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 | 41 | 7080 | 807 | 903 | 96 | 3x2 | - | 903-96= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 309690 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 7,
"serialized": "36071",
"subtrahend_digit": 6
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 0,
"serialized": "09101",
"subtrahend... | 903-96=<sub><pos><state>309690<step>36071<step>09101<step>90180<ans>7080 |
sub | 44 | 9010 | -109 | -773 | -664 | 3x3 | - | -773--664= | scratchpad-v3 | negative | null | negative_result | -- | train | 377466 | [
{
"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": 7,
"output_digit": 0,
"serialized": "76100",
"subtrahend... | -773--664=<sub><neg><state>377466<step>34091<step>76100<step>76010<ans>9010 |
add | 43 | 7211 | 1127 | 857 | -270 | 3x3 | - | 857--270= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 758072 | [
{
"a_digit": 7,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "70070"
},
{
"a_digit": 5,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "57021"
},
{
"a_digit":... | 857--270=<add><pos><state>758072<step>70070<step>57021<step>82111<ans>7211 |
add | 42 | 4411 | 1144 | 603 | 541 | 3x3 | + | 603+541= | scratchpad-v3 | positive | null | overflow | ++ | train | 306145 | [
{
"a_digit": 3,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 4,
"serialized": "31040"
},
{
"a_digit": 0,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 4,
"serialized": "04040"
},
{
"a_digit":... | 603+541=<add><pos><state>306145<step>31040<step>04040<step>65011<ans>4411 |
sub | 43 | 4700 | -74 | -145 | -71 | 3x2 | - | -145--71= | scratchpad-v3 | negative | null | negative_result | -- | train | 541170 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 4,
"serialized": "51040",
"subtrahend_digit": 1
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "47071",
"subtrahend... | -145--71=<sub><neg><state>541170<step>51040<step>47071<step>10100<ans>4700 |
add | 42 | 0361 | 1630 | 709 | 921 | 3x3 | + | 709+921= | scratchpad-v3 | positive | null | overflow | ++ | train | 907129 | [
{
"a_digit": 9,
"b_digit": 1,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "91001"
},
{
"a_digit": 0,
"b_digit": 2,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "02130"
},
{
"a_digit":... | 709+921=<add><pos><state>907129<step>91001<step>02130<step>79061<ans>0361 |
mul | 117 | 692100 | -1296 | 54 | -24 | 2x2 | * | 54*-24= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 450420 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 16,
"running_total": 16,
"serialized": "4416016",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 16,
"kind": "column",
... | 54*-24=<mul><neg><state>450420<step>4416016<col>601<step>4208009<step>5420029<col>902<step>4000002<step>5210012<step>0400012<col>201<step>5000001<step>0200001<col>100<step>0000000<col>000<ans>692100 |
sub | 43 | 8670 | 768 | -37 | -805 | 2x3 | - | -37--805= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 508730 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 5,
"output_digit": 8,
"serialized": "57081",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "03161",
"subtrahend... | -37--805=<sub><pos><state>508730<step>57081<step>03161<step>80170<ans>8670 |
div | 160 | 000.786 | 0.786 | -22 | -28 | 2x2 | / | -22/-28= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 022028 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 28,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -22/-28=<div><pos><state>022028<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02200220<qmul>70196<rem>024<step>02400240<qmul>80224<rem>016<step>01600160<qmul>50140<rem>020<step>02000200<qmul>70196<rem>004<ans>000.786 |
div | 160 | 020.500 | -20.5 | -574 | 28 | 3x2 | / | -574/28= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 574028 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 28,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -574/28=<div><neg><state>574028<step>00050005<qmul>00000<rem>005<step>00570057<qmul>20056<rem>001<step>00140014<qmul>00000<rem>014<step>01400140<qmul>50140<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>020.500 |
sub | 41 | 1200 | 21 | -28 | 49 | 2x2 | + | -28+49= | scratchpad-v3 | positive | null | magnitude_subtraction | -+ | train | 940820 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 1,
"serialized": "98010",
"subtrahend_digit": 8
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 4,
"output_digit": 2,
"serialized": "42020",
"subtrahend... | -28+49=<sub><pos><state>940820<step>98010<step>42020<step>00000<ans>1200 |
sub | 43 | 7710 | 177 | -29 | -206 | 2x3 | - | -29--206= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 602920 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 6,
"output_digit": 7,
"serialized": "69071",
"subtrahend_digit": 9
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 7,
"serialized": "02171",
"subtrahend... | -29--206=<sub><pos><state>602920<step>69071<step>02171<step>20110<ans>7710 |
add | 42 | 1860 | 681 | 210 | 471 | 3x3 | + | 210+471= | scratchpad-v3 | positive | null | no_carry | ++ | train | 012174 | [
{
"a_digit": 0,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 1,
"serialized": "01010"
},
{
"a_digit": 1,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "17080"
},
{
"a_digit":... | 210+471=<add><pos><state>012174<step>01010<step>17080<step>24060<ans>1860 |
div | 160 | 001.000 | 1 | 649 | 649 | 3x3 | / | 649/649= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 649649 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 649,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 649/649=<div><pos><state>649649<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06490649<qmul>10649<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>001.000 |
mul | 117 | 000000 | 0 | 0 | -848 | 1x3 | * | 0*-848= | scratchpad-v3 | negative | null | identity | +- | train | 000848 | [
{
"a_digit": 0,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 0,
"running_total": 0,
"serialized": "0800000",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | 0*-848=<mul><neg><state>000848<step>0800000<col>000<step>0400000<step>0800000<col>000<step>0800000<step>0400000<step>0800000<col>000<step>0800000<step>0400000<col>000<step>0800000<col>000<ans>000000 |
div | 159 | 009.426 | 9.426 | 575 | 61 | 3x2 | / | 575/61= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 575061 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 61,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 575/61=<div><pos><state>575061<step>00050005<qmul>00000<rem>005<step>00570057<qmul>00000<rem>057<step>05750575<qmul>90549<rem>026<step>02600260<qmul>40244<rem>016<step>01600160<qmul>20122<rem>038<step>03800380<qmul>60366<rem>014<step>01400140<qmul>20122<rem>018<ans>009.426 |
mul | 118 | 597252 | 252795 | 285 | 887 | 3x3 | * | 285*887= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 582788 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 35,
"running_total": 35,
"serialized": "5735035",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 35,
"kind": "column",
... | 285*887=<mul><pos><state>582788<step>5735035<col>503<step>5840043<step>8756099<col>909<step>5840049<step>8864113<step>2714127<col>712<step>8864076<step>2816092<col>209<step>2816025<col>502<ans>597252 |
mul | 120 | 699060 | 60996 | -204 | -299 | 3x3 | * | -204*-299= | scratchpad-v3 | positive | null | contains_zero_digit | -- | train | 402992 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 36,
"running_total": 36,
"serialized": "4936036",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 36,
"kind": "column",
... | -204*-299=<mul><pos><state>402992<step>4936036<col>603<step>4936039<step>0900039<col>903<step>4208011<step>0900011<step>2918029<col>902<step>0200002<step>2918020<col>002<step>2204006<col>600<ans>699060 |
mul | 120 | 462917 | 719264 | -728 | -988 | 3x3 | * | -728*-988= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 827889 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 64,
"running_total": 64,
"serialized": "8864064",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 64,
"kind": "column",
... | -728*-988=<mul><pos><state>827889<step>8864064<col>406<step>8864070<step>2816086<col>608<step>8972080<step>2816096<step>7856152<col>215<step>2918033<step>7856089<col>908<step>7963071<col>107<ans>462917 |
sub | 43 | 9680 | 869 | -37 | -906 | 2x3 | - | -37--906= | scratchpad-v3 | positive | null | borrow_through_zero | -- | test | 609730 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 6,
"output_digit": 9,
"serialized": "67091",
"subtrahend_digit": 7
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "03161",
"subtrahend... | -37--906=<sub><pos><state>609730<step>67091<step>03161<step>90180<ans>9680 |
add | 42 | 5170 | -715 | -681 | 34 | 3x2 | - | -681-34= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 186430 | [
{
"a_digit": 1,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "14050"
},
{
"a_digit": 8,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "83011"
},
{
"a_digit":... | -681-34=<add><neg><state>186430<step>14050<step>83011<step>60170<ans>5170 |
mul | 117 | 882750 | 57288 | 682 | 84 | 3x2 | * | 682*84= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 286480 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 8,
"running_total": 8,
"serialized": "2408008",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 8,
"kind": "column",
"o... | 682*84=<mul><pos><state>286480<step>2408008<col>800<step>2816016<step>8432048<col>804<step>2000004<step>8864068<step>6424092<col>209<step>8000009<step>6848057<col>705<step>6000005<col>500<ans>882750 |
sub | 40 | 1500 | 51 | 91 | 40 | 2x2 | - | 91-40= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 190040 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 1,
"output_digit": 1,
"serialized": "10010",
"subtrahend_digit": 0
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 5,
"serialized": "94050",
"subtrahend... | 91-40=<sub><pos><state>190040<step>10010<step>94050<step>00000<ans>1500 |
add | 44 | 4650 | -564 | -432 | -132 | 3x3 | + | -432+-132= | scratchpad-v3 | negative | null | no_carry | -- | train | 234231 | [
{
"a_digit": 2,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 4,
"serialized": "22040"
},
{
"a_digit": 3,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 6,
"serialized": "33060"
},
{
"a_digit":... | -432+-132=<add><neg><state>234231<step>22040<step>33060<step>41050<ans>4650 |
add | 42 | 5550 | 555 | 297 | 258 | 3x3 | + | 297+258= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 792852 | [
{
"a_digit": 7,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 5,
"serialized": "78051"
},
{
"a_digit": 9,
"b_digit": 5,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 5,
"serialized": "95151"
},
{
"a_digit":... | 297+258=<add><pos><state>792852<step>78051<step>95151<step>22150<ans>5550 |
div | 159 | 002.652 | -2.652 | -61 | 23 | 2x2 | / | -61/23= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | test | 061023 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 23,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -61/23=<div><neg><state>061023<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00610061<qmul>20046<rem>015<step>01500150<qmul>60138<rem>012<step>01200120<qmul>50115<rem>005<step>00500050<qmul>20046<rem>004<step>00400040<qmul>10023<rem>017<ans>002.652 |
div | 160 | 001.478 | 1.478 | 263 | 178 | 3x3 | / | 263/178= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | train | 263178 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 178,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 263/178=<div><pos><state>263178<step>00020002<qmul>00000<rem>002<step>00260026<qmul>00000<rem>026<step>02630263<qmul>10178<rem>085<step>08500850<qmul>40712<rem>138<step>13801380<qmul>71246<rem>134<step>13401340<qmul>71246<rem>094<step>09400940<qmul>50890<rem>050<ans>001.478 |
sub | 41 | 7100 | -17 | -24 | -7 | 2x1 | - | -24--7= | scratchpad-v3 | negative | null | negative_result | -- | train | 420700 | [
{
"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": 1,
"serialized": "20110",
"subtrahend... | -24--7=<sub><neg><state>420700<step>47071<step>20110<step>00000<ans>7100 |
div | 162 | 001.127 | 1.127 | -799 | -709 | 3x3 | / | -799/-709= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 799709 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
"divisor": 709,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -799/-709=<div><pos><state>799709<step>00070007<qmul>00000<rem>007<step>00790079<qmul>00000<rem>079<step>07990799<qmul>10709<rem>090<step>09000900<qmul>10709<rem>191<step>19101910<qmul>21418<rem>492<step>49204920<qmul>64254<rem>666<step>66606660<qmul>96381<rem>279<ans>001.127 |
add | 40 | 2470 | 742 | 3 | 739 | 1x3 | + | 3+739= | scratchpad-v3 | positive | null | single_carry | ++ | train | 300937 | [
{
"a_digit": 3,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 2,
"serialized": "39021"
},
{
"a_digit": 0,
"b_digit": 3,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 4,
"serialized": "03140"
},
{
"a_digit":... | 3+739=<add><pos><state>300937<step>39021<step>03140<step>07070<ans>2470 |
div | 160 | 021.000 | -21 | -651 | 31 | 3x2 | / | -651/31= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 651031 | [
{
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{
"kind":... | -651/31=<div><neg><state>651031<step>00060006<qmul>00000<rem>006<step>00650065<qmul>20062<rem>003<step>00310031<qmul>10031<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>021.000 |
div | 160 | 000.791 | 0.791 | -34 | -43 | 2x2 | / | -34/-43= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 034043 | [
{
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{
"kind":... | -34/-43=<div><pos><state>034043<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03400340<qmul>70301<rem>039<step>03900390<qmul>90387<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>60258<rem>042<ans>000.791 |
mul | 118 | 218397 | 793812 | 996 | 797 | 3x3 | * | 996*797= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 699797 | [
{
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},
{
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... | 996*797=<mul><pos><state>699797<step>6742042<col>204<step>6954058<step>9763121<col>112<step>6742054<step>9981135<step>9763198<col>819<step>9763082<step>9981163<col>316<step>9763079<col>907<ans>218397 |
div | 161 | 001.920 | -1.92 | -649 | 338 | 3x3 | / | -649/338= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 649338 | [
{
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{
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{
"kind"... | -649/338=<div><neg><state>649338<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06490649<qmul>10338<rem>311<step>31103110<qmul>93042<rem>068<step>06800680<qmul>20676<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>10338<rem>062<ans>001.920 |
mul | 117 | 497100 | -1794 | 69 | -26 | 2x2 | * | 69*-26= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 960620 | [
{
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},
{
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... | 69*-26=<mul><neg><state>960620<step>9654054<col>405<step>9218023<step>6636059<col>905<step>9000005<step>6212017<step>0600017<col>701<step>6000001<step>0200001<col>100<step>0000000<col>000<ans>497100 |
mul | 119 | 693568 | -865396 | 868 | -997 | 3x3 | * | 868*-997= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 868799 | [
{
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},
{
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"kind": "column",
... | 868*-997=<mul><neg><state>868799<step>8756056<col>605<step>8972077<step>6742119<col>911<step>8972083<step>6954137<step>8756193<col>319<step>6954073<step>8972145<col>514<step>8972086<col>608<ans>693568 |
div | 160 | 000.343 | -0.343 | 70 | -204 | 2x3 | / | 70/-204= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 070204 | [
{
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},
{
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"serialized": "00000"
},
{
"kind"... | 70/-204=<div><neg><state>070204<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>30612<rem>088<step>08800880<qmul>40816<rem>064<step>06400640<qmul>30612<rem>028<step>02800280<qmul>10204<rem>076<ans>000.343 |
sub | 41 | 6280 | -826 | 12 | 838 | 2x3 | - | 12-838= | scratchpad-v3 | negative | null | negative_result | ++ | train | 838210 | [
{
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},
{
"borrow_in": 0,
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"output_digit": 2,
"serialized": "31020",
"subtrahend... | 12-838=<sub><neg><state>838210<step>82060<step>31020<step>80080<ans>6280 |
mul | 118 | 857610 | -16758 | 882 | -19 | 3x2 | * | 882*-19= | scratchpad-v3 | negative | null | medium_column_sum | +- | val | 288910 | [
{
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},
{
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... | 882*-19=<mul><neg><state>288910<step>2918018<col>801<step>2102003<step>8972075<col>507<step>2000007<step>8108015<step>8972087<col>708<step>8000008<step>8108016<col>601<step>8000001<col>100<ans>857610 |
mul | 120 | 757603 | 306757 | -353 | -869 | 3x3 | * | -353*-869= | scratchpad-v3 | positive | null | medium_column_sum | -- | val | 353968 | [
{
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},
{
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... | -353*-869=<mul><pos><state>353968<step>3927027<col>702<step>3618020<step>5945065<col>506<step>3824030<step>5630060<step>3927087<col>708<step>5840048<step>3618066<col>606<step>3824030<col>003<ans>757603 |
mul | 117 | 048600 | 6840 | 38 | 180 | 2x3 | * | 38*180= | scratchpad-v3 | positive | null | contains_zero_digit | ++ | train | 830081 | [
{
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},
{
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"o... | 38*180=<mul><pos><state>830081<step>8000000<col>000<step>8864064<step>3000064<col>406<step>8108014<step>3824038<step>0000038<col>803<step>3103006<step>0800006<col>600<step>0100000<col>000<ans>048600 |
sub | 43 | 8860 | 688 | -17 | -705 | 2x3 | - | -17--705= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 507710 | [
{
"borrow_in": 0,
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"serialized": "57081",
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},
{
"borrow_in": 1,
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"column": 1,
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"output_digit": 8,
"serialized": "01181",
"subtrahend... | -17--705=<sub><pos><state>507710<step>57081<step>01181<step>70160<ans>8860 |
div | 160 | 000.447 | -0.447 | -68 | 152 | 2x3 | / | -68/152= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 068152 | [
{
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | -68/152=<div><neg><state>068152<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00680068<qmul>00000<rem>068<step>06800680<qmul>40608<rem>072<step>07200720<qmul>40608<rem>112<step>11201120<qmul>71064<rem>056<step>05600560<qmul>30456<rem>104<ans>000.447 |
div | 160 | 010.187 | -10.187 | -764 | 75 | 3x2 | / | -764/75= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 764075 | [
{
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | -764/75=<div><neg><state>764075<step>00070007<qmul>00000<rem>007<step>00760076<qmul>10075<rem>001<step>00140014<qmul>00000<rem>014<step>01400140<qmul>10075<rem>065<step>06500650<qmul>80600<rem>050<step>05000500<qmul>60450<rem>050<step>05000500<qmul>60450<rem>050<ans>010.187 |
add | 42 | 8960 | 698 | 316 | 382 | 3x3 | + | 316+382= | scratchpad-v3 | positive | null | no_carry | ++ | train | 613283 | [
{
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},
{
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"serialized": "18090"
},
{
"a_digit":... | 316+382=<add><pos><state>613283<step>62080<step>18090<step>33060<ans>8960 |
sub | 40 | 9000 | 9 | -8 | 17 | 1x2 | + | -8+17= | scratchpad-v3 | positive | null | magnitude_subtraction | -+ | train | 710800 | [
{
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},
{
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"column": 1,
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"output_digit": 0,
"serialized": "10100",
"subtrahend... | -8+17=<sub><pos><state>710800<step>78091<step>10100<step>00000<ans>9000 |
mul | 118 | 084210 | -12480 | 160 | -78 | 3x2 | * | 160*-78= | scratchpad-v3 | negative | null | contains_zero_digit | +- | train | 061870 | [
{
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},
{
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"o... | 160*-78=<mul><neg><state>061870<step>0800000<col>000<step>0700000<step>6848048<col>804<step>0000004<step>6742046<step>1808054<col>405<step>6000005<step>1707012<col>201<step>1000001<col>100<ans>084210 |
div | 162 | 001.169 | 1.169 | -727 | -622 | 3x3 | / | -727/-622= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 727622 | [
{
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},
{
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"serialized": "00000"
},
{
"kind"... | -727/-622=<div><pos><state>727622<step>00070007<qmul>00000<rem>007<step>00720072<qmul>00000<rem>072<step>07270727<qmul>10622<rem>105<step>10501050<qmul>10622<rem>428<step>42804280<qmul>63732<rem>548<step>54805480<qmul>84976<rem>504<step>50405040<qmul>84976<rem>064<ans>001.169 |
div | 158 | 002.667 | 2.667 | -8 | -3 | 1x1 | / | -8/-3= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 008003 | [
{
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},
{
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},
{
"kind": ... | -8/-3=<div><pos><state>008003<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00080008<qmul>20006<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<ans>002.667 |
mul | 119 | 353727 | -727353 | -869 | 837 | 3x3 | * | -869*837= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 968738 | [
{
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},
{
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"kind": "column",
... | -869*837=<mul><neg><state>968738<step>9763063<col>306<step>9327033<step>6742075<col>507<step>9872079<step>6318097<step>8756153<col>315<step>6848063<step>8324087<col>708<step>8864072<col>207<ans>353727 |
div | 161 | 001.000 | -1 | 207 | -207 | 3x3 | / | 207/-207= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 207207 | [
{
"incoming_digit": 2,
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},
{
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"serialized": "00000"
},
{
"kind"... | 207/-207=<div><neg><state>207207<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02070207<qmul>10207<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>001.000 |
sub | 42 | 4100 | 14 | -41 | -55 | 2x2 | - | -41--55= | scratchpad-v3 | positive | null | no_borrow | -- | train | 550140 | [
{
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"serialized": "51040",
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},
{
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"column": 1,
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"output_digit": 1,
"serialized": "54010",
"subtrahend... | -41--55=<sub><pos><state>550140<step>51040<step>54010<step>00000<ans>4100 |
mul | 116 | 570000 | -75 | -75 | 1 | 2x1 | * | -75*1= | scratchpad-v3 | negative | null | identity | -+ | train | 570100 | [
{
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},
{
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"kind": "column",
"o... | -75*1=<mul><neg><state>570100<step>5105005<col>500<step>5000000<step>7107007<col>700<step>5000000<step>7000000<step>0100000<col>000<step>7000000<step>0000000<col>000<step>0000000<col>000<ans>570000 |
add | 44 | 3441 | -1443 | -549 | -894 | 3x3 | + | -549+-894= | scratchpad-v3 | negative | null | overflow | -- | train | 945498 | [
{
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},
{
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"column": 1,
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"serialized": "49141"
},
{
"a_digit":... | -549+-894=<add><neg><state>945498<step>94031<step>49141<step>58141<ans>3441 |
div | 157 | 000.127 | 0.127 | 9 | 71 | 1x2 | / | 9/71= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 009071 | [
{
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},
{
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"serialized": "00000"
},
{
"kind":... | 9/71=<div><pos><state>009071<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00090009<qmul>00000<rem>009<step>00900090<qmul>10071<rem>019<step>01900190<qmul>20142<rem>048<step>04800480<qmul>60426<rem>054<step>05400540<qmul>70497<rem>043<ans>000.127 |
mul | 118 | 255360 | -63552 | -662 | 96 | 3x2 | * | -662*96= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 266690 | [
{
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},
{
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"kind": "column",
... | -662*96=<mul><neg><state>266690<step>2612012<col>201<step>2918019<step>6636055<col>505<step>2000005<step>6954059<step>6636095<col>509<step>6000009<step>6954063<col>306<step>6000006<col>600<ans>255360 |
mul | 119 | 807860 | 68708 | -772 | -89 | 3x2 | * | -772*-89= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 277980 | [
{
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},
{
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"kind": "column",
... | -772*-89=<mul><pos><state>277980<step>2918018<col>801<step>2816017<step>7963080<col>008<step>2000008<step>7856064<step>7963127<col>712<step>7000012<step>7856068<col>806<step>7000006<col>600<ans>807860 |
div | 161 | 000.814 | -0.814 | -320 | 393 | 3x3 | / | -320/393= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 320393 | [
{
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},
{
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{
"kind"... | -320/393=<div><neg><state>320393<step>00030003<qmul>00000<rem>003<step>00320032<qmul>00000<rem>032<step>03200320<qmul>00000<rem>320<step>32003200<qmul>83144<rem>056<step>05600560<qmul>10393<rem>167<step>16701670<qmul>41572<rem>098<step>09800980<qmul>20786<rem>194<ans>000.814 |
mul | 118 | 082940 | -49280 | -55 | 896 | 2x3 | * | -55*896= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 550698 | [
{
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},
{
"carry_in": 0,
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"kind": "column",
... | -55*896=<mul><neg><state>550698<step>5630030<col>003<step>5945048<step>5630078<col>807<step>5840047<step>5945092<step>0600092<col>209<step>5840049<step>0900049<col>904<step>0800004<col>400<ans>082940 |
div | 161 | 000.348 | -0.348 | 261 | -749 | 3x3 | / | 261/-749= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 261749 | [
{
"incoming_digit": 2,
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},
{
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"serialized": "00000"
},
{
"kind"... | 261/-749=<div><neg><state>261749<step>00020002<qmul>00000<rem>002<step>00260026<qmul>00000<rem>026<step>02610261<qmul>00000<rem>261<step>26102610<qmul>32247<rem>363<step>36303630<qmul>42996<rem>634<step>63406340<qmul>85992<rem>348<step>34803480<qmul>42996<rem>484<ans>000.348 |
sub | 43 | 1650 | 561 | -39 | -600 | 2x3 | - | -39--600= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 006930 | [
{
"borrow_in": 0,
"borrow_out": 1,
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},
{
"borrow_in": 1,
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"output_digit": 6,
"serialized": "03161",
"subtrahend... | -39--600=<sub><pos><state>006930<step>09011<step>03161<step>60150<ans>1650 |
mul | 118 | 653748 | 847356 | 879 | 964 | 3x3 | * | 879*964= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 978469 | [
{
"a_digit": 9,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
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"kind": "column",
... | 879*964=<mul><pos><state>978469<step>9436036<col>603<step>9654057<step>7428085<col>508<step>9981089<step>7642131<step>8432163<col>316<step>7963079<step>8648127<col>712<step>8972084<col>408<ans>653748 |
sub | 43 | 3110 | 113 | 811 | -698 | 3x3 | + | 811+-698= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 118896 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 1,
"output_digit": 3,
"serialized": "18031",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 1,
"serialized": "19111",
"subtrahend... | 811+-698=<sub><pos><state>118896<step>18031<step>19111<step>86110<ans>3110 |
add | 42 | 6011 | 1106 | 928 | 178 | 3x3 | + | 928+178= | scratchpad-v3 | positive | null | cascading_carry | ++ | val | 829871 | [
{
"a_digit": 8,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 6,
"serialized": "88061"
},
{
"a_digit": 2,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "27101"
},
{
"a_digit":... | 928+178=<add><pos><state>829871<step>88061<step>27101<step>91111<ans>6011 |
mul | 118 | 689623 | 326986 | 334 | 979 | 3x3 | * | 334*979= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 433979 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 9,
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"column": 0,
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"serialized": "4936036",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 36,
"kind": "column",
... | 334*979=<mul><pos><state>433979<step>4936036<col>603<step>4728031<step>3927058<col>805<step>4936041<step>3721062<step>3927089<col>908<step>3927035<step>3721056<col>605<step>3927032<col>203<ans>689623 |
div | 161 | 000.236 | -0.236 | -235 | 997 | 3x3 | / | -235/997= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | -+ | train | 235997 | [
{
"incoming_digit": 2,
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"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"... | -235/997=<div><neg><state>235997<step>00020002<qmul>00000<rem>002<step>00230023<qmul>00000<rem>023<step>02350235<qmul>00000<rem>235<step>23502350<qmul>21994<rem>356<step>35603560<qmul>32991<rem>569<step>56905690<qmul>54985<rem>705<step>70507050<qmul>76979<rem>071<ans>000.236 |
mul | 118 | 614033 | 330416 | 428 | 772 | 3x3 | * | 428*772= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 824277 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 2,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | 428*772=<mul><pos><state>824277<step>8216016<col>601<step>8756057<step>2204061<col>106<step>8756062<step>2714076<step>4208084<col>408<step>2714022<step>4728050<col>005<step>4728033<col>303<ans>614033 |
sub | 42 | 6700 | 76 | -17 | -93 | 2x2 | - | -17--93= | scratchpad-v3 | positive | null | single_borrow | -- | test | 390710 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 6,
"serialized": "37061",
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 7,
"serialized": "91170",
"subtrahend... | -17--93=<sub><pos><state>390710<step>37061<step>91170<step>00000<ans>6700 |
sub | 42 | 8230 | 328 | 810 | 482 | 3x3 | - | 810-482= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 018284 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 8,
"serialized": "02081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 2,
"serialized": "18121",
"subtrahend... | 810-482=<sub><pos><state>018284<step>02081<step>18121<step>84130<ans>8230 |
mul | 119 | 221727 | -727122 | 759 | -958 | 3x3 | * | 759*-958= | scratchpad-v3 | negative | null | high_column_sum | +- | val | 957859 | [
{
"a_digit": 9,
"a_index": 0,
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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",
... | 759*-958=<mul><neg><state>957859<step>9872072<col>207<step>9545052<step>5840092<col>209<step>9981090<step>5525115<step>7856171<col>117<step>5945062<step>7535097<col>709<step>7963072<col>207<ans>221727 |
add | 42 | 3770 | 773 | 684 | -89 | 3x2 | - | 684--89= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 486980 | [
{
"a_digit": 4,
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"carry_in": 0,
"carry_out": 1,
"column": 0,
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"serialized": "49031"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 7,
"serialized": "88171"
},
{
"a_digit":... | 684--89=<add><pos><state>486980<step>49031<step>88171<step>60170<ans>3770 |
div | 160 | 024.758 | -24.758 | -817 | 33 | 3x2 | / | -817/33= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 817033 | [
{
"incoming_digit": 8,
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"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":... | -817/33=<div><neg><state>817033<step>00080008<qmul>00000<rem>008<step>00810081<qmul>20066<rem>015<step>01570157<qmul>40132<rem>025<step>02500250<qmul>70231<rem>019<step>01900190<qmul>50165<rem>025<step>02500250<qmul>70231<rem>019<step>01900190<qmul>50165<rem>025<ans>024.758 |
add | 44 | 1650 | -561 | -284 | -277 | 3x3 | + | -284+-277= | scratchpad-v3 | negative | null | multi_carry | -- | train | 482772 | [
{
"a_digit": 4,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
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},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "87161"
},
{
"a_digit":... | -284+-277=<add><neg><state>482772<step>47011<step>87161<step>22150<ans>1650 |
mul | 119 | 211520 | 25112 | -292 | -86 | 3x2 | * | -292*-86= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 292680 | [
{
"a_digit": 2,
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"term_index": 0
},
{
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"kind": "column",
... | -292*-86=<mul><pos><state>292680<step>2612012<col>201<step>2816017<step>9654071<col>107<step>2000007<step>9872079<step>2612091<col>109<step>9000009<step>2816025<col>502<step>2000002<col>200<ans>211520 |
mul | 119 | 574771 | -177475 | 229 | -775 | 3x3 | * | 229*-775= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 922577 | [
{
"a_digit": 9,
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"term_index": 0
},
{
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"column": 0,
"column_sum": 45,
"kind": "column",
... | 229*-775=<mul><neg><state>922577<step>9545045<col>504<step>9763067<step>2510077<col>707<step>9763070<step>2714084<step>2510094<col>409<step>2714023<step>2714037<col>703<step>2714017<col>701<ans>574771 |
div | 162 | 000.264 | 0.264 | -173 | -655 | 3x3 | / | -173/-655= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 173655 | [
{
"incoming_digit": 1,
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"partial": 1,
"position": 0,
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},
{
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"serialized": "00000"
},
{
"kind"... | -173/-655=<div><pos><state>173655<step>00010001<qmul>00000<rem>001<step>00170017<qmul>00000<rem>017<step>01730173<qmul>00000<rem>173<step>17301730<qmul>21310<rem>420<step>42004200<qmul>63930<rem>270<step>27002700<qmul>42620<rem>080<step>08000800<qmul>10655<rem>145<ans>000.264 |
mul | 118 | 891654 | 456198 | 834 | 547 | 3x3 | * | 834*547= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 438745 | [
{
"a_digit": 4,
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"column": 0,
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"serialized": "4728028",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 28,
"kind": "column",
... | 834*547=<mul><pos><state>438745<step>4728028<col>802<step>4416018<step>3721039<col>903<step>4520023<step>3412035<step>8756091<col>109<step>3515024<step>8432056<col>605<step>8540045<col>504<ans>891654 |
mul | 119 | 651660 | -66156 | -149 | 444 | 3x3 | * | -149*444= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 941444 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 36,
"running_total": 36,
"serialized": "9436036",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 36,
"kind": "column",
... | -149*444=<mul><neg><state>941444<step>9436036<col>603<step>9436039<step>4416055<col>505<step>9436041<step>4416057<step>1404061<col>106<step>4416022<step>1404026<col>602<step>1404006<col>600<ans>651660 |
add | 44 | 0450 | -540 | -362 | -178 | 3x3 | + | -362+-178= | scratchpad-v3 | negative | null | multi_carry | -- | val | 263871 | [
{
"a_digit": 2,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "28001"
},
{
"a_digit": 6,
"b_digit": 7,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 4,
"serialized": "67141"
},
{
"a_digit":... | -362+-178=<add><neg><state>263871<step>28001<step>67141<step>31150<ans>0450 |
add | 44 | 3241 | -1423 | -693 | -730 | 3x3 | + | -693+-730= | scratchpad-v3 | negative | null | overflow | -- | val | 396037 | [
{
"a_digit": 3,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "30030"
},
{
"a_digit": 9,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "93021"
},
{
"a_digit":... | -693+-730=<add><neg><state>396037<step>30030<step>93021<step>67141<ans>3241 |
div | 160 | 004.809 | -4.809 | 428 | -89 | 3x2 | / | 428/-89= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 428089 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 428/-89=<div><neg><state>428089<step>00040004<qmul>00000<rem>004<step>00420042<qmul>00000<rem>042<step>04280428<qmul>40356<rem>072<step>07200720<qmul>80712<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>80712<rem>088<step>08800880<qmul>90801<rem>079<ans>004.809 |
div | 161 | 001.241 | -1.241 | -840 | 677 | 3x3 | / | -840/677= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 840677 | [
{
"incoming_digit": 8,
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"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"... | -840/677=<div><neg><state>840677<step>00080008<qmul>00000<rem>008<step>00840084<qmul>00000<rem>084<step>08400840<qmul>10677<rem>163<step>16301630<qmul>21354<rem>276<step>27602760<qmul>42708<rem>052<step>05200520<qmul>00000<rem>520<step>52005200<qmul>74739<rem>461<ans>001.241 |
add | 42 | 3041 | 1403 | 705 | 698 | 3x3 | + | 705+698= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 507896 | [
{
"a_digit": 5,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 3,
"serialized": "58031"
},
{
"a_digit": 0,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "09101"
},
{
"a_digit":... | 705+698=<add><pos><state>507896<step>58031<step>09101<step>76141<ans>3041 |
mul | 119 | 241191 | -191142 | 666 | -287 | 3x3 | * | 666*-287= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 666782 | [
{
"a_digit": 6,
"a_index": 0,
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"column": 0,
"kind": "term",
"product": 42,
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"serialized": "6742042",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 42,
"kind": "column",
... | 666*-287=<mul><neg><state>666782<step>6742042<col>204<step>6848052<step>6742094<col>409<step>6212021<step>6848069<step>6742111<col>111<step>6212023<step>6848071<col>107<step>6212019<col>901<ans>241191 |
sub | 44 | 1120 | -211 | -529 | -318 | 3x3 | - | -529--318= | scratchpad-v3 | negative | null | negative_result | -- | train | 925813 | [
{
"borrow_in": 0,
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"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... | -529--318=<sub><neg><state>925813<step>98010<step>21010<step>53020<ans>1120 |
add | 44 | 5031 | -1305 | -668 | -637 | 3x3 | + | -668+-637= | scratchpad-v3 | negative | null | cascading_carry | -- | train | 866736 | [
{
"a_digit": 8,
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},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "63101"
},
{
"a_digit":... | -668+-637=<add><neg><state>866736<step>87051<step>63101<step>66131<ans>5031 |
div | 161 | 000.183 | -0.183 | 176 | -962 | 3x3 | / | 176/-962= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 176962 | [
{
"incoming_digit": 1,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 176/-962=<div><neg><state>176962<step>00010001<qmul>00000<rem>001<step>00170017<qmul>00000<rem>017<step>01760176<qmul>00000<rem>176<step>17601760<qmul>10962<rem>798<step>79807980<qmul>87696<rem>284<step>28402840<qmul>21924<rem>916<step>91609160<qmul>98658<rem>502<ans>000.183 |
div | 158 | 000.731 | 0.731 | 38 | 52 | 2x2 | / | 38/52= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 038052 | [
{
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},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 38/52=<div><pos><state>038052<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00380038<qmul>00000<rem>038<step>03800380<qmul>70364<rem>016<step>01600160<qmul>30156<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>70364<rem>036<ans>000.731 |
mul | 119 | 678358 | -853876 | -866 | 986 | 3x3 | * | -866*986= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 668689 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 36,
"running_total": 36,
"serialized": "6636036",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 36,
"kind": "column",
... | -866*986=<mul><neg><state>668689<step>6636036<col>603<step>6848051<step>6636087<col>708<step>6954062<step>6848110<step>8648158<col>815<step>6954069<step>8864133<col>313<step>8972085<col>508<ans>678358 |
sub | 41 | 4680 | 864 | 903 | 39 | 3x2 | - | 903-39= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 309930 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 4,
"serialized": "39041",
"subtrahend_digit": 9
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "03161",
"subtrahend... | 903-39=<sub><pos><state>309930<step>39041<step>03161<step>90180<ans>4680 |
add | 42 | 1080 | 801 | 413 | 388 | 3x3 | + | 413+388= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 314883 | [
{
"a_digit": 3,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "38011"
},
{
"a_digit": 1,
"b_digit": 8,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "18101"
},
{
"a_digit":... | 413+388=<add><pos><state>314883<step>38011<step>18101<step>43180<ans>1080 |
div | 161 | 001.008 | -1.008 | 995 | -987 | 3x3 | / | 995/-987= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 995987 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 987,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 995/-987=<div><neg><state>995987<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09950995<qmul>10987<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>00000<rem>800<step>80008000<qmul>87896<rem>104<step>10401040<qmul>10987<rem>053<ans>001.008 |
div | 158 | 000.488 | 0.488 | 20 | 41 | 2x2 | / | 20/41= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | val | 020041 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 41,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 20/41=<div><pos><state>020041<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>40164<rem>036<step>03600360<qmul>80328<rem>032<step>03200320<qmul>70287<rem>033<step>03300330<qmul>80328<rem>002<ans>000.488 |
div | 20 | <nan> | NAN | -352 | 0 | 3x1 | / | -352/0= | scratchpad-v3 | positive | round-half-up | nan | -+ | train | 352000 | [] | -352/0=<div><pos><state>352000<ans><nan> |
div | 162 | 001.280 | 1.28 | -682 | -533 | 3x3 | / | -682/-533= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 682533 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 533,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -682/-533=<div><pos><state>682533<step>00060006<qmul>00000<rem>006<step>00680068<qmul>00000<rem>068<step>06820682<qmul>10533<rem>149<step>14901490<qmul>21066<rem>424<step>42404240<qmul>73731<rem>509<step>50905090<qmul>94797<rem>293<step>29302930<qmul>52665<rem>265<ans>001.280 |
add | 42 | 4280 | 824 | 569 | 255 | 3x3 | + | 569+255= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 965552 | [
{
"a_digit": 9,
"b_digit": 5,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 4,
"serialized": "95041"
},
{
"a_digit": 6,
"b_digit": 5,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "65121"
},
{
"a_digit":... | 569+255=<add><pos><state>965552<step>95041<step>65121<step>52180<ans>4280 |
add | 43 | 3160 | -613 | -41 | -572 | 2x3 | + | -41+-572= | scratchpad-v3 | negative | null | single_carry | -- | train | 140275 | [
{
"a_digit": 1,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "12030"
},
{
"a_digit": 4,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "47011"
},
{
"a_digit":... | -41+-572=<add><neg><state>140275<step>12030<step>47011<step>05160<ans>3160 |
div | 160 | 039.435 | -39.435 | -907 | 23 | 3x2 | / | -907/23= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 907023 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 23,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -907/23=<div><neg><state>907023<step>00090009<qmul>00000<rem>009<step>00900090<qmul>30069<rem>021<step>02170217<qmul>90207<rem>010<step>01000100<qmul>40092<rem>008<step>00800080<qmul>30069<rem>011<step>01100110<qmul>40092<rem>018<step>01800180<qmul>70161<rem>019<ans>039.435 |
div | 159 | 088.875 | -88.875 | 711 | -8 | 3x1 | / | 711/-8= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 711008 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
"divisor": 8,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 711/-8=<div><neg><state>711008<step>00070007<qmul>00000<rem>007<step>00710071<qmul>80064<rem>007<step>00710071<qmul>80064<rem>007<step>00700070<qmul>80064<rem>006<step>00600060<qmul>70056<rem>004<step>00400040<qmul>50040<rem>000<step>00000000<qmul>00000<rem>000<ans>088.875 |
div | 160 | 000.236 | 0.236 | 144 | 611 | 3x3 | / | 144/611= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 144611 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 611,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 144/611=<div><pos><state>144611<step>00010001<qmul>00000<rem>001<step>00140014<qmul>00000<rem>014<step>01440144<qmul>00000<rem>144<step>14401440<qmul>21222<rem>218<step>21802180<qmul>31833<rem>347<step>34703470<qmul>53055<rem>415<step>41504150<qmul>63666<rem>484<ans>000.236 |
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