>00700070<qmul>10046<rem>024<step>02470247<qmul>50230<rem>017<step>01700170<qmul>30138<rem>032<step>03200320<qmul>60276<rem>044<step>04400440<qmul>90414<rem>026<step>02600260<qmul>50230<rem>030<ans>015.370 |
mul | 120 | 441266 | 662144 | -739 | -896 | 3x3 | * | -739*-896= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 937698 | [
{
"a_digit": 9,
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},
{
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"kind": "column",
... | -739*-896=<mul><pos><state>937698<step>9654054<col>405<step>9981086<step>3618104<col>410<step>9872082<step>3927109<step>7642151<col>115<step>3824039<step>7963102<col>210<step>7856066<col>606<ans>441266 |
div | 160 | 003.600 | -3.6 | -342 | 95 | 3x2 | / | -342/95= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 342095 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -342/95=<div><neg><state>342095<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03420342<qmul>30285<rem>057<step>05700570<qmul>60570<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>003.600 |
mul | 118 | 019710 | -17910 | -398 | 45 | 3x2 | * | -398*45= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 893540 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 5,
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"column": 0,
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"serialized": "8540040",
"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 40,
"kind": "column",
... | -398*45=<mul><neg><state>893540<step>8540040<col>004<step>8432036<step>9545081<col>108<step>8000008<step>9436044<step>3515059<col>905<step>9000005<step>3412017<col>701<step>3000001<col>100<ans>019710 |
mul | 119 | 369350 | 53963 | -593 | -91 | 3x2 | * | -593*-91= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 395190 | [
{
"a_digit": 3,
"a_index": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"o... | -593*-91=<mul><pos><state>395190<step>3103003<col>300<step>3927027<step>9109036<col>603<step>3000003<step>9981084<step>5105089<col>908<step>9000008<step>5945053<col>305<step>5000005<col>500<ans>369350 |
mul | 120 | 077358 | 853770 | -894 | -955 | 3x3 | * | -894*-955= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 498559 | [
{
"a_digit": 4,
"a_index": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 20,
"kind": "column",
... | -894*-955=<mul><pos><state>498559<step>4520020<col>002<step>4520022<step>9545067<col>706<step>4936042<step>9545087<step>8540127<col>712<step>9981093<step>8540133<col>313<step>8972085<col>508<ans>077358 |
div | 160 | 006.000 | -6 | 252 | -42 | 3x2 | / | 252/-42= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 252042 | [
{
"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":... | 252/-42=<div><neg><state>252042<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02520252<qmul>60252<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>006.000 |
add | 44 | 1301 | -1031 | -786 | -245 | 3x3 | + | -786+-245= | scratchpad-v3 | negative | null | cascading_carry | -- | test | 687542 | [
{
"a_digit": 6,
"b_digit": 5,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "65011"
},
{
"a_digit": 8,
"b_digit": 4,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "84131"
},
{
"a_digit":... | -786+-245=<add><neg><state>687542<step>65011<step>84131<step>72101<ans>1301 |
add | 44 | 1231 | -1321 | -414 | -907 | 3x3 | + | -414+-907= | scratchpad-v3 | negative | null | overflow | -- | train | 414709 | [
{
"a_digit": 4,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "47011"
},
{
"a_digit": 1,
"b_digit": 0,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 2,
"serialized": "10120"
},
{
"a_digit":... | -414+-907=<add><neg><state>414709<step>47011<step>10120<step>49031<ans>1231 |
div | 159 | 007.679 | 7.679 | 645 | 84 | 3x2 | / | 645/84= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | train | 645084 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 645/84=<div><pos><state>645084<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06450645<qmul>70588<rem>057<step>05700570<qmul>60504<rem>066<step>06600660<qmul>70588<rem>072<step>07200720<qmul>80672<rem>048<step>04800480<qmul>50420<rem>060<ans>007.679 |
div | 161 | 001.031 | -1.031 | 901 | -874 | 3x3 | / | 901/-874= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 901874 | [
{
"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"... | 901/-874=<div><neg><state>901874<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09010901<qmul>10874<rem>027<step>02700270<qmul>00000<rem>270<step>27002700<qmul>32622<rem>078<step>07800780<qmul>00000<rem>780<step>78007800<qmul>86992<rem>808<ans>001.031 |
add | 42 | 2190 | 912 | 585 | 327 | 3x3 | + | 585+327= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 585723 | [
{
"a_digit": 5,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "57021"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "82111"
},
{
"a_digit":... | 585+327=<add><pos><state>585723<step>57021<step>82111<step>53190<ans>2190 |
add | 42 | 7790 | 977 | 535 | 442 | 3x3 | + | 535+442= | scratchpad-v3 | positive | null | no_carry | ++ | train | 535244 | [
{
"a_digit": 5,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
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"serialized": "52070"
},
{
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"carry_in": 0,
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"column": 1,
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"serialized": "34070"
},
{
"a_digit":... | 535+442=<add><pos><state>535244<step>52070<step>34070<step>54090<ans>7790 |
div | 159 | 008.929 | 8.929 | 875 | 98 | 3x2 | / | 875/98= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | train | 875098 | [
{
"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":... | 875/98=<div><pos><state>875098<step>00080008<qmul>00000<rem>008<step>00870087<qmul>00000<rem>087<step>08750875<qmul>80784<rem>091<step>09100910<qmul>90882<rem>028<step>02800280<qmul>20196<rem>084<step>08400840<qmul>80784<rem>056<step>05600560<qmul>50490<rem>070<ans>008.929 |
sub | 44 | 5300 | -35 | -892 | -857 | 3x3 | - | -892--857= | scratchpad-v3 | negative | null | negative_result | -- | train | 298758 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
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"serialized": "27051",
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},
{
"borrow_in": 1,
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"column": 1,
"minuend_digit": 9,
"output_digit": 3,
"serialized": "95130",
"subtrahend... | -892--857=<sub><neg><state>298758<step>27051<step>95130<step>88000<ans>5300 |
mul | 118 | 070501 | 105070 | 395 | 266 | 3x3 | * | 395*266= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 593662 | [
{
"a_digit": 5,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 30,
"kind": "column",
... | 395*266=<mul><pos><state>593662<step>5630030<col>003<step>5630033<step>9654087<col>708<step>5210018<step>9654072<step>3618090<col>009<step>9218027<step>3618045<col>504<step>3206010<col>001<ans>070501 |
mul | 119 | 229809 | -908922 | -969 | 938 | 3x3 | * | -969*938= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 969839 | [
{
"a_digit": 9,
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"column": 0,
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"serialized": "9872072",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 72,
"kind": "column",
... | -969*938=<mul><neg><state>969839<step>9872072<col>207<step>9327034<step>6848082<col>208<step>9981089<step>6318107<step>9872179<col>917<step>6954071<step>9327098<col>809<step>9981090<col>009<ans>229809 |
sub | 44 | 4630 | 364 | -247 | -611 | 3x3 | - | -247--611= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 116742 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 1,
"output_digit": 4,
"serialized": "17041",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 6,
"serialized": "14161",
"subtrahend... | -247--611=<sub><pos><state>116742<step>17041<step>14161<step>62130<ans>4630 |
sub | 43 | 2300 | -32 | -668 | 636 | 3x3 | + | -668+636= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 866636 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 8,
"output_digit": 2,
"serialized": "86020",
"subtrahend_digit": 6
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 3,
"serialized": "63030",
"subtrahend... | -668+636=<sub><neg><state>866636<step>86020<step>63030<step>66000<ans>2300 |
add | 41 | 0310 | 130 | 4 | -126 | 1x3 | - | 4--126= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 400621 | [
{
"a_digit": 4,
"b_digit": 6,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "46001"
},
{
"a_digit": 0,
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"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "02130"
},
{
"a_digit":... | 4--126=<add><pos><state>400621<step>46001<step>02130<step>01010<ans>0310 |
sub | 42 | 5430 | 345 | 942 | 597 | 3x3 | - | 942-597= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 249795 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 5,
"serialized": "27051",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 4,
"serialized": "49141",
"subtrahend... | 942-597=<sub><pos><state>249795<step>27051<step>49141<step>95130<ans>5430 |
sub | 44 | 0550 | 550 | -253 | -803 | 3x3 | - | -253--803= | scratchpad-v3 | positive | null | single_borrow | -- | train | 308352 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 3,
"output_digit": 0,
"serialized": "33000",
"subtrahend_digit": 3
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 5,
"serialized": "05051",
"subtrahend... | -253--803=<sub><pos><state>308352<step>33000<step>05051<step>82150<ans>0550 |
mul | 119 | 912429 | -924219 | 927 | -997 | 3x3 | * | 927*-997= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 729799 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 49,
"running_total": 49,
"serialized": "7749049",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 49,
"kind": "column",
... | 927*-997=<mul><neg><state>729799<step>7749049<col>904<step>7963067<step>2714081<col>108<step>7963071<step>2918089<step>9763152<col>215<step>2918033<step>9981114<col>411<step>9981092<col>209<ans>912429 |
mul | 120 | 225328 | 823522 | -997 | -826 | 3x3 | * | -997*-826= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 799628 | [
{
"a_digit": 7,
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"running_total": 42,
"serialized": "7642042",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 42,
"kind": "column",
... | -997*-826=<mul><pos><state>799628<step>7642042<col>204<step>7214018<step>9654072<col>207<step>7856063<step>9218081<step>9654135<col>513<step>9872085<step>9218103<col>310<step>9872082<col>208<ans>225328 |
mul | 119 | 420801 | -108024 | 168 | -643 | 3x3 | * | 168*-643= | scratchpad-v3 | negative | null | medium_column_sum | +- | test | 861346 | [
{
"a_digit": 8,
"a_index": 0,
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"column": 0,
"kind": "term",
"product": 24,
"running_total": 24,
"serialized": "8324024",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 24,
"kind": "column",
... | 168*-643=<mul><neg><state>861346<step>8324024<col>402<step>8432034<step>6318052<col>205<step>8648053<step>6424077<step>1303080<col>008<step>6636044<step>1404048<col>804<step>1606010<col>001<ans>420801 |
div | 160 | 061.333 | 61.333 | -368 | -6 | 3x1 | / | -368/-6= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 368006 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -368/-6=<div><pos><state>368006<step>00030003<qmul>00000<rem>003<step>00360036<qmul>60036<rem>000<step>00080008<qmul>10006<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<ans>061.333 |
mul | 118 | 219637 | 736912 | 848 | 869 | 3x3 | * | 848*869= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 848968 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 72,
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"serialized": "8972072",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 7,
"column": 0,
"column_sum": 72,
"kind": "column",
... | 848*869=<mul><pos><state>848968<step>8972072<col>207<step>8648055<step>4936091<col>109<step>8864073<step>4624097<step>8972169<col>916<step>4832048<step>8648096<col>609<step>8864073<col>307<ans>219637 |
sub | 42 | 3000 | -3 | -76 | -73 | 2x2 | - | -76--73= | scratchpad-v3 | negative | null | negative_result | -- | train | 670370 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 6,
"output_digit": 3,
"serialized": "63030",
"subtrahend_digit": 3
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 7,
"output_digit": 0,
"serialized": "77000",
"subtrahend... | -76--73=<sub><neg><state>670370<step>63030<step>77000<step>00000<ans>3000 |
sub | 44 | 2200 | 22 | -135 | -157 | 3x3 | - | -135--157= | scratchpad-v3 | positive | null | no_borrow | -- | val | 751531 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 7,
"output_digit": 2,
"serialized": "75020",
"subtrahend_digit": 5
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 5,
"output_digit": 2,
"serialized": "53020",
"subtrahend... | -135--157=<sub><pos><state>751531<step>75020<step>53020<step>11000<ans>2200 |
mul | 119 | 097533 | -335790 | 585 | -574 | 3x3 | * | 585*-574= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 585475 | [
{
"a_digit": 5,
"a_index": 0,
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},
{
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... | 585*-574=<mul><neg><state>585475<step>5420020<col>002<step>5735037<step>8432069<col>906<step>5525031<step>8756087<step>5420107<col>710<step>8540050<step>5735085<col>508<step>5525033<col>303<ans>097533 |
div | 162 | 000.384 | 0.384 | -274 | -714 | 3x3 | / | -274/-714= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 274714 | [
{
"incoming_digit": 2,
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},
{
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{
"kind"... | -274/-714=<div><pos><state>274714<step>00020002<qmul>00000<rem>002<step>00270027<qmul>00000<rem>027<step>02740274<qmul>00000<rem>274<step>27402740<qmul>32142<rem>598<step>59805980<qmul>85712<rem>268<step>26802680<qmul>32142<rem>538<step>53805380<qmul>74998<rem>382<ans>000.384 |
mul | 118 | 046530 | -35640 | 440 | -81 | 3x2 | * | 440*-81= | scratchpad-v3 | negative | null | contains_zero_digit | +- | test | 044180 | [
{
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{
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"o... | 440*-81=<mul><neg><state>044180<step>0100000<col>000<step>0800000<step>4104004<col>400<step>0000000<step>4832032<step>4104036<col>603<step>4000003<step>4832035<col>503<step>4000003<col>300<ans>046530 |
sub | 40 | 7200 | 27 | 41 | 14 | 2x2 | - | 41-14= | scratchpad-v3 | positive | null | single_borrow | ++ | val | 140410 | [
{
"borrow_in": 0,
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
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"output_digit": 2,
"serialized": "41120",
"subtrahend... | 41-14=<sub><pos><state>140410<step>14071<step>41120<step>00000<ans>7200 |
sub | 44 | 6510 | -156 | -362 | -206 | 3x3 | - | -362--206= | scratchpad-v3 | negative | null | negative_result | -- | train | 263602 | [
{
"borrow_in": 0,
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},
{
"borrow_in": 1,
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"serialized": "60150",
"subtrahend... | -362--206=<sub><neg><state>263602<step>26061<step>60150<step>32010<ans>6510 |
div | 19 | <nan> | NAN | -41 | 0 | 2x1 | / | -41/0= | scratchpad-v3 | positive | round-half-up | nan | -+ | train | 041000 | [] | -41/0=<div><pos><state>041000<ans><nan> |
sub | 40 | 2200 | -22 | 19 | 41 | 2x2 | - | 19-41= | scratchpad-v3 | negative | null | negative_result | ++ | train | 140910 | [
{
"borrow_in": 0,
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},
{
"borrow_in": 1,
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"serialized": "41120",
"subtrahend... | 19-41=<sub><neg><state>140910<step>19021<step>41120<step>00000<ans>2200 |
add | 44 | 0250 | -520 | -210 | -310 | 3x3 | + | -210+-310= | scratchpad-v3 | negative | null | no_carry | -- | train | 012013 | [
{
"a_digit": 0,
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{
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"serialized": "11020"
},
{
"a_digit":... | -210+-310=<add><neg><state>012013<step>00000<step>11020<step>23050<ans>0250 |
div | 159 | 000.949 | -0.949 | -75 | 79 | 2x2 | / | -75/79= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 075079 | [
{
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},
{
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"serialized": "00000"
},
{
"kind":... | -75/79=<div><neg><state>075079<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07500750<qmul>90711<rem>039<step>03900390<qmul>40316<rem>074<step>07400740<qmul>90711<rem>029<step>02900290<qmul>30237<rem>053<ans>000.949 |
add | 44 | 3021 | -1203 | -844 | -359 | 3x3 | + | -844+-359= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 448953 | [
{
"a_digit": 4,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
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},
{
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"carry_in": 1,
"carry_out": 1,
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"serialized": "45101"
},
{
"a_digit":... | -844+-359=<add><neg><state>448953<step>49031<step>45101<step>83121<ans>3021 |
mul | 119 | 359695 | -596953 | 749 | -797 | 3x3 | * | 749*-797= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 947797 | [
{
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},
{
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"kind": "column",
... | 749*-797=<mul><neg><state>947797<step>9763063<col>306<step>9981087<step>4728115<col>511<step>9763074<step>4936110<step>7749159<col>915<step>4728043<step>7963106<col>610<step>7749059<col>905<ans>359695 |
div | 159 | 001.500 | 1.5 | 129 | 86 | 3x2 | / | 129/86= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 129086 | [
{
"incoming_digit": 1,
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},
{
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"serialized": "00000"
},
{
"kind":... | 129/86=<div><pos><state>129086<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01290129<qmul>10086<rem>043<step>04300430<qmul>50430<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.500 |
div | 162 | 004.059 | 4.059 | -759 | -187 | 3x3 | / | -759/-187= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 759187 | [
{
"incoming_digit": 7,
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},
{
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{
"kind"... | -759/-187=<div><pos><state>759187<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07590759<qmul>40748<rem>011<step>01100110<qmul>00000<rem>110<step>11001100<qmul>50935<rem>165<step>16501650<qmul>81496<rem>154<step>15401540<qmul>81496<rem>044<ans>004.059 |
mul | 119 | 365266 | -662563 | -737 | 899 | 3x3 | * | -737*899= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 737998 | [
{
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},
{
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"kind": "column",
... | -737*899=<mul><neg><state>737998<step>7963063<col>306<step>7963069<step>3927096<col>609<step>7856065<step>3927092<step>7963155<col>515<step>3824039<step>7963102<col>210<step>7856066<col>606<ans>365266 |
div | 159 | 000.098 | 0.098 | 84 | 861 | 2x3 | / | 84/861= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | test | 084861 | [
{
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},
{
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{
"kind"... | 84/861=<div><pos><state>084861<step>00000000<qmul>00000<rem>000<step>00080008<qmul>00000<rem>008<step>00840084<qmul>00000<rem>084<step>08400840<qmul>00000<rem>840<step>84008400<qmul>97749<rem>651<step>65106510<qmul>76027<rem>483<step>48304830<qmul>54305<rem>525<ans>000.098 |
div | 161 | 001.004 | -1.004 | -700 | 697 | 3x3 | / | -700/697= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 700697 | [
{
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},
{
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"serialized": "00000"
},
{
"kind"... | -700/697=<div><neg><state>700697<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>10697<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>00000<rem>300<step>30003000<qmul>42788<rem>212<step>21202120<qmul>32091<rem>029<ans>001.004 |
mul | 119 | 335337 | -733533 | -969 | 757 | 3x3 | * | -969*757= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 969757 | [
{
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},
{
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... | -969*757=<mul><neg><state>969757<step>9763063<col>306<step>9545051<step>6742093<col>309<step>9763072<step>6530102<step>9763165<col>516<step>6742058<step>9545103<col>310<step>9763073<col>307<ans>335337 |
add | 41 | 9310 | 139 | 55 | -84 | 2x2 | - | 55--84= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 550480 | [
{
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},
{
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"serialized": "58031"
},
{
"a_digit":... | 55--84=<add><pos><state>550480<step>54090<step>58031<step>00110<ans>9310 |
div | 162 | 001.209 | 1.209 | -936 | -774 | 3x3 | / | -936/-774= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 936774 | [
{
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},
{
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},
{
"kind"... | -936/-774=<div><pos><state>936774<step>00090009<qmul>00000<rem>009<step>00930093<qmul>00000<rem>093<step>09360936<qmul>10774<rem>162<step>16201620<qmul>21548<rem>072<step>07200720<qmul>00000<rem>720<step>72007200<qmul>96966<rem>234<step>23402340<qmul>32322<rem>018<ans>001.209 |
mul | 118 | 549347 | 743945 | 779 | 955 | 3x3 | * | 779*955= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 977559 | [
{
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},
{
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"kind": "column",
... | 779*955=<mul><pos><state>977559<step>9545045<col>504<step>9545049<step>7535084<col>408<step>9981089<step>7535124<step>7535159<col>915<step>7963078<step>7535113<col>311<step>7963074<col>407<ans>549347 |
div | 157 | 000.010 | 0.01 | 1 | 99 | 1x2 | / | 1/99= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | train | 001099 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind":... | 1/99=<div><pos><state>001099<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>10099<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>10099<rem>001<ans>000.010 |
mul | 117 | 825000 | -528 | 22 | -24 | 2x2 | * | 22*-24= | scratchpad-v3 | negative | null | repeated_digit | +- | test | 220420 | [
{
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"term_index": 0
},
{
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"kind": "column",
"o... | 22*-24=<mul><neg><state>220420<step>2408008<col>800<step>2204004<step>2408012<col>201<step>2000001<step>2204005<step>0400005<col>500<step>2000000<step>0200000<col>000<step>0000000<col>000<ans>825000 |
div | 159 | 000.053 | 0.053 | -1 | -19 | 1x2 | / | -1/-19= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 001019 | [
{
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},
{
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"serialized": "00000"
},
{
"kind":... | -1/-19=<div><pos><state>001019<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<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>000.053 |
mul | 120 | 270192 | 291072 | -758 | -384 | 3x3 | * | -758*-384= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 857483 | [
{
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},
{
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"kind": "column",
... | -758*-384=<mul><pos><state>857483<step>8432032<col>203<step>8864067<step>5420087<col>708<step>8324032<step>5840072<step>7428100<col>010<step>5315025<step>7856081<col>108<step>7321029<col>902<ans>270192 |
sub | 43 | 8020 | 208 | -98 | -306 | 2x3 | - | -98--306= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 603890 | [
{
"borrow_in": 0,
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{
"borrow_in": 1,
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"column": 1,
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"serialized": "09101",
"subtrahend... | -98--306=<sub><pos><state>603890<step>68081<step>09101<step>30120<ans>8020 |
add | 44 | 5260 | -625 | -398 | -227 | 3x3 | + | -398+-227= | scratchpad-v3 | negative | null | multi_carry | -- | train | 893722 | [
{
"a_digit": 8,
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},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "92121"
},
{
"a_digit":... | -398+-227=<add><neg><state>893722<step>87051<step>92121<step>32160<ans>5260 |
div | 160 | 003.966 | -3.966 | 234 | -59 | 3x2 | / | 234/-59= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 234059 | [
{
"incoming_digit": 2,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | 234/-59=<div><neg><state>234059<step>00020002<qmul>00000<rem>002<step>00230023<qmul>00000<rem>023<step>02340234<qmul>30177<rem>057<step>05700570<qmul>90531<rem>039<step>03900390<qmul>60354<rem>036<step>03600360<qmul>60354<rem>006<step>00600060<qmul>10059<rem>001<ans>003.966 |
div | 161 | 001.790 | -1.79 | -829 | 463 | 3x3 | / | -829/463= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | val | 829463 | [
{
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"position": 0,
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},
{
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"serialized": "00000"
},
{
"kind"... | -829/463=<div><neg><state>829463<step>00080008<qmul>00000<rem>008<step>00820082<qmul>00000<rem>082<step>08290829<qmul>10463<rem>366<step>36603660<qmul>73241<rem>419<step>41904190<qmul>94167<rem>023<step>02300230<qmul>00000<rem>230<step>23002300<qmul>41852<rem>448<ans>001.790 |
add | 42 | 5701 | 1075 | 448 | 627 | 3x3 | + | 448+627= | scratchpad-v3 | positive | null | overflow | ++ | train | 844726 | [
{
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},
{
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},
{
"a_digit":... | 448+627=<add><pos><state>844726<step>87051<step>42170<step>46001<ans>5701 |
mul | 120 | 227898 | 898722 | -918 | -979 | 3x3 | * | -918*-979= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 819979 | [
{
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{
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"column_sum": 72,
"kind": "column",
... | -918*-979=<mul><pos><state>819979<step>8972072<col>207<step>8756063<step>1909072<col>207<step>8972079<step>1707086<step>9981167<col>716<step>1909025<step>9763088<col>808<step>9981089<col>908<ans>227898 |
mul | 117 | 279000 | -972 | 1 | -972 | 1x3 | * | 1*-972= | scratchpad-v3 | negative | null | identity | +- | train | 100279 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 2,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 2,
"running_total": 2,
"serialized": "1202002",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 2,
"kind": "column",
"o... | 1*-972=<mul><neg><state>100279<step>1202002<col>200<step>1707007<step>0200007<col>700<step>1909009<step>0700009<step>0200009<col>900<step>0900000<step>0700000<col>000<step>0900000<col>000<ans>279000 |
div | 159 | 000.468 | 0.468 | 51 | 109 | 2x3 | / | 51/109= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 051109 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 109,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 51/109=<div><pos><state>051109<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00510051<qmul>00000<rem>051<step>05100510<qmul>40436<rem>074<step>07400740<qmul>60654<rem>086<step>08600860<qmul>70763<rem>097<step>09700970<qmul>80872<rem>098<ans>000.468 |
mul | 120 | 264767 | 767462 | -769 | -998 | 3x3 | * | -769*-998= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 967899 | [
{
"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",
... | -769*-998=<mul><pos><state>967899<step>9872072<col>207<step>9981088<step>6848136<col>613<step>9981094<step>6954148<step>7856204<col>420<step>6954074<step>7963137<col>713<step>7963076<col>607<ans>264767 |
add | 43 | 7060 | -607 | -570 | -37 | 3x2 | + | -570+-37= | scratchpad-v3 | negative | null | single_carry | -- | train | 075730 | [
{
"a_digit": 0,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "07070"
},
{
"a_digit": 7,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "73001"
},
{
"a_digit":... | -570+-37=<add><neg><state>075730<step>07070<step>73001<step>50160<ans>7060 |
div | 162 | 001.379 | 1.379 | -793 | -575 | 3x3 | / | -793/-575= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 793575 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
"divisor": 575,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -793/-575=<div><pos><state>793575<step>00070007<qmul>00000<rem>007<step>00790079<qmul>00000<rem>079<step>07930793<qmul>10575<rem>218<step>21802180<qmul>31725<rem>455<step>45504550<qmul>74025<rem>525<step>52505250<qmul>95175<rem>075<step>07500750<qmul>10575<rem>175<ans>001.379 |
div | 159 | 131.143 | -131.143 | 918 | -7 | 3x1 | / | 918/-7= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 918007 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 7,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 1,
"quotient_product": 7,
"serialized": "10007"
},
{
"kind": ... | 918/-7=<div><neg><state>918007<step>00090009<qmul>10007<rem>002<step>00210021<qmul>30021<rem>000<step>00080008<qmul>10007<rem>001<step>00100010<qmul>10007<rem>003<step>00300030<qmul>40028<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<ans>131.143 |
add | 44 | 5121 | -1215 | -969 | -246 | 3x3 | + | -969+-246= | scratchpad-v3 | negative | null | overflow | -- | train | 969642 | [
{
"a_digit": 9,
"b_digit": 6,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 5,
"serialized": "96051"
},
{
"a_digit": 6,
"b_digit": 4,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "64111"
},
{
"a_digit":... | -969+-246=<add><neg><state>969642<step>96051<step>64111<step>92121<ans>5121 |
mul | 118 | 036465 | 564630 | 885 | 638 | 3x3 | * | 885*638= | scratchpad-v3 | positive | null | medium_column_sum | ++ | test | 588836 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 40,
"running_total": 40,
"serialized": "5840040",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 40,
"kind": "column",
... | 885*638=<mul><pos><state>588836<step>5840040<col>004<step>5315019<step>8864083<col>308<step>5630038<step>8324062<step>8864126<col>612<step>8648060<step>8324084<col>408<step>8648056<col>605<ans>036465 |
sub | 42 | 0000 | 0 | 308 | 308 | 3x3 | - | 308-308= | scratchpad-v3 | positive | null | identity | ++ | train | 803803 | [
{
"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... | 308-308=<sub><pos><state>803803<step>88000<step>00000<step>33000<ans>0000 |
div | 158 | 004.167 | -4.167 | 25 | -6 | 2x1 | / | 25/-6= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 025006 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 6,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 25/-6=<div><neg><state>025006<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00250025<qmul>40024<rem>001<step>00100010<qmul>10006<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<ans>004.167 |
mul | 118 | 709200 | 2907 | -57 | -51 | 2x2 | * | -57*-51= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 750150 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"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... | -57*-51=<mul><pos><state>750150<step>7107007<col>700<step>7535035<step>5105040<col>004<step>7000004<step>5525029<step>0100029<col>902<step>5000002<step>0500002<col>200<step>0000000<col>000<ans>709200 |
mul | 116 | 578000 | 875 | 25 | 35 | 2x2 | * | 25*35= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 520530 | [
{
"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",
... | 25*35=<mul><pos><state>520530<step>5525025<col>502<step>5315017<step>2510027<col>702<step>5000002<step>2306008<step>0500008<col>800<step>2000000<step>0300000<col>000<step>0000000<col>000<ans>578000 |
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