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 | 44 | 6970 | 796 | -135 | -931 | 3x3 | - | -135--931= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 139531 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 1,
"output_digit": 6,
"serialized": "15061",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 9,
"serialized": "33191",
"subtrahend... | -135--931=<sub><pos><state>139531<step>15061<step>33191<step>91170<ans>6970 |
add | 42 | 2060 | 602 | 358 | 244 | 3x3 | + | 358+244= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 853442 | [
{
"a_digit": 8,
"b_digit": 4,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 2,
"serialized": "84021"
},
{
"a_digit": 5,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "54101"
},
{
"a_digit":... | 358+244=<add><pos><state>853442<step>84021<step>54101<step>32160<ans>2060 |
mul | 119 | 496653 | -356694 | 442 | -807 | 3x3 | * | 442*-807= | scratchpad-v3 | negative | null | contains_zero_digit | +- | train | 244708 | [
{
"a_digit": 2,
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"column": 0,
"kind": "term",
"product": 14,
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"serialized": "2714014",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 14,
"kind": "column",
... | 442*-807=<mul><neg><state>244708<step>2714014<col>401<step>2000001<step>4728029<col>902<step>2816018<step>4000018<step>4728046<col>604<step>4832036<step>4000036<col>603<step>4832035<col>503<ans>496653 |
div | 162 | 000.730 | 0.73 | -452 | -619 | 3x3 | / | -452/-619= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 452619 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 619,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -452/-619=<div><pos><state>452619<step>00040004<qmul>00000<rem>004<step>00450045<qmul>00000<rem>045<step>04520452<qmul>00000<rem>452<step>45204520<qmul>74333<rem>187<step>18701870<qmul>31857<rem>013<step>01300130<qmul>00000<rem>130<step>13001300<qmul>21238<rem>062<ans>000.730 |
sub | 43 | 9780 | 879 | -25 | -904 | 2x3 | - | -25--904= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 409520 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 9,
"serialized": "45091",
"subtrahend_digit": 5
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 7,
"serialized": "02171",
"subtrahend... | -25--904=<sub><pos><state>409520<step>45091<step>02171<step>90180<ans>9780 |
mul | 118 | 197150 | -51791 | 773 | -67 | 3x2 | * | 773*-67= | scratchpad-v3 | negative | null | medium_column_sum | +- | test | 377760 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 21,
"running_total": 21,
"serialized": "3721021",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 21,
"kind": "column",
... | 773*-67=<mul><neg><state>377760<step>3721021<col>102<step>3618020<step>7749069<col>906<step>3000006<step>7642048<step>7749097<col>709<step>7000009<step>7642051<col>105<step>7000005<col>500<ans>197150 |
add | 43 | 5311 | -1135 | -845 | 290 | 3x3 | - | -845-290= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 548092 | [
{
"a_digit": 5,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "50050"
},
{
"a_digit": 4,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "49031"
},
{
"a_digit":... | -845-290=<add><neg><state>548092<step>50050<step>49031<step>82111<ans>5311 |
sub | 41 | 5010 | 105 | 162 | 57 | 3x2 | - | 162-57= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 261750 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 5,
"serialized": "27051",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 0,
"serialized": "65100",
"subtrahend... | 162-57=<sub><pos><state>261750<step>27051<step>65100<step>10010<ans>5010 |
sub | 44 | 9140 | 419 | -299 | -718 | 3x3 | - | -299--718= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 817992 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 8,
"output_digit": 9,
"serialized": "89091",
"subtrahend_digit": 9
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 1,
"serialized": "19111",
"subtrahend... | -299--718=<sub><pos><state>817992<step>89091<step>19111<step>72140<ans>9140 |
add | 41 | 5910 | -195 | -7 | 188 | 1x3 | - | -7-188= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 700881 | [
{
"a_digit": 7,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 5,
"serialized": "78051"
},
{
"a_digit": 0,
"b_digit": 8,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "08190"
},
{
"a_digit":... | -7-188=<add><neg><state>700881<step>78051<step>08190<step>01010<ans>5910 |
mul | 119 | 031339 | -933130 | -998 | 935 | 3x3 | * | -998*935= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 899539 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 40,
"running_total": 40,
"serialized": "8540040",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 40,
"kind": "column",
... | -998*935=<mul><neg><state>899539<step>8540040<col>004<step>8324028<step>9545073<col>307<step>8972079<step>9327106<step>9545151<col>115<step>9981096<step>9327123<col>312<step>9981093<col>309<ans>031339 |
div | 160 | 000.424 | 0.424 | -28 | -66 | 2x2 | / | -28/-66= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 028066 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 66,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -28/-66=<div><pos><state>028066<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00280028<qmul>00000<rem>028<step>02800280<qmul>40264<rem>016<step>01600160<qmul>20132<rem>028<step>02800280<qmul>40264<rem>016<step>01600160<qmul>20132<rem>028<ans>000.424 |
mul | 118 | 060060 | 60060 | 572 | 105 | 3x3 | * | 572*105= | scratchpad-v3 | positive | null | contains_zero_digit | ++ | train | 275501 | [
{
"a_digit": 2,
"a_index": 0,
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"b_index": 0,
"column": 0,
"kind": "term",
"product": 10,
"running_total": 10,
"serialized": "2510010",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 10,
"kind": "column",
... | 572*105=<mul><pos><state>275501<step>2510010<col>001<step>2000001<step>7535036<col>603<step>2102005<step>7000005<step>5525030<col>003<step>7107010<step>5000010<col>001<step>5105006<col>600<ans>060060 |
sub | 42 | 2850 | -582 | 18 | -600 | 2x3 | + | 18+-600= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | train | 006810 | [
{
"borrow_in": 0,
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"output_digit": 2,
"serialized": "08021",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 8,
"serialized": "01181",
"subtrahend... | 18+-600=<sub><neg><state>006810<step>08021<step>01181<step>60150<ans>2850 |
sub | 42 | 0400 | 40 | -10 | -50 | 2x2 | - | -10--50= | scratchpad-v3 | positive | null | no_borrow | -- | train | 050010 | [
{
"borrow_in": 0,
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"serialized": "00000",
"subtrahend_digit": 0
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 5,
"output_digit": 4,
"serialized": "51040",
"subtrahend... | -10--50=<sub><pos><state>050010<step>00000<step>51040<step>00000<ans>0400 |
mul | 119 | 648648 | -846846 | 858 | -987 | 3x3 | * | 858*-987= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 858789 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 7,
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"column": 0,
"kind": "term",
"product": 56,
"running_total": 56,
"serialized": "8756056",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 5,
"column": 0,
"column_sum": 56,
"kind": "column",
... | 858*-987=<mul><neg><state>858789<step>8756056<col>605<step>8864069<step>5735104<col>410<step>8972082<step>5840122<step>8756178<col>817<step>5945062<step>8864126<col>612<step>8972084<col>408<ans>648648 |
add | 42 | 4340 | -434 | -432 | -2 | 3x1 | + | -432+-2= | scratchpad-v3 | negative | null | no_carry | -- | train | 234200 | [
{
"a_digit": 2,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 4,
"serialized": "22040"
},
{
"a_digit": 3,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "30030"
},
{
"a_digit":... | -432+-2=<add><neg><state>234200<step>22040<step>30030<step>40040<ans>4340 |
mul | 118 | 827010 | -10728 | -596 | 18 | 3x2 | * | -596*18= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 695810 | [
{
"a_digit": 6,
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"column": 0,
"kind": "term",
"product": 48,
"running_total": 48,
"serialized": "6848048",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 48,
"kind": "column",
... | -596*18=<mul><neg><state>695810<step>6848048<col>804<step>6106010<step>9872082<col>208<step>6000008<step>9109017<step>5840057<col>705<step>9000005<step>5105010<col>001<step>5000001<col>100<ans>827010 |
sub | 43 | 1550 | -551 | 137 | -688 | 3x3 | + | 137+-688= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | train | 886731 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 8,
"output_digit": 1,
"serialized": "87010",
"subtrahend_digit": 7
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 8,
"output_digit": 5,
"serialized": "83050",
"subtrahend... | 137+-688=<sub><neg><state>886731<step>87010<step>83050<step>61050<ans>1550 |
add | 44 | 3021 | -1203 | -759 | -444 | 3x3 | + | -759+-444= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 957444 | [
{
"a_digit": 9,
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"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 3,
"serialized": "94031"
},
{
"a_digit": 5,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "54101"
},
{
"a_digit":... | -759+-444=<add><neg><state>957444<step>94031<step>54101<step>74121<ans>3021 |
sub | 41 | 7400 | -47 | -99 | 52 | 2x2 | + | -99+52= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 990250 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 9,
"output_digit": 7,
"serialized": "92070",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 4,
"serialized": "95040",
"subtrahend... | -99+52=<sub><neg><state>990250<step>92070<step>95040<step>00000<ans>7400 |
div | 161 | 001.931 | -1.931 | 952 | -493 | 3x3 | / | 952/-493= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 952493 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 493,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 952/-493=<div><neg><state>952493<step>00090009<qmul>00000<rem>009<step>00950095<qmul>00000<rem>095<step>09520952<qmul>10493<rem>459<step>45904590<qmul>94437<rem>153<step>15301530<qmul>31479<rem>051<step>05100510<qmul>10493<rem>017<step>01700170<qmul>00000<rem>170<ans>001.931 |
add | 44 | 9430 | -349 | -234 | -115 | 3x3 | + | -234+-115= | scratchpad-v3 | negative | null | no_carry | -- | train | 432511 | [
{
"a_digit": 4,
"b_digit": 5,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "45090"
},
{
"a_digit": 3,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 4,
"serialized": "31040"
},
{
"a_digit":... | -234+-115=<add><neg><state>432511<step>45090<step>31040<step>21030<ans>9430 |
add | 44 | 6521 | -1256 | -968 | -288 | 3x3 | + | -968+-288= | scratchpad-v3 | negative | null | overflow | -- | train | 869882 | [
{
"a_digit": 8,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 6,
"serialized": "88061"
},
{
"a_digit": 6,
"b_digit": 8,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 5,
"serialized": "68151"
},
{
"a_digit":... | -968+-288=<add><neg><state>869882<step>88061<step>68151<step>92121<ans>6521 |
sub | 41 | 9370 | 739 | 800 | 61 | 3x2 | - | 800-61= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 008160 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 9,
"serialized": "01091",
"subtrahend_digit": 1
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 3,
"serialized": "06131",
"subtrahend... | 800-61=<sub><pos><state>008160<step>01091<step>06131<step>80170<ans>9370 |
div | 161 | 000.574 | -0.574 | -105 | 183 | 3x3 | / | -105/183= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | -+ | test | 105183 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 183,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -105/183=<div><neg><state>105183<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01050105<qmul>00000<rem>105<step>10501050<qmul>50915<rem>135<step>13501350<qmul>71281<rem>069<step>06900690<qmul>30549<rem>141<step>14101410<qmul>71281<rem>129<ans>000.574 |
div | 159 | 000.922 | -0.922 | 59 | -64 | 2x2 | / | 59/-64= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | val | 059064 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | 59/-64=<div><neg><state>059064<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00590059<qmul>00000<rem>059<step>05900590<qmul>90576<rem>014<step>01400140<qmul>20128<rem>012<step>01200120<qmul>10064<rem>056<step>05600560<qmul>80512<rem>048<ans>000.922 |
sub | 44 | 1000 | -1 | -799 | -798 | 3x3 | - | -799--798= | scratchpad-v3 | negative | null | negative_result | -- | train | 997897 | [
{
"borrow_in": 0,
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"column": 0,
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"output_digit": 1,
"serialized": "98010",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 0,
"serialized": "99000",
"subtrahend... | -799--798=<sub><neg><state>997897<step>98010<step>99000<step>77000<ans>1000 |
mul | 119 | 919188 | -881919 | 899 | -981 | 3x3 | * | 899*-981= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 998189 | [
{
"a_digit": 9,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 9,
"kind": "column",
"o... | 899*-981=<mul><neg><state>998189<step>9109009<col>900<step>9872072<step>9109081<col>108<step>9981089<step>9872161<step>8108169<col>916<step>9981097<step>8864161<col>116<step>8972088<col>808<ans>919188 |
mul | 119 | 281796 | -697182 | -887 | 786 | 3x3 | * | -887*786= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 788687 | [
{
"a_digit": 7,
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"column": 0,
"kind": "term",
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"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 42,
"kind": "column",
... | -887*786=<mul><neg><state>788687<step>7642042<col>204<step>7856060<step>8648108<col>810<step>7749059<step>8864123<step>8648171<col>117<step>8756073<step>8864137<col>713<step>8756069<col>906<ans>281796 |
div | 162 | 002.627 | 2.627 | -528 | -201 | 3x3 | / | -528/-201= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 528201 | [
{
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},
{
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"serialized": "00000"
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{
"kind"... | -528/-201=<div><pos><state>528201<step>00050005<qmul>00000<rem>005<step>00520052<qmul>00000<rem>052<step>05280528<qmul>20402<rem>126<step>12601260<qmul>61206<rem>054<step>05400540<qmul>20402<rem>138<step>13801380<qmul>61206<rem>174<step>17401740<qmul>81608<rem>132<ans>002.627 |
div | 160 | 012.465 | -12.465 | 536 | -43 | 3x2 | / | 536/-43= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 536043 | [
{
"incoming_digit": 5,
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},
{
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"serialized": "00000"
},
{
"kind":... | 536/-43=<div><neg><state>536043<step>00050005<qmul>00000<rem>005<step>00530053<qmul>10043<rem>010<step>01060106<qmul>20086<rem>020<step>02000200<qmul>40172<rem>028<step>02800280<qmul>60258<rem>022<step>02200220<qmul>50215<rem>005<step>00500050<qmul>10043<rem>007<ans>012.465 |
div | 161 | 001.196 | -1.196 | 970 | -811 | 3x3 | / | 970/-811= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 970811 | [
{
"incoming_digit": 9,
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},
{
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"serialized": "00000"
},
{
"kind"... | 970/-811=<div><neg><state>970811<step>00090009<qmul>00000<rem>009<step>00970097<qmul>00000<rem>097<step>09700970<qmul>10811<rem>159<step>15901590<qmul>10811<rem>779<step>77907790<qmul>97299<rem>491<step>49104910<qmul>64866<rem>044<step>04400440<qmul>00000<rem>440<ans>001.196 |
mul | 119 | 645012 | -210546 | 378 | -557 | 3x3 | * | 378*-557= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 873755 | [
{
"a_digit": 8,
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},
{
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"column_sum": 56,
"kind": "column",
... | 378*-557=<mul><neg><state>873755<step>8756056<col>605<step>8540045<step>7749094<col>409<step>8540049<step>7535084<step>3721105<col>510<step>7535045<step>3515060<col>006<step>3515021<col>102<ans>645012 |
sub | 42 | 8260 | -628 | 185 | 813 | 3x3 | - | 185-813= | scratchpad-v3 | negative | null | negative_result | ++ | train | 318581 | [
{
"borrow_in": 0,
"borrow_out": 1,
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"serialized": "35081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 2,
"serialized": "18121",
"subtrahend... | 185-813=<sub><neg><state>318581<step>35081<step>18121<step>81160<ans>8260 |
div | 162 | 001.129 | 1.129 | -585 | -518 | 3x3 | / | -585/-518= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 585518 | [
{
"incoming_digit": 5,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | -585/-518=<div><pos><state>585518<step>00050005<qmul>00000<rem>005<step>00580058<qmul>00000<rem>058<step>05850585<qmul>10518<rem>067<step>06700670<qmul>10518<rem>152<step>15201520<qmul>21036<rem>484<step>48404840<qmul>94662<rem>178<step>17801780<qmul>31554<rem>226<ans>001.129 |
mul | 119 | 804123 | -321408 | -576 | 558 | 3x3 | * | -576*558= | scratchpad-v3 | negative | null | medium_column_sum | -+ | val | 675855 | [
{
"a_digit": 6,
"a_index": 0,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 48,
"kind": "column",
... | -576*558=<mul><neg><state>675855<step>6848048<col>804<step>6530034<step>7856090<col>009<step>6530039<step>7535074<step>5840114<col>411<step>7535046<step>5525071<col>107<step>5525032<col>203<ans>804123 |
mul | 119 | 771914 | -419177 | 719 | -583 | 3x3 | * | 719*-583= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 917385 | [
{
"a_digit": 9,
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | 719*-583=<mul><neg><state>917385<step>9327027<col>702<step>9872074<step>1303077<col>707<step>9545052<step>1808060<step>7321081<col>108<step>1505013<step>7856069<col>906<step>7535041<col>104<ans>771914 |
add | 42 | 2041 | 1402 | 417 | 985 | 3x3 | + | 417+985= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 714589 | [
{
"a_digit": 7,
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"carry_in": 0,
"carry_out": 1,
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"serialized": "75021"
},
{
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"carry_out": 1,
"column": 1,
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"serialized": "18101"
},
{
"a_digit":... | 417+985=<add><pos><state>714589<step>75021<step>18101<step>49141<ans>2041 |
mul | 118 | 516271 | 172615 | 437 | 395 | 3x3 | * | 437*395= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 734593 | [
{
"a_digit": 7,
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},
{
"carry_in": 0,
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"kind": "column",
... | 437*395=<mul><pos><state>734593<step>7535035<col>503<step>7963066<step>3515081<col>108<step>7321029<step>3927056<step>4520076<col>607<step>3309016<step>4936052<col>205<step>4312017<col>701<ans>516271 |
add | 44 | 1460 | -641 | -179 | -462 | 3x3 | + | -179+-462= | scratchpad-v3 | negative | null | multi_carry | -- | train | 971264 | [
{
"a_digit": 9,
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},
{
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"serialized": "76141"
},
{
"a_digit":... | -179+-462=<add><neg><state>971264<step>92011<step>76141<step>14160<ans>1460 |
add | 40 | 7020 | 207 | 202 | 5 | 3x1 | + | 202+5= | scratchpad-v3 | positive | null | no_carry | ++ | train | 202500 | [
{
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},
{
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},
{
"a_digit":... | 202+5=<add><pos><state>202500<step>25070<step>00000<step>20020<ans>7020 |
mul | 119 | 441729 | -927144 | -978 | 948 | 3x3 | * | -978*948= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 879849 | [
{
"a_digit": 8,
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},
{
"carry_in": 0,
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"column": 0,
"column_sum": 64,
"kind": "column",
... | -978*948=<mul><neg><state>879849<step>8864064<col>406<step>8432038<step>7856094<col>409<step>8972081<step>7428109<step>9872181<col>118<step>7963081<step>9436117<col>711<step>9981092<col>209<ans>441729 |
sub | 42 | 1510 | -151 | 805 | 956 | 3x3 | - | 805-956= | scratchpad-v3 | negative | null | negative_result | ++ | train | 659508 | [
{
"borrow_in": 0,
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"output_digit": 1,
"serialized": "65010",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 5,
"output_digit": 5,
"serialized": "50050",
"subtrahend... | 805-956=<sub><neg><state>659508<step>65010<step>50050<step>98010<ans>1510 |
div | 159 | 000.000 | 0 | 0 | -830 | 1x3 | / | 0/-830= | scratchpad-v3 | negative | round-half-up | zero_numerator | +- | train | 000830 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 0/-830=<div><neg><state>000830<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 |
div | 158 | 000.000 | 0 | 0 | 586 | 1x3 | / | 0/586= | scratchpad-v3 | positive | round-half-up | zero_numerator | ++ | train | 000586 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 0/586=<div><pos><state>000586<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 |
add | 43 | 9840 | -489 | -462 | -27 | 3x2 | + | -462+-27= | scratchpad-v3 | negative | null | no_carry | -- | train | 264720 | [
{
"a_digit": 2,
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"carry_in": 0,
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"column": 0,
"output_digit": 9,
"serialized": "27090"
},
{
"a_digit": 6,
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"carry_out": 0,
"column": 1,
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"serialized": "62080"
},
{
"a_digit":... | -462+-27=<add><neg><state>264720<step>27090<step>62080<step>40040<ans>9840 |
add | 44 | 9621 | -1269 | -364 | -905 | 3x3 | + | -364+-905= | scratchpad-v3 | negative | null | overflow | -- | train | 463509 | [
{
"a_digit": 4,
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"carry_in": 0,
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"column": 0,
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"serialized": "45090"
},
{
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"carry_out": 0,
"column": 1,
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"serialized": "60060"
},
{
"a_digit":... | -364+-905=<add><neg><state>463509<step>45090<step>60060<step>39021<ans>9621 |
add | 42 | 1041 | 1401 | 988 | 413 | 3x3 | + | 988+413= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 889314 | [
{
"a_digit": 8,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "83011"
},
{
"a_digit": 8,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "81101"
},
{
"a_digit":... | 988+413=<add><pos><state>889314<step>83011<step>81101<step>94141<ans>1041 |
mul | 118 | 802120 | -21208 | -44 | 482 | 2x3 | * | -44*482= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 440284 | [
{
"a_digit": 4,
"a_index": 0,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 8,
"kind": "column",
"o... | -44*482=<mul><neg><state>440284<step>4208008<col>800<step>4832032<step>4208040<col>004<step>4416020<step>4832052<step>0200052<col>205<step>4416021<step>0800021<col>102<step>0400002<col>200<ans>802120 |
div | 19 | <nan> | NAN | 231 | 0 | 3x1 | / | 231/0= | scratchpad-v3 | positive | round-half-up | nan | ++ | test | 231000 | [] | 231/0=<div><pos><state>231000<ans><nan> |
mul | 119 | 411738 | -837114 | -849 | 986 | 3x3 | * | -849*986= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 948689 | [
{
"a_digit": 9,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 54,
"kind": "column",
... | -849*986=<mul><neg><state>948689<step>9654054<col>405<step>9872077<step>4624101<col>110<step>9981091<step>4832123<step>8648171<col>117<step>4936053<step>8864117<col>711<step>8972083<col>308<ans>411738 |
div | 160 | 001.204 | 1.204 | 754 | 626 | 3x3 | / | 754/626= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 754626 | [
{
"incoming_digit": 7,
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"partial": 7,
"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 754/626=<div><pos><state>754626<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07540754<qmul>10626<rem>128<step>12801280<qmul>21252<rem>028<step>02800280<qmul>00000<rem>280<step>28002800<qmul>42504<rem>296<step>29602960<qmul>42504<rem>456<ans>001.204 |
add | 39 | 4400 | 44 | 8 | 36 | 1x2 | + | 8+36= | scratchpad-v3 | positive | null | single_carry | ++ | train | 800630 | [
{
"a_digit": 8,
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},
{
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"carry_out": 0,
"column": 1,
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"serialized": "03140"
},
{
"a_digit":... | 8+36=<add><pos><state>800630<step>86041<step>03140<step>00000<ans>4400 |
mul | 119 | 095892 | -298590 | 538 | -555 | 3x3 | * | 538*-555= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 835555 | [
{
"a_digit": 8,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 40,
"kind": "column",
... | 538*-555=<mul><neg><state>835555<step>8540040<col>004<step>8540044<step>3515059<col>905<step>8540045<step>3515060<step>5525085<col>508<step>3515023<step>5525048<col>804<step>5525029<col>902<ans>095892 |
div | 158 | 029.714 | 29.714 | 208 | 7 | 3x1 | / | 208/7= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 208007 | [
{
"incoming_digit": 2,
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"serialized": "00020002"
},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind": ... | 208/7=<div><pos><state>208007<step>00020002<qmul>00000<rem>002<step>00200020<qmul>20014<rem>006<step>00680068<qmul>90063<rem>005<step>00500050<qmul>70049<rem>001<step>00100010<qmul>10007<rem>003<step>00300030<qmul>40028<rem>002<step>00200020<qmul>20014<rem>006<ans>029.714 |
div | 160 | 027.294 | -27.294 | -464 | 17 | 3x2 | / | -464/17= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 464017 | [
{
"incoming_digit": 4,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | -464/17=<div><neg><state>464017<step>00040004<qmul>00000<rem>004<step>00460046<qmul>20034<rem>012<step>01240124<qmul>70119<rem>005<step>00500050<qmul>20034<rem>016<step>01600160<qmul>90153<rem>007<step>00700070<qmul>40068<rem>002<step>00200020<qmul>10017<rem>003<ans>027.294 |
mul | 116 | 080600 | 6080 | 64 | 95 | 2x2 | * | 64*95= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 460590 | [
{
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"term_index": 0
},
{
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"column": 0,
"column_sum": 20,
"kind": "column",
... | 64*95=<mul><pos><state>460590<step>4520020<col>002<step>4936038<step>6530068<col>806<step>4000006<step>6954060<step>0500060<col>006<step>6000006<step>0900006<col>600<step>0000000<col>000<ans>080600 |
mul | 116 | 638000 | 836 | 38 | 22 | 2x2 | * | 38*22= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 830220 | [
{
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},
{
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"kind": "column",
... | 38*22=<mul><pos><state>830220<step>8216016<col>601<step>8216017<step>3206023<col>302<step>8000002<step>3206008<step>0200008<col>800<step>3000000<step>0200000<col>000<step>0000000<col>000<ans>638000 |
div | 160 | 026.833 | 26.833 | -161 | -6 | 3x1 | / | -161/-6= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 161006 | [
{
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},
{
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"serialized": "00000"
},
{
"kind": ... | -161/-6=<div><pos><state>161006<step>00010001<qmul>00000<rem>001<step>00160016<qmul>20012<rem>004<step>00410041<qmul>60036<rem>005<step>00500050<qmul>80048<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<ans>026.833 |
sub | 42 | 2700 | 72 | 312 | 240 | 3x3 | - | 312-240= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 213042 | [
{
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"borrow_out": 0,
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{
"borrow_in": 0,
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"minuend_digit": 1,
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"serialized": "14071",
"subtrahend... | 312-240=<sub><pos><state>213042<step>20020<step>14071<step>32100<ans>2700 |
sub | 43 | 4030 | 304 | -99 | -403 | 2x3 | - | -99--403= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 304990 | [
{
"borrow_in": 0,
"borrow_out": 1,
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{
"borrow_in": 1,
"borrow_out": 1,
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"serialized": "09101",
"subtrahend... | -99--403=<sub><pos><state>304990<step>39041<step>09101<step>40130<ans>4030 |
add | 44 | 2590 | -952 | -354 | -598 | 3x3 | + | -354+-598= | scratchpad-v3 | negative | null | multi_carry | -- | train | 453895 | [
{
"a_digit": 4,
"b_digit": 8,
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},
{
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"serialized": "59151"
},
{
"a_digit":... | -354+-598=<add><neg><state>453895<step>48021<step>59151<step>35190<ans>2590 |
add | 41 | 1740 | 471 | 412 | 59 | 3x2 | + | 412+59= | scratchpad-v3 | positive | null | single_carry | ++ | train | 214950 | [
{
"a_digit": 2,
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"carry_in": 0,
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{
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"carry_out": 0,
"column": 1,
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"serialized": "15170"
},
{
"a_digit":... | 412+59=<add><pos><state>214950<step>29011<step>15170<step>40040<ans>1740 |
add | 42 | 0890 | 980 | 343 | 637 | 3x3 | + | 343+637= | scratchpad-v3 | positive | null | single_carry | ++ | train | 343736 | [
{
"a_digit": 3,
"b_digit": 7,
"carry_in": 0,
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},
{
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"column": 1,
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"serialized": "43180"
},
{
"a_digit":... | 343+637=<add><pos><state>343736<step>37001<step>43180<step>36090<ans>0890 |
mul | 117 | 837210 | 12738 | 33 | 386 | 2x3 | * | 33*386= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 330683 | [
{
"a_digit": 3,
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"term_index": 0
},
{
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"kind": "column",
... | 33*386=<mul><pos><state>330683<step>3618018<col>801<step>3824025<step>3618043<col>304<step>3309013<step>3824037<step>0600037<col>703<step>3309012<step>0800012<col>201<step>0300001<col>100<ans>837210 |
mul | 119 | 479500 | 5974 | -58 | -103 | 2x3 | * | -58*-103= | scratchpad-v3 | positive | null | contains_zero_digit | -- | test | 850301 | [
{
"a_digit": 8,
"a_index": 0,
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},
{
"carry_in": 0,
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"kind": "column",
... | -58*-103=<mul><pos><state>850301<step>8324024<col>402<step>8000002<step>5315017<col>701<step>8108009<step>5000009<step>0300009<col>900<step>5105005<step>0000005<col>500<step>0100000<col>000<ans>479500 |
mul | 118 | 200700 | -7002 | 389 | -18 | 3x2 | * | 389*-18= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 983810 | [
{
"a_digit": 9,
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"serialized": "9872072",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 72,
"kind": "column",
... | 389*-18=<mul><neg><state>983810<step>9872072<col>207<step>9109016<step>8864080<col>008<step>9000008<step>8108016<step>3824040<col>004<step>8000004<step>3103007<col>700<step>3000000<col>000<ans>200700 |
mul | 120 | 422629 | 926224 | -976 | -949 | 3x3 | * | -976*-949= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 679949 | [
{
"a_digit": 6,
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | -976*-949=<mul><pos><state>679949<step>6954054<col>405<step>6424029<step>7963092<col>209<step>6954063<step>7428091<step>9981172<col>217<step>7963080<step>9436116<col>611<step>9981092<col>209<ans>422629 |
mul | 119 | 428666 | -666824 | -856 | 779 | 3x3 | * | -856*779= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 658977 | [
{
"a_digit": 6,
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"term_index": 0
},
{
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... | -856*779=<mul><neg><state>658977<step>6954054<col>405<step>6742047<step>5945092<col>209<step>6742051<step>5735086<step>8972158<col>815<step>5735050<step>8756106<col>610<step>8756066<col>606<ans>428666 |
mul | 117 | 070200 | -2070 | -46 | 45 | 2x2 | * | -46*45= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 640540 | [
{
"a_digit": 6,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 30,
"kind": "column",
... | -46*45=<mul><neg><state>640540<step>6530030<col>003<step>6424027<step>4520047<col>704<step>6000004<step>4416020<step>0500020<col>002<step>4000002<step>0400002<col>200<step>0000000<col>000<ans>070200 |
mul | 118 | 472806 | 608274 | 719 | 846 | 3x3 | * | 719*846= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 917648 | [
{
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},
{
"carry_in": 0,
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"kind": "column",
... | 719*846=<mul><pos><state>917648<step>9654054<col>405<step>9436041<step>1606047<col>704<step>9872076<step>1404080<step>7642122<col>212<step>1808020<step>7428048<col>804<step>7856060<col>006<ans>472806 |
add | 44 | 7250 | -527 | -323 | -204 | 3x3 | + | -323+-204= | scratchpad-v3 | negative | null | no_carry | -- | train | 323402 | [
{
"a_digit": 3,
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"carry_in": 0,
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},
{
"a_digit": 2,
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"carry_out": 0,
"column": 1,
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"serialized": "20020"
},
{
"a_digit":... | -323+-204=<add><neg><state>323402<step>34070<step>20020<step>32050<ans>7250 |
mul | 119 | 900477 | -774009 | 789 | -981 | 3x3 | * | 789*-981= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 987189 | [
{
"a_digit": 9,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 9,
"kind": "column",
"o... | 789*-981=<mul><neg><state>987189<step>9109009<col>900<step>9872072<step>8108080<col>008<step>9981089<step>8864153<step>7107160<col>016<step>8972088<step>7856144<col>414<step>7963077<col>707<ans>900477 |
div | 161 | 001.017 | -1.017 | 894 | -879 | 3x3 | / | 894/-879= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 894879 | [
{
"incoming_digit": 8,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 894/-879=<div><neg><state>894879<step>00080008<qmul>00000<rem>008<step>00890089<qmul>00000<rem>089<step>08940894<qmul>10879<rem>015<step>01500150<qmul>00000<rem>150<step>15001500<qmul>10879<rem>621<step>62106210<qmul>76153<rem>057<step>05700570<qmul>00000<rem>570<ans>001.017 |
sub | 44 | 4800 | 84 | -147 | -231 | 3x3 | - | -147--231= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 132741 | [
{
"borrow_in": 0,
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"serialized": "17041",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 8,
"serialized": "34181",
"subtrahend... | -147--231=<sub><pos><state>132741<step>17041<step>34181<step>21100<ans>4800 |
mul | 118 | 401720 | -27104 | 968 | -28 | 3x2 | * | 968*-28= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 869820 | [
{
"a_digit": 8,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 64,
"kind": "column",
... | 968*-28=<mul><neg><state>869820<step>8864064<col>406<step>8216022<step>6848070<col>007<step>8000007<step>6212019<step>9872091<col>109<step>6000009<step>9218027<col>702<step>9000002<col>200<ans>401720 |
mul | 119 | 367978 | -879763 | 947 | -929 | 3x3 | * | 947*-929= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 749929 | [
{
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 63,
"kind": "column",
... | 947*-929=<mul><neg><state>749929<step>7963063<col>306<step>7214020<step>4936056<col>605<step>7963068<step>4208076<step>9981157<col>715<step>4936051<step>9218069<col>906<step>9981087<col>708<ans>367978 |
mul | 120 | 843188 | 881348 | -997 | -884 | 3x3 | * | -997*-884= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 799488 | [
{
"a_digit": 7,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 28,
"kind": "column",
... | -997*-884=<mul><pos><state>799488<step>7428028<col>802<step>7856058<step>9436094<col>409<step>7856065<step>9872137<step>9436173<col>317<step>9872089<step>9872161<col>116<step>9872088<col>808<ans>843188 |
add | 43 | 1360 | -631 | -570 | -61 | 3x2 | + | -570+-61= | scratchpad-v3 | negative | null | single_carry | -- | train | 075160 | [
{
"a_digit": 0,
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},
{
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"carry_in": 0,
"carry_out": 1,
"column": 1,
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"serialized": "76031"
},
{
"a_digit":... | -570+-61=<add><neg><state>075160<step>01010<step>76031<step>50160<ans>1360 |
mul | 120 | 585306 | 603585 | -765 | -789 | 3x3 | * | -765*-789= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 567987 | [
{
"a_digit": 5,
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"column": 0,
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"serialized": "5945045",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 45,
"kind": "column",
... | -765*-789=<mul><pos><state>567987<step>5945045<col>504<step>5840044<step>6954098<col>809<step>5735044<step>6848092<step>7963155<col>515<step>6742057<step>7856113<col>311<step>7749060<col>006<ans>585306 |
add | 41 | 6510 | -156 | -156 | 0 | 3x1 | - | -156-0= | scratchpad-v3 | negative | null | identity | -+ | test | 651000 | [
{
"a_digit": 6,
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"serialized": "60060"
},
{
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"carry_out": 0,
"column": 1,
"output_digit": 5,
"serialized": "50050"
},
{
"a_digit":... | -156-0=<add><neg><state>651000<step>60060<step>50050<step>10010<ans>6510 |
sub | 41 | 7710 | 177 | 244 | 67 | 3x2 | - | 244-67= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 442760 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "47071",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "46171",
"subtrahend... | 244-67=<sub><pos><state>442760<step>47071<step>46171<step>20110<ans>7710 |
div | 159 | 001.313 | -1.313 | 21 | -16 | 2x2 | / | 21/-16= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 021016 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | 21/-16=<div><neg><state>021016<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00210021<qmul>10016<rem>005<step>00500050<qmul>30048<rem>002<step>00200020<qmul>10016<rem>004<step>00400040<qmul>20032<rem>008<step>00800080<qmul>50080<rem>000<ans>001.313 |
div | 160 | 001.381 | 1.381 | 710 | 514 | 3x3 | / | 710/514= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 710514 | [
{
"incoming_digit": 7,
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},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 710/514=<div><pos><state>710514<step>00070007<qmul>00000<rem>007<step>00710071<qmul>00000<rem>071<step>07100710<qmul>10514<rem>196<step>19601960<qmul>31542<rem>418<step>41804180<qmul>84112<rem>068<step>06800680<qmul>10514<rem>166<step>16601660<qmul>31542<rem>118<ans>001.381 |
add | 42 | 7140 | -417 | -409 | -8 | 3x1 | + | -409+-8= | scratchpad-v3 | negative | null | single_carry | -- | train | 904800 | [
{
"a_digit": 9,
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"carry_in": 0,
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"serialized": "98071"
},
{
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"carry_out": 0,
"column": 1,
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"serialized": "00110"
},
{
"a_digit":... | -409+-8=<add><neg><state>904800<step>98071<step>00110<step>40040<ans>7140 |
div | 161 | 011.412 | 11.412 | -970 | -85 | 3x2 | / | -970/-85= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 970085 | [
{
"incoming_digit": 9,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | -970/-85=<div><pos><state>970085<step>00090009<qmul>00000<rem>009<step>00970097<qmul>10085<rem>012<step>01200120<qmul>10085<rem>035<step>03500350<qmul>40340<rem>010<step>01000100<qmul>10085<rem>015<step>01500150<qmul>10085<rem>065<step>06500650<qmul>70595<rem>055<ans>011.412 |
mul | 117 | 629730 | 37926 | 774 | 49 | 3x2 | * | 774*49= | scratchpad-v3 | positive | null | medium_column_sum | ++ | val | 477940 | [
{
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{
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"kind": "column",
... | 774*49=<mul><pos><state>477940<step>4936036<col>603<step>4416019<step>7963082<col>208<step>4000008<step>7428036<step>7963099<col>909<step>7000009<step>7428037<col>703<step>7000003<col>300<ans>629730 |
sub | 42 | 9100 | 19 | 463 | 444 | 3x3 | - | 463-444= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 364444 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 9,
"serialized": "34091",
"subtrahend_digit": 4
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 1,
"serialized": "64110",
"subtrahend... | 463-444=<sub><pos><state>364444<step>34091<step>64110<step>44000<ans>9100 |
add | 44 | 1061 | -1601 | -825 | -776 | 3x3 | + | -825+-776= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 528677 | [
{
"a_digit": 5,
"b_digit": 6,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "56011"
},
{
"a_digit": 2,
"b_digit": 7,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "27101"
},
{
"a_digit":... | -825+-776=<add><neg><state>528677<step>56011<step>27101<step>87161<ans>1061 |
add | 43 | 6580 | -856 | -801 | -55 | 3x2 | + | -801+-55= | scratchpad-v3 | negative | null | no_carry | -- | train | 108550 | [
{
"a_digit": 1,
"b_digit": 5,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 6,
"serialized": "15060"
},
{
"a_digit": 0,
"b_digit": 5,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 5,
"serialized": "05050"
},
{
"a_digit":... | -801+-55=<add><neg><state>108550<step>15060<step>05050<step>80080<ans>6580 |
div | 159 | 000.444 | -0.444 | -32 | 72 | 2x2 | / | -32/72= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 032072 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 72,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -32/72=<div><neg><state>032072<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00320032<qmul>00000<rem>032<step>03200320<qmul>40288<rem>032<step>03200320<qmul>40288<rem>032<step>03200320<qmul>40288<rem>032<step>03200320<qmul>40288<rem>032<ans>000.444 |
div | 160 | 000.367 | 0.367 | -11 | -30 | 2x2 | / | -11/-30= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 011030 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 30,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -11/-30=<div><pos><state>011030<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00110011<qmul>00000<rem>011<step>01100110<qmul>30090<rem>020<step>02000200<qmul>60180<rem>020<step>02000200<qmul>60180<rem>020<step>02000200<qmul>60180<rem>020<ans>000.367 |
sub | 43 | 8710 | -178 | -248 | -70 | 3x2 | - | -248--70= | scratchpad-v3 | negative | null | negative_result | -- | train | 842070 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 8,
"output_digit": 8,
"serialized": "80080",
"subtrahend_digit": 0
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "47071",
"subtrahend... | -248--70=<sub><neg><state>842070<step>80080<step>47071<step>20110<ans>8710 |
sub | 43 | 2900 | 92 | 739 | -647 | 3x3 | + | 739+-647= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 937746 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 2,
"serialized": "97020",
"subtrahend_digit": 7
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 9,
"serialized": "34091",
"subtrahend... | 739+-647=<sub><pos><state>937746<step>97020<step>34091<step>76100<ans>2900 |
mul | 119 | 823475 | -574328 | -697 | 824 | 3x3 | * | -697*824= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 796428 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 28,
"running_total": 28,
"serialized": "7428028",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 28,
"kind": "column",
... | -697*824=<mul><neg><state>796428<step>7428028<col>802<step>7214016<step>9436052<col>205<step>7856061<step>9218079<step>6424103<col>310<step>9872082<step>6212094<col>409<step>6848057<col>705<ans>823475 |
div | 161 | 067.000 | 67 | -938 | -14 | 3x2 | / | -938/-14= | scratchpad-v3 | positive | round-half-up | exact | -- | train | 938014 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 14,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -938/-14=<div><pos><state>938014<step>00090009<qmul>00000<rem>009<step>00930093<qmul>60084<rem>009<step>00980098<qmul>70098<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>067.000 |
div | 161 | 012.303 | 12.303 | -406 | -33 | 3x2 | / | -406/-33= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 406033 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 33,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -406/-33=<div><pos><state>406033<step>00040004<qmul>00000<rem>004<step>00400040<qmul>10033<rem>007<step>00760076<qmul>20066<rem>010<step>01000100<qmul>30099<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>30099<rem>001<step>00100010<qmul>00000<rem>010<ans>012.303 |
sub | 42 | 5560 | 655 | 937 | 282 | 3x3 | - | 937-282= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 739282 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 7,
"output_digit": 5,
"serialized": "72050",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 5,
"serialized": "38051",
"subtrahend... | 937-282=<sub><pos><state>739282<step>72050<step>38051<step>92160<ans>5560 |
add | 43 | 9540 | -459 | -67 | -392 | 2x3 | + | -67+-392= | scratchpad-v3 | negative | null | single_carry | -- | val | 760293 | [
{
"a_digit": 7,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "72090"
},
{
"a_digit": 6,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 5,
"serialized": "69051"
},
{
"a_digit":... | -67+-392=<add><neg><state>760293<step>72090<step>69051<step>03140<ans>9540 |
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