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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
add | 44 | 6341 | -1436 | -661 | -775 | 3x3 | + | -661+-775= | scratchpad-v3 | negative | null | overflow | -- | val | 166577 | [
{
"a_digit": 1,
"b_digit": 5,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 6,
"serialized": "15060"
},
{
"a_digit": 6,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "67031"
},
{
"a_digit":... | -661+-775=<add><neg><state>166577<step>15060<step>67031<step>67141<ans>6341 |
add | 41 | 3710 | -173 | -173 | 0 | 3x1 | + | -173+0= | scratchpad-v3 | negative | null | identity | -+ | train | 371000 | [
{
"a_digit": 3,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "30030"
},
{
"a_digit": 7,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "70070"
},
{
"a_digit":... | -173+0=<add><neg><state>371000<step>30030<step>70070<step>10010<ans>3710 |
mul | 116 | 374400 | 4473 | 63 | 71 | 2x2 | * | 63*71= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 360170 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 3,
"running_total": 3,
"serialized": "3103003",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 3,
"kind": "column",
"o... | 63*71=<mul><pos><state>360170<step>3103003<col>300<step>3721021<step>6106027<col>702<step>3000002<step>6742044<step>0100044<col>404<step>6000004<step>0700004<col>400<step>0000000<col>000<ans>374400 |
sub | 42 | 5900 | 95 | -9 | -104 | 1x3 | - | -9--104= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 401900 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 5,
"serialized": "49051",
"subtrahend_digit": 9
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 9,
"serialized": "00191",
"subtrahend... | -9--104=<sub><pos><state>401900<step>49051<step>00191<step>10100<ans>5900 |
add | 41 | 0380 | -830 | 0 | -830 | 1x3 | + | 0+-830= | scratchpad-v3 | negative | null | identity | +- | train | 000038 | [
{
"a_digit": 0,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 0,
"serialized": "00000"
},
{
"a_digit": 0,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "03030"
},
{
"a_digit":... | 0+-830=<add><neg><state>000038<step>00000<step>03030<step>08080<ans>0380 |
mul | 117 | 018400 | -4810 | -74 | 65 | 2x2 | * | -74*65= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 470560 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 20,
"running_total": 20,
"serialized": "4520020",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 20,
"kind": "column",
... | -74*65=<mul><neg><state>470560<step>4520020<col>002<step>4624026<step>7535061<col>106<step>4000006<step>7642048<step>0500048<col>804<step>7000004<step>0600004<col>400<step>0000000<col>000<ans>018400 |
mul | 116 | 804000 | 408 | 24 | 17 | 2x2 | * | 24*17= | scratchpad-v3 | positive | null | low_column_sum | ++ | val | 420710 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 28,
"running_total": 28,
"serialized": "4728028",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 28,
"kind": "column",
... | 24*17=<mul><pos><state>420710<step>4728028<col>802<step>4104006<step>2714020<col>002<step>4000002<step>2102004<step>0700004<col>400<step>2000000<step>0100000<col>000<step>0000000<col>000<ans>804000 |
add | 40 | 2310 | 132 | 0 | 132 | 1x3 | + | 0+132= | scratchpad-v3 | positive | null | identity | ++ | train | 000231 | [
{
"a_digit": 0,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 2,
"serialized": "02020"
},
{
"a_digit": 0,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "03030"
},
{
"a_digit":... | 0+132=<add><pos><state>000231<step>02020<step>03030<step>01010<ans>2310 |
div | 161 | 002.266 | -2.266 | -963 | 425 | 3x3 | / | -963/425= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 963425 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 425,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -963/425=<div><neg><state>963425<step>00090009<qmul>00000<rem>009<step>00960096<qmul>00000<rem>096<step>09630963<qmul>20850<rem>113<step>11301130<qmul>20850<rem>280<step>28002800<qmul>62550<rem>250<step>25002500<qmul>52125<rem>375<step>37503750<qmul>83400<rem>350<ans>002.266 |
div | 159 | 000.179 | -0.179 | -12 | 67 | 2x2 | / | -12/67= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 012067 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 67,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -12/67=<div><neg><state>012067<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01200120<qmul>10067<rem>053<step>05300530<qmul>70469<rem>061<step>06100610<qmul>90603<rem>007<step>00700070<qmul>10067<rem>003<ans>000.179 |
add | 42 | 7881 | 1887 | 905 | 982 | 3x3 | + | 905+982= | scratchpad-v3 | positive | null | overflow | ++ | train | 509289 | [
{
"a_digit": 5,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "52070"
},
{
"a_digit": 0,
"b_digit": 8,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "08080"
},
{
"a_digit":... | 905+982=<add><pos><state>509289<step>52070<step>08080<step>99081<ans>7881 |
sub | 42 | 5750 | 575 | 729 | 154 | 3x3 | - | 729-154= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 927451 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 5,
"serialized": "94050",
"subtrahend_digit": 4
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 7,
"serialized": "25071",
"subtrahend... | 729-154=<sub><pos><state>927451<step>94050<step>25071<step>71150<ans>5750 |
sub | 43 | 1050 | 501 | -21 | -522 | 2x3 | - | -21--522= | scratchpad-v3 | positive | null | no_borrow | -- | train | 225120 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 2,
"output_digit": 1,
"serialized": "21010",
"subtrahend_digit": 1
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 2,
"output_digit": 0,
"serialized": "22000",
"subtrahend... | -21--522=<sub><pos><state>225120<step>21010<step>22000<step>50050<ans>1050 |
sub | 42 | 8400 | 48 | 614 | 566 | 3x3 | - | 614-566= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 416665 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 8,
"serialized": "46081",
"subtrahend_digit": 6
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 4,
"serialized": "16141",
"subtrahend... | 614-566=<sub><pos><state>416665<step>46081<step>16141<step>65100<ans>8400 |
mul | 118 | 580620 | -26085 | -555 | 47 | 3x2 | * | -555*47= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 555740 | [
{
"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",
... | -555*47=<mul><neg><state>555740<step>5735035<col>503<step>5420023<step>5735058<col>805<step>5000005<step>5420025<step>5735060<col>006<step>5000006<step>5420026<col>602<step>5000002<col>200<ans>580620 |
mul | 117 | 693000 | -396 | -11 | 36 | 2x2 | * | -11*36= | scratchpad-v3 | negative | null | repeated_digit | -+ | train | 110630 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 6,
"running_total": 6,
"serialized": "1606006",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 6,
"kind": "column",
"o... | -11*36=<mul><neg><state>110630<step>1606006<col>600<step>1303003<step>1606009<col>900<step>1000000<step>1303003<step>0600003<col>300<step>1000000<step>0300000<col>000<step>0000000<col>000<ans>693000 |
mul | 117 | 552300 | -3255 | 93 | -35 | 2x2 | * | 93*-35= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 390530 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 15,
"running_total": 15,
"serialized": "3515015",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 15,
"kind": "column",
... | 93*-35=<mul><neg><state>390530<step>3515015<col>501<step>3309010<step>9545055<col>505<step>3000005<step>9327032<step>0500032<col>203<step>9000003<step>0300003<col>300<step>0000000<col>000<ans>552300 |
sub | 40 | 5100 | 15 | 92 | 77 | 2x2 | - | 92-77= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 290770 | [
{
"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": 9,
"output_digit": 1,
"serialized": "97110",
"subtrahend... | 92-77=<sub><pos><state>290770<step>27051<step>97110<step>00000<ans>5100 |
div | 160 | 010.500 | -10.5 | 546 | -52 | 3x2 | / | 546/-52= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 546052 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 52,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 546/-52=<div><neg><state>546052<step>00050005<qmul>00000<rem>005<step>00540054<qmul>10052<rem>002<step>00260026<qmul>00000<rem>026<step>02600260<qmul>50260<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>010.500 |
div | 160 | 017.615 | -17.615 | -229 | 13 | 3x2 | / | -229/13= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 229013 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 13,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -229/13=<div><neg><state>229013<step>00020002<qmul>00000<rem>002<step>00220022<qmul>10013<rem>009<step>00990099<qmul>70091<rem>008<step>00800080<qmul>60078<rem>002<step>00200020<qmul>10013<rem>007<step>00700070<qmul>50065<rem>005<step>00500050<qmul>30039<rem>011<ans>017.615 |
mul | 119 | 563780 | -87365 | -505 | 173 | 3x3 | * | -505*173= | scratchpad-v3 | negative | null | contains_zero_digit | -+ | train | 505371 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 3,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 15,
"running_total": 15,
"serialized": "5315015",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 15,
"kind": "column",
... | -505*173=<mul><neg><state>505371<step>5315015<col>501<step>5735036<step>0300036<col>603<step>5105008<step>0700008<step>5315023<col>302<step>0100002<step>5735037<col>703<step>5105008<col>800<ans>563780 |
div | 160 | 005.979 | -5.979 | 287 | -48 | 3x2 | / | 287/-48= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 287048 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 48,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 287/-48=<div><neg><state>287048<step>00020002<qmul>00000<rem>002<step>00280028<qmul>00000<rem>028<step>02870287<qmul>50240<rem>047<step>04700470<qmul>90432<rem>038<step>03800380<qmul>70336<rem>044<step>04400440<qmul>90432<rem>008<step>00800080<qmul>10048<rem>032<ans>005.979 |
div | 160 | 000.313 | 0.313 | 184 | 588 | 3x3 | / | 184/588= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 184588 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 588,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 184/588=<div><pos><state>184588<step>00010001<qmul>00000<rem>001<step>00180018<qmul>00000<rem>018<step>01840184<qmul>00000<rem>184<step>18401840<qmul>31764<rem>076<step>07600760<qmul>10588<rem>172<step>17201720<qmul>21176<rem>544<step>54405440<qmul>95292<rem>148<ans>000.313 |
sub | 42 | 4540 | -454 | 528 | 982 | 3x3 | - | 528-982= | scratchpad-v3 | negative | null | negative_result | ++ | train | 289825 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 4,
"serialized": "28041",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 8,
"output_digit": 5,
"serialized": "82150",
"subtrahend... | 528-982=<sub><neg><state>289825<step>28041<step>82150<step>95040<ans>4540 |
div | 162 | 000.916 | 0.916 | -206 | -225 | 3x3 | / | -206/-225= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 206225 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 225,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -206/-225=<div><pos><state>206225<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02060206<qmul>00000<rem>206<step>20602060<qmul>92025<rem>035<step>03500350<qmul>10225<rem>125<step>12501250<qmul>51125<rem>125<step>12501250<qmul>51125<rem>125<ans>000.916 |
mul | 119 | 476619 | -916674 | -946 | 969 | 3x3 | * | -946*969= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 649969 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 54,
"running_total": 54,
"serialized": "6954054",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 5,
"column": 0,
"column_sum": 54,
"kind": "column",
... | -946*969=<mul><neg><state>649969<step>6954054<col>405<step>6636041<step>4936077<col>707<step>6954061<step>4624085<step>9981166<col>616<step>4936052<step>9654106<col>610<step>9981091<col>109<ans>476619 |
div | 159 | 051.000 | -51 | 357 | -7 | 3x1 | / | 357/-7= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 357007 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
"divisor": 7,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 357/-7=<div><neg><state>357007<step>00030003<qmul>00000<rem>003<step>00350035<qmul>50035<rem>000<step>00070007<qmul>10007<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>051.000 |
sub | 42 | 7810 | 187 | 329 | 142 | 3x3 | - | 329-142= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 923241 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 7,
"serialized": "92070",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 8,
"serialized": "24081",
"subtrahend... | 329-142=<sub><pos><state>923241<step>92070<step>24081<step>31110<ans>7810 |
mul | 119 | 011092 | -290110 | -866 | 335 | 3x3 | * | -866*335= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 668533 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 30,
"running_total": 30,
"serialized": "6530030",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 3,
"column": 0,
"column_sum": 30,
"kind": "column",
... | -866*335=<mul><neg><state>668533<step>6530030<col>003<step>6318021<step>6530051<col>105<step>6318023<step>6318041<step>8540081<col>108<step>6318026<step>8324050<col>005<step>8324029<col>902<ans>011092 |
div | 160 | 000.311 | 0.311 | 131 | 421 | 3x3 | / | 131/421= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | test | 131421 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 421,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 131/421=<div><pos><state>131421<step>00010001<qmul>00000<rem>001<step>00130013<qmul>00000<rem>013<step>01310131<qmul>00000<rem>131<step>13101310<qmul>31263<rem>047<step>04700470<qmul>10421<rem>049<step>04900490<qmul>10421<rem>069<step>06900690<qmul>10421<rem>269<ans>000.311 |
add | 41 | 5780 | 875 | 74 | 801 | 2x3 | + | 74+801= | scratchpad-v3 | positive | null | no_carry | ++ | train | 470108 | [
{
"a_digit": 4,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "41050"
},
{
"a_digit": 7,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "70070"
},
{
"a_digit":... | 74+801=<add><pos><state>470108<step>41050<step>70070<step>08080<ans>5780 |
div | 161 | 000.374 | -0.374 | 161 | -430 | 3x3 | / | 161/-430= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 161430 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 430,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 161/-430=<div><neg><state>161430<step>00010001<qmul>00000<rem>001<step>00160016<qmul>00000<rem>016<step>01610161<qmul>00000<rem>161<step>16101610<qmul>31290<rem>320<step>32003200<qmul>73010<rem>190<step>19001900<qmul>41720<rem>180<step>18001800<qmul>41720<rem>080<ans>000.374 |
div | 160 | 000.970 | 0.97 | -32 | -33 | 2x2 | / | -32/-33= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 032033 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 33,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -32/-33=<div><pos><state>032033<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00320032<qmul>00000<rem>032<step>03200320<qmul>90297<rem>023<step>02300230<qmul>60198<rem>032<step>03200320<qmul>90297<rem>023<step>02300230<qmul>60198<rem>032<ans>000.970 |
sub | 44 | 9900 | 99 | -447 | -546 | 3x3 | - | -447--546= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 645744 | [
{
"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": 4,
"output_digit": 9,
"serialized": "44191",
"subtrahend... | -447--546=<sub><pos><state>645744<step>67091<step>44191<step>54100<ans>9900 |
add | 40 | 8750 | 578 | 0 | 578 | 1x3 | + | 0+578= | scratchpad-v3 | positive | null | identity | ++ | train | 000875 | [
{
"a_digit": 0,
"b_digit": 8,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 8,
"serialized": "08080"
},
{
"a_digit": 0,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "07070"
},
{
"a_digit":... | 0+578=<add><pos><state>000875<step>08080<step>07070<step>05050<ans>8750 |
div | 159 | 007.167 | 7.167 | -43 | -6 | 2x1 | / | -43/-6= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 043006 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 6,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -43/-6=<div><pos><state>043006<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00430043<qmul>70042<rem>001<step>00100010<qmul>10006<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<ans>007.167 |
sub | 43 | 6870 | 786 | -14 | -800 | 2x3 | - | -14--800= | scratchpad-v3 | positive | null | borrow_through_zero | -- | test | 008410 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "04061",
"subtrahend_digit": 4
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 8,
"serialized": "01181",
"subtrahend... | -14--800=<sub><pos><state>008410<step>04061<step>01181<step>80170<ans>6870 |
mul | 119 | 021297 | -792120 | 920 | -861 | 3x3 | * | 920*-861= | scratchpad-v3 | negative | null | contains_zero_digit | +- | train | 029168 | [
{
"a_digit": 0,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 0,
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"serialized": "0100000",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | 920*-861=<mul><neg><state>029168<step>0100000<col>000<step>0600000<step>2102002<col>200<step>0800000<step>2612012<step>9109021<col>102<step>2816018<step>9654072<col>207<step>9872079<col>907<ans>021297 |
div | 161 | 001.096 | -1.096 | 934 | -852 | 3x3 | / | 934/-852= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 934852 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 852,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 934/-852=<div><neg><state>934852<step>00090009<qmul>00000<rem>009<step>00930093<qmul>00000<rem>093<step>09340934<qmul>10852<rem>082<step>08200820<qmul>00000<rem>820<step>82008200<qmul>97668<rem>532<step>53205320<qmul>65112<rem>208<step>20802080<qmul>21704<rem>376<ans>001.096 |
add | 42 | 4071 | 1704 | 868 | 836 | 3x3 | + | 868+836= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 868638 | [
{
"a_digit": 8,
"b_digit": 6,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 4,
"serialized": "86041"
},
{
"a_digit": 6,
"b_digit": 3,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "63101"
},
{
"a_digit":... | 868+836=<add><pos><state>868638<step>86041<step>63101<step>88171<ans>4071 |
add | 42 | 6170 | 716 | 439 | 277 | 3x3 | + | 439+277= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 934772 | [
{
"a_digit": 9,
"b_digit": 7,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 6,
"serialized": "97061"
},
{
"a_digit": 3,
"b_digit": 7,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "37111"
},
{
"a_digit":... | 439+277=<add><pos><state>934772<step>97061<step>37111<step>42170<ans>6170 |
mul | 117 | 885000 | -588 | 12 | -49 | 2x2 | * | 12*-49= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 210940 | [
{
"a_digit": 2,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 18,
"running_total": 18,
"serialized": "2918018",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 18,
"kind": "column",
... | 12*-49=<mul><neg><state>210940<step>2918018<col>801<step>2408009<step>1909018<col>801<step>2000001<step>1404005<step>0900005<col>500<step>1000000<step>0400000<col>000<step>0000000<col>000<ans>885000 |
sub | 42 | 2570 | -752 | 188 | 940 | 3x3 | - | 188-940= | scratchpad-v3 | negative | null | negative_result | ++ | train | 049881 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 2,
"serialized": "08021",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 5,
"serialized": "48151",
"subtrahend... | 188-940=<sub><neg><state>049881<step>08021<step>48151<step>91170<ans>2570 |
add | 42 | 1190 | 911 | 522 | 389 | 3x3 | + | 522+389= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 225983 | [
{
"a_digit": 2,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "29011"
},
{
"a_digit": 2,
"b_digit": 8,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "28111"
},
{
"a_digit":... | 522+389=<add><pos><state>225983<step>29011<step>28111<step>53190<ans>1190 |
div | 160 | 103.800 | 103.8 | -519 | -5 | 3x1 | / | -519/-5= | scratchpad-v3 | positive | round-half-up | exact | -- | train | 519005 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 5,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 1,
"quotient_product": 5,
"serialized": "10005"
},
{
"kind": ... | -519/-5=<div><pos><state>519005<step>00050005<qmul>10005<rem>000<step>00010001<qmul>00000<rem>001<step>00190019<qmul>30015<rem>004<step>00400040<qmul>80040<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>103.800 |
mul | 116 | 639000 | 936 | 26 | 36 | 2x2 | * | 26*36= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 620630 | [
{
"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",
... | 26*36=<mul><pos><state>620630<step>6636036<col>603<step>6318021<step>2612033<col>303<step>6000003<step>2306009<step>0600009<col>900<step>2000000<step>0300000<col>000<step>0000000<col>000<ans>639000 |
mul | 117 | 084000 | -480 | 1 | -480 | 1x3 | * | 1*-480= | scratchpad-v3 | negative | null | identity | +- | train | 100084 | [
{
"a_digit": 1,
"a_index": 0,
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"column": 0,
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"serialized": "1000000",
"term_index": 0
},
{
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"column": 0,
"column_sum": 0,
"kind": "column",
"o... | 1*-480=<mul><neg><state>100084<step>1000000<col>000<step>1808008<step>0000008<col>800<step>1404004<step>0800004<step>0000004<col>400<step>0400000<step>0800000<col>000<step>0400000<col>000<ans>084000 |
div | 162 | 000.635 | 0.635 | -195 | -307 | 3x3 | / | -195/-307= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 195307 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 307,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -195/-307=<div><pos><state>195307<step>00010001<qmul>00000<rem>001<step>00190019<qmul>00000<rem>019<step>01950195<qmul>00000<rem>195<step>19501950<qmul>61842<rem>108<step>10801080<qmul>30921<rem>159<step>15901590<qmul>51535<rem>055<step>05500550<qmul>10307<rem>243<ans>000.635 |
add | 44 | 3570 | -753 | -463 | -290 | 3x3 | + | -463+-290= | scratchpad-v3 | negative | null | single_carry | -- | train | 364092 | [
{
"a_digit": 3,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "30030"
},
{
"a_digit": 6,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 5,
"serialized": "69051"
},
{
"a_digit":... | -463+-290=<add><neg><state>364092<step>30030<step>69051<step>42170<ans>3570 |
div | 159 | 001.797 | 1.797 | 124 | 69 | 3x2 | / | 124/69= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 124069 | [
{
"incoming_digit": 1,
"kind": "partial",
"partial": 1,
"position": 0,
"remainder_in": 0,
"serialized": "00010001"
},
{
"divisor": 69,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 124/69=<div><pos><state>124069<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01240124<qmul>10069<rem>055<step>05500550<qmul>70483<rem>067<step>06700670<qmul>90621<rem>049<step>04900490<qmul>70483<rem>007<step>00700070<qmul>10069<rem>001<ans>001.797 |
div | 159 | 032.556 | -32.556 | -293 | 9 | 3x1 | / | -293/9= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 293009 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 9,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -293/9=<div><neg><state>293009<step>00020002<qmul>00000<rem>002<step>00290029<qmul>30027<rem>002<step>00230023<qmul>20018<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<ans>032.556 |
add | 44 | 5640 | -465 | -253 | -212 | 3x3 | + | -253+-212= | scratchpad-v3 | negative | null | no_carry | -- | train | 352212 | [
{
"a_digit": 3,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "32050"
},
{
"a_digit": 5,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 6,
"serialized": "51060"
},
{
"a_digit":... | -253+-212=<add><neg><state>352212<step>32050<step>51060<step>22040<ans>5640 |
add | 41 | 7960 | 697 | 670 | 27 | 3x2 | + | 670+27= | scratchpad-v3 | positive | null | no_carry | ++ | train | 076720 | [
{
"a_digit": 0,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "07070"
},
{
"a_digit": 7,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "72090"
},
{
"a_digit":... | 670+27=<add><pos><state>076720<step>07070<step>72090<step>60060<ans>7960 |
add | 44 | 7311 | -1137 | -824 | -313 | 3x3 | + | -824+-313= | scratchpad-v3 | negative | null | overflow | -- | val | 428313 | [
{
"a_digit": 4,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "43070"
},
{
"a_digit": 2,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "21030"
},
{
"a_digit":... | -824+-313=<add><neg><state>428313<step>43070<step>21030<step>83011<ans>7311 |
div | 157 | 000.000 | 0 | 0 | 94 | 1x2 | / | 0/94= | scratchpad-v3 | positive | round-half-up | zero_numerator | ++ | train | 000094 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 94,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 0/94=<div><pos><state>000094<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 | 160 | 000.678 | 0.678 | -59 | -87 | 2x2 | / | -59/-87= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 059087 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 87,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -59/-87=<div><pos><state>059087<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00590059<qmul>00000<rem>059<step>05900590<qmul>60522<rem>068<step>06800680<qmul>70609<rem>071<step>07100710<qmul>80696<rem>014<step>01400140<qmul>10087<rem>053<ans>000.678 |
mul | 119 | 311412 | -214113 | 479 | -447 | 3x3 | * | 479*-447= | scratchpad-v3 | negative | null | medium_column_sum | +- | val | 974744 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 63,
"running_total": 63,
"serialized": "9763063",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 63,
"kind": "column",
... | 479*-447=<mul><neg><state>974744<step>9763063<col>306<step>9436042<step>7749091<col>109<step>9436045<step>7428073<step>4728101<col>110<step>7428038<step>4416054<col>405<step>4416021<col>102<ans>311412 |
sub | 44 | 3400 | 43 | -182 | -225 | 3x3 | - | -182--225= | scratchpad-v3 | positive | null | single_borrow | -- | train | 522281 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 3,
"serialized": "52030",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 4,
"serialized": "28041",
"subtrahend... | -182--225=<sub><pos><state>522281<step>52030<step>28041<step>21100<ans>3400 |
sub | 43 | 3000 | -3 | -414 | 411 | 3x3 | + | -414+411= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 414114 | [
{
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{
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"serialized": "11000",
"subtrahend... | -414+411=<sub><neg><state>414114<step>41030<step>11000<step>44000<ans>3000 |
mul | 118 | 329084 | 480923 | 811 | 593 | 3x3 | * | 811*593= | scratchpad-v3 | positive | null | medium_column_sum | ++ | val | 118395 | [
{
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},
{
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"o... | 811*593=<mul><pos><state>118395<step>1303003<col>300<step>1909009<step>1303012<col>201<step>1505006<step>1909015<step>8324039<col>903<step>1505008<step>8972080<col>008<step>8540048<col>804<ans>329084 |
div | 161 | 001.066 | -1.066 | -963 | 903 | 3x3 | / | -963/903= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 963903 | [
{
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},
{
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{
"kind"... | -963/903=<div><neg><state>963903<step>00090009<qmul>00000<rem>009<step>00960096<qmul>00000<rem>096<step>09630963<qmul>10903<rem>060<step>06000600<qmul>00000<rem>600<step>60006000<qmul>65418<rem>582<step>58205820<qmul>65418<rem>402<step>40204020<qmul>43612<rem>408<ans>001.066 |
add | 44 | 0911 | -1190 | -417 | -773 | 3x3 | + | -417+-773= | scratchpad-v3 | negative | null | overflow | -- | train | 714377 | [
{
"a_digit": 7,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 0,
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},
{
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"serialized": "17190"
},
{
"a_digit":... | -417+-773=<add><neg><state>714377<step>73001<step>17190<step>47011<ans>0911 |
mul | 116 | 546100 | 1645 | 47 | 35 | 2x2 | * | 47*35= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 740530 | [
{
"a_digit": 7,
"a_index": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 35,
"kind": "column",
... | 47*35=<mul><pos><state>740530<step>7535035<col>503<step>7321024<step>4520044<col>404<step>7000004<step>4312016<step>0500016<col>601<step>4000001<step>0300001<col>100<step>0000000<col>000<ans>546100 |
div | 161 | 001.000 | -1 | -622 | 622 | 3x3 | / | -622/622= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 622622 | [
{
"incoming_digit": 6,
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"remainder_in": 0,
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},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -622/622=<div><neg><state>622622<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06220622<qmul>10622<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 |
add | 43 | 6770 | 776 | 370 | -406 | 3x3 | - | 370--406= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 073604 | [
{
"a_digit": 0,
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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": "70070"
},
{
"a_digit":... | 370--406=<add><pos><state>073604<step>06060<step>70070<step>34070<ans>6770 |
div | 158 | 000.490 | 0.49 | 48 | 98 | 2x2 | / | 48/98= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 048098 | [
{
"incoming_digit": 0,
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"serialized": "00000000"
},
{
"divisor": 98,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 48/98=<div><pos><state>048098<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00480048<qmul>00000<rem>048<step>04800480<qmul>40392<rem>088<step>08800880<qmul>80784<rem>096<step>09600960<qmul>90882<rem>078<step>07800780<qmul>70686<rem>094<ans>000.490 |
add | 42 | 5280 | -825 | -24 | 801 | 2x3 | - | -24-801= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 420108 | [
{
"a_digit": 4,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "41050"
},
{
"a_digit": 2,
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"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 2,
"serialized": "20020"
},
{
"a_digit":... | -24-801=<add><neg><state>420108<step>41050<step>20020<step>08080<ans>5280 |
div | 159 | 000.357 | -0.357 | -15 | 42 | 2x2 | / | -15/42= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 015042 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind":... | -15/42=<div><neg><state>015042<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00150015<qmul>00000<rem>015<step>01500150<qmul>30126<rem>024<step>02400240<qmul>50210<rem>030<step>03000300<qmul>70294<rem>006<step>00600060<qmul>10042<rem>018<ans>000.357 |
div | 161 | 001.543 | -1.543 | -466 | 302 | 3x3 | / | -466/302= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 466302 | [
{
"incoming_digit": 4,
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"serialized": "00040004"
},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind"... | -466/302=<div><neg><state>466302<step>00040004<qmul>00000<rem>004<step>00460046<qmul>00000<rem>046<step>04660466<qmul>10302<rem>164<step>16401640<qmul>51510<rem>130<step>13001300<qmul>41208<rem>092<step>09200920<qmul>30906<rem>014<step>01400140<qmul>00000<rem>140<ans>001.543 |
add | 42 | 9950 | 599 | 475 | 124 | 3x3 | + | 475+124= | scratchpad-v3 | positive | null | no_carry | ++ | train | 574421 | [
{
"a_digit": 5,
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"carry_in": 0,
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"serialized": "54090"
},
{
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"carry_in": 0,
"carry_out": 0,
"column": 1,
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"serialized": "72090"
},
{
"a_digit":... | 475+124=<add><pos><state>574421<step>54090<step>72090<step>41050<ans>9950 |
sub | 41 | 8100 | 18 | 103 | 85 | 3x2 | - | 103-85= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 301580 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 3,
"output_digit": 8,
"serialized": "35081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | 103-85=<sub><pos><state>301580<step>35081<step>08111<step>10100<ans>8100 |
div | 160 | 002.398 | -2.398 | 223 | -93 | 3x2 | / | 223/-93= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 223093 | [
{
"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":... | 223/-93=<div><neg><state>223093<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02230223<qmul>20186<rem>037<step>03700370<qmul>30279<rem>091<step>09100910<qmul>90837<rem>073<step>07300730<qmul>70651<rem>079<step>07900790<qmul>80744<rem>046<ans>002.398 |
sub | 40 | 7000 | -7 | 10 | 17 | 2x2 | - | 10-17= | scratchpad-v3 | negative | null | negative_result | ++ | train | 710010 | [
{
"borrow_in": 0,
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"serialized": "70070",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 1,
"output_digit": 0,
"serialized": "11000",
"subtrahend... | 10-17=<sub><neg><state>710010<step>70070<step>11000<step>00000<ans>7000 |
sub | 40 | 2000 | -2 | 81 | 83 | 2x2 | - | 81-83= | scratchpad-v3 | negative | null | negative_result | ++ | train | 380180 | [
{
"borrow_in": 0,
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"column": 0,
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"output_digit": 2,
"serialized": "31020",
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},
{
"borrow_in": 0,
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"column": 1,
"minuend_digit": 8,
"output_digit": 0,
"serialized": "88000",
"subtrahend... | 81-83=<sub><neg><state>380180<step>31020<step>88000<step>00000<ans>2000 |
div | 161 | 005.361 | 5.361 | -445 | -83 | 3x2 | / | -445/-83= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | test | 445083 | [
{
"incoming_digit": 4,
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"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind":... | -445/-83=<div><pos><state>445083<step>00040004<qmul>00000<rem>004<step>00440044<qmul>00000<rem>044<step>04450445<qmul>50415<rem>030<step>03000300<qmul>30249<rem>051<step>05100510<qmul>60498<rem>012<step>01200120<qmul>10083<rem>037<step>03700370<qmul>40332<rem>038<ans>005.361 |
sub | 42 | 5190 | 915 | 999 | -84 | 3x2 | + | 999+-84= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 999480 | [
{
"borrow_in": 0,
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"column": 0,
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"output_digit": 5,
"serialized": "94050",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 1,
"serialized": "98010",
"subtrahend... | 999+-84=<sub><pos><state>999480<step>94050<step>98010<step>90090<ans>5190 |
sub | 43 | 8160 | 618 | -89 | -707 | 2x3 | - | -89--707= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 707980 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 7,
"output_digit": 8,
"serialized": "79081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | -89--707=<sub><pos><state>707980<step>79081<step>08111<step>70160<ans>8160 |
div | 161 | 001.000 | -1 | 894 | -894 | 3x3 | / | 894/-894= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 894894 | [
{
"incoming_digit": 8,
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"position": 0,
"remainder_in": 0,
"serialized": "00080008"
},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 894/-894=<div><neg><state>894894<step>00080008<qmul>00000<rem>008<step>00890089<qmul>00000<rem>089<step>08940894<qmul>10894<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 | 118 | 033100 | 1330 | -95 | -14 | 2x2 | * | -95*-14= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 590410 | [
{
"a_digit": 5,
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"column": 0,
"kind": "term",
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"serialized": "5420020",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 20,
"kind": "column",
... | -95*-14=<mul><pos><state>590410<step>5420020<col>002<step>5105007<step>9436043<col>304<step>5000004<step>9109013<step>0400013<col>301<step>9000001<step>0100001<col>100<step>0000000<col>000<ans>033100 |
add | 44 | 6311 | -1136 | -190 | -946 | 3x3 | + | -190+-946= | scratchpad-v3 | negative | null | overflow | -- | train | 091649 | [
{
"a_digit": 0,
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},
{
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"carry_in": 0,
"carry_out": 1,
"column": 1,
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"serialized": "94031"
},
{
"a_digit":... | -190+-946=<add><neg><state>091649<step>06060<step>94031<step>19111<ans>6311 |
mul | 116 | 239100 | 1932 | 21 | 92 | 2x2 | * | 21*92= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 120290 | [
{
"a_digit": 1,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 2,
"kind": "column",
"o... | 21*92=<mul><pos><state>120290<step>1202002<col>200<step>1909009<step>2204013<col>301<step>1000001<step>2918019<step>0200019<col>901<step>2000001<step>0900001<col>100<step>0000000<col>000<ans>239100 |
mul | 119 | 638638 | -836836 | -847 | 988 | 3x3 | * | -847*988= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 748889 | [
{
"a_digit": 7,
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"serialized": "7856056",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 56,
"kind": "column",
... | -847*988=<mul><neg><state>748889<step>7856056<col>605<step>7856061<step>4832093<col>309<step>7963072<step>4832104<step>8864168<col>816<step>4936052<step>8864116<col>611<step>8972083<col>308<ans>638638 |
div | 158 | 045.000 | 45 | 270 | 6 | 3x1 | / | 270/6= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 270006 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
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"serialized": "00020002"
},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind": ... | 270/6=<div><pos><state>270006<step>00020002<qmul>00000<rem>002<step>00270027<qmul>40024<rem>003<step>00300030<qmul>50030<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>045.000 |
div | 160 | 000.588 | -0.588 | -80 | 136 | 2x3 | / | -80/136= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 080136 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind"... | -80/136=<div><neg><state>080136<step>00000000<qmul>00000<rem>000<step>00080008<qmul>00000<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>50680<rem>120<step>12001200<qmul>81088<rem>112<step>11201120<qmul>81088<rem>032<step>03200320<qmul>20272<rem>048<ans>000.588 |
div | 160 | 001.977 | 1.977 | 957 | 484 | 3x3 | / | 957/484= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 957484 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
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"serialized": "00090009"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
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"serialized": "00000"
},
{
"kind"... | 957/484=<div><pos><state>957484<step>00090009<qmul>00000<rem>009<step>00950095<qmul>00000<rem>095<step>09570957<qmul>10484<rem>473<step>47304730<qmul>94356<rem>374<step>37403740<qmul>73388<rem>352<step>35203520<qmul>73388<rem>132<step>13201320<qmul>20968<rem>352<ans>001.977 |
add | 42 | 1320 | -231 | -89 | 142 | 2x3 | - | -89-142= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 980241 | [
{
"a_digit": 9,
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"serialized": "92011"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "84131"
},
{
"a_digit":... | -89-142=<add><neg><state>980241<step>92011<step>84131<step>01120<ans>1320 |
div | 158 | 000.222 | 0.222 | 10 | 45 | 2x2 | / | 10/45= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | train | 010045 | [
{
"incoming_digit": 0,
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"position": 0,
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},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 10/45=<div><pos><state>010045<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<ans>000.222 |
div | 158 | 077.833 | 77.833 | 467 | 6 | 3x1 | / | 467/6= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | test | 467006 | [
{
"incoming_digit": 4,
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"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 6,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 467/6=<div><pos><state>467006<step>00040004<qmul>00000<rem>004<step>00460046<qmul>70042<rem>004<step>00470047<qmul>70042<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>077.833 |
div | 161 | 002.824 | -2.824 | -768 | 272 | 3x3 | / | -768/272= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 768272 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
"divisor": 272,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -768/272=<div><neg><state>768272<step>00070007<qmul>00000<rem>007<step>00760076<qmul>00000<rem>076<step>07680768<qmul>20544<rem>224<step>22402240<qmul>82176<rem>064<step>06400640<qmul>20544<rem>096<step>09600960<qmul>30816<rem>144<step>14401440<qmul>51360<rem>080<ans>002.824 |
mul | 119 | 525098 | -890525 | -895 | 995 | 3x3 | * | -895*995= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 598599 | [
{
"a_digit": 5,
"a_index": 0,
"b_digit": 5,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 25,
"running_total": 25,
"serialized": "5525025",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 2,
"column": 0,
"column_sum": 25,
"kind": "column",
... | -895*995=<mul><neg><state>598599<step>5525025<col>502<step>5945047<step>9545092<col>209<step>5945054<step>9981135<step>8540175<col>517<step>9981098<step>8972170<col>017<step>8972089<col>908<ans>525098 |
add | 42 | 3790 | 973 | 485 | 488 | 3x3 | + | 485+488= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 584884 | [
{
"a_digit": 5,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 3,
"serialized": "58031"
},
{
"a_digit": 8,
"b_digit": 8,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 7,
"serialized": "88171"
},
{
"a_digit":... | 485+488=<add><pos><state>584884<step>58031<step>88171<step>44190<ans>3790 |
mul | 120 | 165792 | 297561 | -781 | -381 | 3x3 | * | -781*-381= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 187183 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 1,
"running_total": 1,
"serialized": "1101001",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 1,
"kind": "column",
"o... | -781*-381=<mul><pos><state>187183<step>1101001<col>100<step>1808008<step>8108016<col>601<step>1303004<step>8864068<step>7107075<col>507<step>8324031<step>7856087<col>708<step>7321029<col>902<ans>165792 |
mul | 118 | 241243 | 342142 | 347 | 986 | 3x3 | * | 347*986= | scratchpad-v3 | positive | null | medium_column_sum | ++ | val | 743689 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 42,
"running_total": 42,
"serialized": "7642042",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 42,
"kind": "column",
... | 347*986=<mul><pos><state>743689<step>7642042<col>204<step>7856060<step>4624084<col>408<step>7963071<step>4832103<step>3618121<col>112<step>4936048<step>3824072<col>207<step>3927034<col>403<ans>241243 |
mul | 118 | 467100 | 1764 | -49 | -36 | 2x2 | * | -49*-36= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 940630 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 54,
"running_total": 54,
"serialized": "9654054",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 5,
"column": 0,
"column_sum": 54,
"kind": "column",
... | -49*-36=<mul><pos><state>940630<step>9654054<col>405<step>9327032<step>4624056<col>605<step>9000005<step>4312017<step>0600017<col>701<step>4000001<step>0300001<col>100<step>0000000<col>000<ans>467100 |
add | 43 | 3580 | -853 | -461 | 392 | 3x3 | - | -461-392= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 164293 | [
{
"a_digit": 1,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 3,
"serialized": "12030"
},
{
"a_digit": 6,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 5,
"serialized": "69051"
},
{
"a_digit":... | -461-392=<add><neg><state>164293<step>12030<step>69051<step>43180<ans>3580 |
add | 42 | 1180 | -811 | -71 | 740 | 2x3 | - | -71-740= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 170047 | [
{
"a_digit": 1,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 1,
"serialized": "10010"
},
{
"a_digit": 7,
"b_digit": 4,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "74011"
},
{
"a_digit":... | -71-740=<add><neg><state>170047<step>10010<step>74011<step>07180<ans>1180 |
add | 42 | 1761 | 1671 | 877 | 794 | 3x3 | + | 877+794= | scratchpad-v3 | positive | null | overflow | ++ | train | 778497 | [
{
"a_digit": 7,
"b_digit": 4,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "74011"
},
{
"a_digit": 7,
"b_digit": 9,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 7,
"serialized": "79171"
},
{
"a_digit":... | 877+794=<add><pos><state>778497<step>74011<step>79171<step>87161<ans>1761 |
add | 41 | 9540 | -459 | -459 | 0 | 3x1 | + | -459+0= | scratchpad-v3 | negative | null | identity | -+ | train | 954000 | [
{
"a_digit": 9,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 9,
"serialized": "90090"
},
{
"a_digit": 5,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 5,
"serialized": "50050"
},
{
"a_digit":... | -459+0=<add><neg><state>954000<step>90090<step>50050<step>40040<ans>9540 |
add | 42 | 2301 | 1032 | 771 | 261 | 3x3 | + | 771+261= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 177162 | [
{
"a_digit": 1,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 2,
"serialized": "11020"
},
{
"a_digit": 7,
"b_digit": 6,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "76031"
},
{
"a_digit":... | 771+261=<add><pos><state>177162<step>11020<step>76031<step>72101<ans>2301 |
sub | 42 | 8740 | 478 | 532 | -54 | 3x2 | + | 532+-54= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 235450 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 8,
"serialized": "24081",
"subtrahend_digit": 4
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 7,
"serialized": "35171",
"subtrahend... | 532+-54=<sub><pos><state>235450<step>24081<step>35171<step>50140<ans>8740 |
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