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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mul | 118 | 449157 | 751944 | 969 | 776 | 3x3 | * | 969*776= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 969677 | [
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{
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... | 969*776=<mul><pos><state>969677<step>9654054<col>405<step>9763068<step>6636104<col>410<step>9763073<step>6742115<step>9654169<col>916<step>6742058<step>9763121<col>112<step>9763075<col>507<ans>449157 |
add | 42 | 1070 | 701 | 229 | 472 | 3x3 | + | 229+472= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 922274 | [
{
"a_digit": 9,
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"carry_in": 0,
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"serialized": "92011"
},
{
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"carry_out": 1,
"column": 1,
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"serialized": "27101"
},
{
"a_digit":... | 229+472=<add><pos><state>922274<step>92011<step>27101<step>24170<ans>1070 |
sub | 41 | 7350 | -537 | 2 | -539 | 1x3 | + | 2+-539= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | train | 935200 | [
{
"borrow_in": 0,
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"output_digit": 7,
"serialized": "92070",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 3,
"output_digit": 3,
"serialized": "30030",
"subtrahend... | 2+-539=<sub><neg><state>935200<step>92070<step>30030<step>50050<ans>7350 |
mul | 119 | 037016 | -610730 | -785 | 778 | 3x3 | * | -785*778= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 587877 | [
{
"a_digit": 5,
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},
{
"carry_in": 0,
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"kind": "column",
... | -785*778=<mul><neg><state>587877<step>5840040<col>004<step>5735039<step>8864103<col>310<step>5735045<step>8756101<step>7856157<col>715<step>8756071<step>7749120<col>012<step>7749061<col>106<ans>037016 |
mul | 117 | 428100 | -1824 | 57 | -32 | 2x2 | * | 57*-32= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 750230 | [
{
"a_digit": 7,
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"column": 0,
"kind": "term",
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"serialized": "7214014",
"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | 57*-32=<mul><neg><state>750230<step>7214014<col>401<step>7321022<step>5210032<col>203<step>7000003<step>5315018<step>0200018<col>801<step>5000001<step>0300001<col>100<step>0000000<col>000<ans>428100 |
div | 159 | 000.013 | -0.013 | -5 | 377 | 1x3 | / | -5/377= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 005377 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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{
"kind"... | -5/377=<div><neg><state>005377<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>10377<rem>123<step>12301230<qmul>31131<rem>099<step>09900990<qmul>20754<rem>236<ans>000.013 |
mul | 118 | 329208 | 802923 | 957 | 839 | 3x3 | * | 957*839= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 759938 | [
{
"a_digit": 7,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column_sum": 63,
"kind": "column",
... | 957*839=<mul><pos><state>759938<step>7963063<col>306<step>7321027<step>5945072<col>207<step>7856063<step>5315078<step>9981159<col>915<step>5840055<step>9327082<col>208<step>9872080<col>008<ans>329208 |
div | 161 | 000.331 | -0.331 | 293 | -884 | 3x3 | / | 293/-884= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 293884 | [
{
"incoming_digit": 2,
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},
{
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"position": 0,
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},
{
"kind"... | 293/-884=<div><neg><state>293884<step>00020002<qmul>00000<rem>002<step>00290029<qmul>00000<rem>029<step>02930293<qmul>00000<rem>293<step>29302930<qmul>32652<rem>278<step>27802780<qmul>32652<rem>128<step>12801280<qmul>10884<rem>396<step>39603960<qmul>43536<rem>424<ans>000.331 |
sub | 42 | 4000 | -4 | -25 | -21 | 2x2 | - | -25--21= | scratchpad-v3 | negative | null | negative_result | -- | train | 520120 | [
{
"borrow_in": 0,
"borrow_out": 0,
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},
{
"borrow_in": 0,
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"column": 1,
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"output_digit": 0,
"serialized": "22000",
"subtrahend... | -25--21=<sub><neg><state>520120<step>51040<step>22000<step>00000<ans>4000 |
div | 161 | 001.725 | -1.725 | 997 | -578 | 3x3 | / | 997/-578= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 997578 | [
{
"incoming_digit": 9,
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"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 997/-578=<div><neg><state>997578<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09970997<qmul>10578<rem>419<step>41904190<qmul>74046<rem>144<step>14401440<qmul>21156<rem>284<step>28402840<qmul>42312<rem>528<step>52805280<qmul>95202<rem>078<ans>001.725 |
div | 160 | 001.412 | 1.412 | 802 | 568 | 3x3 | / | 802/568= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | train | 802568 | [
{
"incoming_digit": 8,
"kind": "partial",
"partial": 8,
"position": 0,
"remainder_in": 0,
"serialized": "00080008"
},
{
"divisor": 568,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
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"serialized": "00000"
},
{
"kind"... | 802/568=<div><pos><state>802568<step>00080008<qmul>00000<rem>008<step>00800080<qmul>00000<rem>080<step>08020802<qmul>10568<rem>234<step>23402340<qmul>42272<rem>068<step>06800680<qmul>10568<rem>112<step>11201120<qmul>10568<rem>552<step>55205520<qmul>95112<rem>408<ans>001.412 |
sub | 41 | 1500 | -51 | 65 | 116 | 2x3 | - | 65-116= | scratchpad-v3 | negative | null | negative_result | ++ | train | 611560 | [
{
"borrow_in": 0,
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"serialized": "65010",
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},
{
"borrow_in": 0,
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"serialized": "16051",
"subtrahend... | 65-116=<sub><neg><state>611560<step>65010<step>16051<step>10100<ans>1500 |
add | 41 | 5430 | 345 | 290 | 55 | 3x2 | + | 290+55= | scratchpad-v3 | positive | null | single_carry | ++ | train | 092550 | [
{
"a_digit": 0,
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{
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"column": 1,
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"serialized": "95041"
},
{
"a_digit":... | 290+55=<add><pos><state>092550<step>05050<step>95041<step>20130<ans>5430 |
add | 42 | 7750 | -577 | -9 | -568 | 1x3 | + | -9+-568= | scratchpad-v3 | negative | null | single_carry | -- | train | 900865 | [
{
"a_digit": 9,
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},
{
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"serialized": "06170"
},
{
"a_digit":... | -9+-568=<add><neg><state>900865<step>98071<step>06170<step>05050<ans>7750 |
sub | 40 | 8100 | 18 | 87 | 69 | 2x2 | - | 87-69= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 780960 | [
{
"borrow_in": 0,
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"serialized": "79081",
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},
{
"borrow_in": 1,
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"column": 1,
"minuend_digit": 8,
"output_digit": 1,
"serialized": "86110",
"subtrahend... | 87-69=<sub><pos><state>780960<step>79081<step>86110<step>00000<ans>8100 |
sub | 42 | 7310 | -137 | 336 | 473 | 3x3 | - | 336-473= | scratchpad-v3 | negative | null | negative_result | ++ | train | 374633 | [
{
"borrow_in": 0,
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"serialized": "36071",
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},
{
"borrow_in": 1,
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"output_digit": 3,
"serialized": "73130",
"subtrahend... | 336-473=<sub><neg><state>374633<step>36071<step>73130<step>43010<ans>7310 |
div | 160 | 000.125 | -0.125 | 53 | -424 | 2x3 | / | 53/-424= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 053424 | [
{
"incoming_digit": 0,
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"serialized": "00000000"
},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind"... | 53/-424=<div><neg><state>053424<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00530053<qmul>00000<rem>053<step>05300530<qmul>10424<rem>106<step>10601060<qmul>20848<rem>212<step>21202120<qmul>52120<rem>000<step>00000000<qmul>00000<rem>000<ans>000.125 |
add | 41 | 6280 | 826 | 90 | 736 | 2x3 | + | 90+736= | scratchpad-v3 | positive | null | single_carry | ++ | train | 090637 | [
{
"a_digit": 0,
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},
{
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"column": 1,
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"serialized": "93021"
},
{
"a_digit":... | 90+736=<add><pos><state>090637<step>06060<step>93021<step>07180<ans>6280 |
sub | 43 | 0540 | -450 | -983 | 533 | 3x3 | + | -983+533= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 389335 | [
{
"borrow_in": 0,
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},
{
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"output_digit": 5,
"serialized": "83050",
"subtrahend... | -983+533=<sub><neg><state>389335<step>33000<step>83050<step>95040<ans>0540 |
div | 161 | 000.669 | -0.669 | 210 | -314 | 3x3 | / | 210/-314= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 210314 | [
{
"incoming_digit": 2,
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},
{
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},
{
"kind"... | 210/-314=<div><neg><state>210314<step>00020002<qmul>00000<rem>002<step>00210021<qmul>00000<rem>021<step>02100210<qmul>00000<rem>210<step>21002100<qmul>61884<rem>216<step>21602160<qmul>61884<rem>276<step>27602760<qmul>82512<rem>248<step>24802480<qmul>72198<rem>282<ans>000.669 |
div | 161 | 016.583 | 16.583 | -398 | -24 | 3x2 | / | -398/-24= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 398024 | [
{
"incoming_digit": 3,
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},
{
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"serialized": "00000"
},
{
"kind":... | -398/-24=<div><pos><state>398024<step>00030003<qmul>00000<rem>003<step>00390039<qmul>10024<rem>015<step>01580158<qmul>60144<rem>014<step>01400140<qmul>50120<rem>020<step>02000200<qmul>80192<rem>008<step>00800080<qmul>30072<rem>008<step>00800080<qmul>30072<rem>008<ans>016.583 |
mul | 118 | 543431 | 134345 | 485 | 277 | 3x3 | * | 485*277= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 584772 | [
{
"a_digit": 5,
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"kind": "term",
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},
{
"carry_in": 0,
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"kind": "column",
... | 485*277=<mul><pos><state>584772<step>5735035<col>503<step>5735038<step>8756094<col>409<step>5210019<step>8756075<step>4728103<col>310<step>8216026<step>4728054<col>405<step>4208013<col>301<ans>543431 |
div | 161 | 001.082 | -1.082 | -822 | 760 | 3x3 | / | -822/760= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 822760 | [
{
"incoming_digit": 8,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | -822/760=<div><neg><state>822760<step>00080008<qmul>00000<rem>008<step>00820082<qmul>00000<rem>082<step>08220822<qmul>10760<rem>062<step>06200620<qmul>00000<rem>620<step>62006200<qmul>86080<rem>120<step>12001200<qmul>10760<rem>440<step>44004400<qmul>53800<rem>600<ans>001.082 |
div | 158 | 000.000 | 0 | 0 | -71 | 1x2 | / | 0/-71= | scratchpad-v3 | negative | round-half-up | zero_numerator | +- | train | 000071 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | 0/-71=<div><neg><state>000071<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 |
sub | 43 | 1160 | -611 | -999 | 388 | 3x3 | + | -999+388= | scratchpad-v3 | negative | null | magnitude_subtraction | -+ | train | 999883 | [
{
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},
{
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"output_digit": 1,
"serialized": "98010",
"subtrahend... | -999+388=<sub><neg><state>999883<step>98010<step>98010<step>93060<ans>1160 |
div | 159 | 004.250 | 4.25 | 221 | 52 | 3x2 | / | 221/52= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 221052 | [
{
"incoming_digit": 2,
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{
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"serialized": "00000"
},
{
"kind":... | 221/52=<div><pos><state>221052<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02210221<qmul>40208<rem>013<step>01300130<qmul>20104<rem>026<step>02600260<qmul>50260<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>004.250 |
sub | 44 | 0000 | 0 | -709 | -709 | 3x3 | - | -709--709= | scratchpad-v3 | positive | null | identity | -- | train | 907907 | [
{
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{
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"subtrahend... | -709--709=<sub><pos><state>907907<step>99000<step>00000<step>77000<ans>0000 |
mul | 118 | 069000 | 960 | -48 | -20 | 2x2 | * | -48*-20= | scratchpad-v3 | positive | null | contains_zero_digit | -- | train | 840020 | [
{
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{
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"o... | -48*-20=<mul><pos><state>840020<step>8000000<col>000<step>8216016<step>4000016<col>601<step>8000001<step>4208009<step>0000009<col>900<step>4000000<step>0200000<col>000<step>0000000<col>000<ans>069000 |
div | 159 | 000.506 | -0.506 | 39 | -77 | 2x2 | / | 39/-77= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 039077 | [
{
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},
{
"kind":... | 39/-77=<div><neg><state>039077<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00390039<qmul>00000<rem>039<step>03900390<qmul>50385<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>60462<rem>038<step>03800380<qmul>40308<rem>072<ans>000.506 |
div | 160 | 076.286 | 76.286 | -534 | -7 | 3x1 | / | -534/-7= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 534007 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -534/-7=<div><pos><state>534007<step>00050005<qmul>00000<rem>005<step>00530053<qmul>70049<rem>004<step>00440044<qmul>60042<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<step>00400040<qmul>50035<rem>005<step>00500050<qmul>70049<rem>001<ans>076.286 |
sub | 42 | 5520 | 255 | 885 | 630 | 3x3 | - | 885-630= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 588036 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 5,
"serialized": "50050",
"subtrahend_digit": 0
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 8,
"output_digit": 5,
"serialized": "83050",
"subtrahend... | 885-630=<sub><pos><state>588036<step>50050<step>83050<step>86020<ans>5520 |
add | 42 | 3311 | 1133 | 615 | 518 | 3x3 | + | 615+518= | scratchpad-v3 | positive | null | overflow | ++ | train | 516815 | [
{
"a_digit": 5,
"b_digit": 8,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 3,
"serialized": "58031"
},
{
"a_digit": 1,
"b_digit": 1,
"carry_in": 1,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "11130"
},
{
"a_digit":... | 615+518=<add><pos><state>516815<step>58031<step>11130<step>65011<ans>3311 |
mul | 118 | 869730 | -37968 | -791 | 48 | 3x2 | * | -791*48= | scratchpad-v3 | negative | null | medium_column_sum | -+ | train | 197840 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
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"serialized": "1808008",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 8,
"kind": "column",
"o... | -791*48=<mul><neg><state>197840<step>1808008<col>800<step>1404004<step>9872076<col>607<step>1000007<step>9436043<step>7856099<col>909<step>9000009<step>7428037<col>703<step>7000003<col>300<ans>869730 |
mul | 119 | 235917 | -719532 | 828 | -869 | 3x3 | * | 828*-869= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 828968 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 72,
"running_total": 72,
"serialized": "8972072",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 7,
"column": 0,
"column_sum": 72,
"kind": "column",
... | 828*-869=<mul><neg><state>828968<step>8972072<col>207<step>8648055<step>2918073<col>307<step>8864071<step>2612083<step>8972155<col>515<step>2816031<step>8648079<col>907<step>8864071<col>107<ans>235917 |
add | 44 | 0250 | -520 | -137 | -383 | 3x3 | + | -137+-383= | scratchpad-v3 | negative | null | multi_carry | -- | train | 731383 | [
{
"a_digit": 7,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "73001"
},
{
"a_digit": 3,
"b_digit": 8,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 2,
"serialized": "38121"
},
{
"a_digit":... | -137+-383=<add><neg><state>731383<step>73001<step>38121<step>13150<ans>0250 |
sub | 42 | 6440 | -446 | 544 | 990 | 3x3 | - | 544-990= | scratchpad-v3 | negative | null | negative_result | ++ | train | 099445 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "04061",
"subtrahend_digit": 4
},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 4,
"serialized": "94140",
"subtrahend... | 544-990=<sub><neg><state>099445<step>04061<step>94140<step>95040<ans>6440 |
div | 160 | 008.000 | -8 | 248 | -31 | 3x2 | / | 248/-31= | scratchpad-v3 | negative | round-half-up | exact | +- | train | 248031 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 31,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 248/-31=<div><neg><state>248031<step>00020002<qmul>00000<rem>002<step>00240024<qmul>00000<rem>024<step>02480248<qmul>80248<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>008.000 |
mul | 119 | 414172 | -271414 | 286 | -949 | 3x3 | * | 286*-949= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 682949 | [
{
"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",
... | 286*-949=<mul><neg><state>682949<step>6954054<col>405<step>6424029<step>8972101<col>110<step>6954064<step>8432096<step>2918114<col>411<step>8972083<step>2408091<col>109<step>2918027<col>702<ans>414172 |
div | 161 | 001.217 | -1.217 | -902 | 741 | 3x3 | / | -902/741= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 902741 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 741,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -902/741=<div><neg><state>902741<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09020902<qmul>10741<rem>161<step>16101610<qmul>21482<rem>128<step>12801280<qmul>10741<rem>539<step>53905390<qmul>75187<rem>203<step>20302030<qmul>21482<rem>548<ans>001.217 |
mul | 117 | 455100 | 1554 | 111 | 14 | 3x2 | * | 111*14= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 111410 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 4,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 4,
"running_total": 4,
"serialized": "1404004",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 4,
"kind": "column",
"o... | 111*14=<mul><pos><state>111410<step>1404004<col>400<step>1101001<step>1404005<col>500<step>1000000<step>1101001<step>1404005<col>500<step>1000000<step>1101001<col>100<step>1000000<col>000<ans>455100 |
sub | 42 | 3610 | 163 | 599 | 436 | 3x3 | - | 599-436= | scratchpad-v3 | positive | null | no_borrow | ++ | train | 995634 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 3,
"serialized": "96030",
"subtrahend_digit": 6
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 9,
"output_digit": 6,
"serialized": "93060",
"subtrahend... | 599-436=<sub><pos><state>995634<step>96030<step>93060<step>54010<ans>3610 |
div | 160 | 000.952 | 0.952 | -59 | -62 | 2x2 | / | -59/-62= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 059062 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 62,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -59/-62=<div><pos><state>059062<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00590059<qmul>00000<rem>059<step>05900590<qmul>90558<rem>032<step>03200320<qmul>50310<rem>010<step>01000100<qmul>10062<rem>038<step>03800380<qmul>60372<rem>008<ans>000.952 |
sub | 41 | 8180 | 818 | 906 | 88 | 3x2 | - | 906-88= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 609880 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 6,
"output_digit": 8,
"serialized": "68081",
"subtrahend_digit": 8
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | 906-88=<sub><pos><state>609880<step>68081<step>08111<step>90180<ans>8180 |
add | 41 | 6810 | 186 | 184 | -2 | 3x1 | - | 184--2= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 481200 | [
{
"a_digit": 4,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 6,
"serialized": "42060"
},
{
"a_digit": 8,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "80080"
},
{
"a_digit":... | 184--2=<add><pos><state>481200<step>42060<step>80080<step>10010<ans>6810 |
add | 42 | 5101 | 1015 | 482 | 533 | 3x3 | + | 482+533= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 284335 | [
{
"a_digit": 2,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 5,
"serialized": "23050"
},
{
"a_digit": 8,
"b_digit": 3,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "83011"
},
{
"a_digit":... | 482+533=<add><pos><state>284335<step>23050<step>83011<step>45101<ans>5101 |
mul | 120 | 670647 | 746076 | -948 | -787 | 3x3 | * | -948*-787= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 849787 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 7,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 56,
"running_total": 56,
"serialized": "8756056",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 5,
"column": 0,
"column_sum": 56,
"kind": "column",
... | -948*-787=<mul><pos><state>849787<step>8756056<col>605<step>8864069<step>4728097<col>709<step>8756065<step>4832097<step>9763160<col>016<step>4728044<step>9872116<col>611<step>9763074<col>407<ans>670647 |
sub | 41 | 8050 | 508 | 600 | 92 | 3x2 | - | 600-92= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 006290 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 0,
"output_digit": 8,
"serialized": "02081",
"subtrahend_digit": 2
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 0,
"serialized": "09101",
"subtrahend... | 600-92=<sub><pos><state>006290<step>02081<step>09101<step>60150<ans>8050 |
div | 159 | 000.769 | -0.769 | -20 | 26 | 2x2 | / | -20/26= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 020026 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 26,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -20/26=<div><neg><state>020026<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>70182<rem>018<step>01800180<qmul>60156<rem>024<step>02400240<qmul>90234<rem>006<step>00600060<qmul>20052<rem>008<ans>000.769 |
mul | 119 | 606792 | -297606 | 386 | -771 | 3x3 | * | 386*-771= | scratchpad-v3 | negative | null | medium_column_sum | +- | test | 683177 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 1,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 6,
"running_total": 6,
"serialized": "6106006",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 6,
"kind": "column",
"o... | 386*-771=<mul><neg><state>683177<step>6106006<col>600<step>6742042<step>8108050<col>005<step>6742047<step>8756103<step>3103106<col>610<step>8756066<step>3721087<col>708<step>3721029<col>902<ans>606792 |
div | 160 | 062.333 | 62.333 | -561 | -9 | 3x1 | / | -561/-9= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 561009 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 9,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | -561/-9=<div><pos><state>561009<step>00050005<qmul>00000<rem>005<step>00560056<qmul>60054<rem>002<step>00210021<qmul>20018<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<ans>062.333 |
add | 41 | 8380 | -838 | 0 | -838 | 1x3 | + | 0+-838= | scratchpad-v3 | negative | null | identity | +- | train | 000838 | [
{
"a_digit": 0,
"b_digit": 8,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 8,
"serialized": "08080"
},
{
"a_digit": 0,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 3,
"serialized": "03030"
},
{
"a_digit":... | 0+-838=<add><neg><state>000838<step>08080<step>03030<step>08080<ans>8380 |
div | 162 | 001.414 | 1.414 | -990 | -700 | 3x3 | / | -990/-700= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 990700 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 700,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -990/-700=<div><pos><state>990700<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09900990<qmul>10700<rem>290<step>29002900<qmul>42800<rem>100<step>10001000<qmul>10700<rem>300<step>30003000<qmul>42800<rem>200<step>20002000<qmul>21400<rem>600<ans>001.414 |
sub | 40 | 1100 | -11 | 55 | 66 | 2x2 | - | 55-66= | scratchpad-v3 | negative | null | negative_result | ++ | train | 660550 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 6,
"output_digit": 1,
"serialized": "65010",
"subtrahend_digit": 5
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 1,
"serialized": "65010",
"subtrahend... | 55-66=<sub><neg><state>660550<step>65010<step>65010<step>00000<ans>1100 |
sub | 43 | 7450 | 547 | -55 | -602 | 2x3 | - | -55--602= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 206550 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 7,
"serialized": "25071",
"subtrahend_digit": 5
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 4,
"serialized": "05141",
"subtrahend... | -55--602=<sub><pos><state>206550<step>25071<step>05141<step>60150<ans>7450 |
div | 162 | 000.415 | 0.415 | -227 | -547 | 3x3 | / | -227/-547= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 227547 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 547,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -227/-547=<div><pos><state>227547<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02270227<qmul>00000<rem>227<step>22702270<qmul>42188<rem>082<step>08200820<qmul>10547<rem>273<step>27302730<qmul>42188<rem>542<step>54205420<qmul>94923<rem>497<ans>000.415 |
add | 44 | 1640 | -461 | -182 | -279 | 3x3 | + | -182+-279= | scratchpad-v3 | negative | null | multi_carry | -- | train | 281972 | [
{
"a_digit": 2,
"b_digit": 9,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 1,
"serialized": "29011"
},
{
"a_digit": 8,
"b_digit": 7,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 6,
"serialized": "87161"
},
{
"a_digit":... | -182+-279=<add><neg><state>281972<step>29011<step>87161<step>12140<ans>1640 |
div | 162 | 000.979 | 0.979 | -565 | -577 | 3x3 | / | -565/-577= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 565577 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 577,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -565/-577=<div><pos><state>565577<step>00050005<qmul>00000<rem>005<step>00560056<qmul>00000<rem>056<step>05650565<qmul>00000<rem>565<step>56505650<qmul>95193<rem>457<step>45704570<qmul>74039<rem>531<step>53105310<qmul>95193<rem>117<step>11701170<qmul>21154<rem>016<ans>000.979 |
div | 160 | 001.442 | 1.442 | 789 | 547 | 3x3 | / | 789/547= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 789547 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
"divisor": 547,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 789/547=<div><pos><state>789547<step>00070007<qmul>00000<rem>007<step>00780078<qmul>00000<rem>078<step>07890789<qmul>10547<rem>242<step>24202420<qmul>42188<rem>232<step>23202320<qmul>42188<rem>132<step>13201320<qmul>21094<rem>226<step>22602260<qmul>42188<rem>072<ans>001.442 |
sub | 42 | 0030 | -300 | 239 | 539 | 3x3 | - | 239-539= | scratchpad-v3 | negative | null | negative_result | ++ | train | 935932 | [
{
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{
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"serialized": "33000",
"subtrahend... | 239-539=<sub><neg><state>935932<step>99000<step>33000<step>52030<ans>0030 |
sub | 43 | 9430 | 349 | -59 | -408 | 2x3 | - | -59--408= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 804950 | [
{
"borrow_in": 0,
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{
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"borrow_out": 1,
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"serialized": "05141",
"subtrahend... | -59--408=<sub><pos><state>804950<step>89091<step>05141<step>40130<ans>9430 |
div | 159 | 000.803 | -0.803 | -57 | 71 | 2x2 | / | -57/71= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | -+ | train | 057071 | [
{
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{
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{
"kind":... | -57/71=<div><neg><state>057071<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00570057<qmul>00000<rem>057<step>05700570<qmul>80568<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>20142<rem>058<step>05800580<qmul>80568<rem>012<ans>000.803 |
add | 42 | 4061 | 1604 | 703 | 901 | 3x3 | + | 703+901= | scratchpad-v3 | positive | null | overflow | ++ | train | 307109 | [
{
"a_digit": 3,
"b_digit": 1,
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{
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},
{
"a_digit":... | 703+901=<add><pos><state>307109<step>31040<step>00000<step>79061<ans>4061 |
sub | 40 | 8200 | -28 | 18 | 46 | 2x2 | - | 18-46= | scratchpad-v3 | negative | null | negative_result | ++ | train | 640810 | [
{
"borrow_in": 0,
"borrow_out": 1,
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
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"output_digit": 2,
"serialized": "41120",
"subtrahend... | 18-46=<sub><neg><state>640810<step>68081<step>41120<step>00000<ans>8200 |
div | 159 | 078.000 | -78 | -702 | 9 | 3x1 | / | -702/9= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 702009 | [
{
"incoming_digit": 7,
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},
{
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"serialized": "00000"
},
{
"kind": ... | -702/9=<div><neg><state>702009<step>00070007<qmul>00000<rem>007<step>00700070<qmul>70063<rem>007<step>00720072<qmul>80072<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>078.000 |
mul | 118 | 443166 | 661344 | 664 | 996 | 3x3 | * | 664*996= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 466699 | [
{
"a_digit": 4,
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | 664*996=<mul><pos><state>466699<step>4624024<col>402<step>4936038<step>6636074<col>407<step>4936043<step>6954097<step>6636133<col>313<step>6954067<step>6954121<col>112<step>6954066<col>606<ans>443166 |
div | 157 | 026.000 | 26 | 78 | 3 | 2x1 | / | 78/3= | scratchpad-v3 | positive | round-half-up | exact | ++ | train | 078003 | [
{
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{
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{
"kind": ... | 78/3=<div><pos><state>078003<step>00000000<qmul>00000<rem>000<step>00070007<qmul>20006<rem>001<step>00180018<qmul>60018<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>026.000 |
mul | 118 | 083200 | 2380 | -70 | -34 | 2x2 | * | -70*-34= | scratchpad-v3 | positive | null | contains_zero_digit | -- | train | 070430 | [
{
"a_digit": 0,
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{
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"o... | -70*-34=<mul><pos><state>070430<step>0400000<col>000<step>0300000<step>7428028<col>802<step>0000002<step>7321023<step>0400023<col>302<step>7000002<step>0300002<col>200<step>0000000<col>000<ans>083200 |
add | 41 | 6550 | 556 | 514 | 42 | 3x2 | + | 514+42= | scratchpad-v3 | positive | null | no_carry | ++ | train | 415240 | [
{
"a_digit": 4,
"b_digit": 2,
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"serialized": "42060"
},
{
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"column": 1,
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"serialized": "14050"
},
{
"a_digit":... | 514+42=<add><pos><state>415240<step>42060<step>14050<step>50050<ans>6550 |
div | 160 | 133.167 | 133.167 | -799 | -6 | 3x1 | / | -799/-6= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 799006 | [
{
"incoming_digit": 7,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "10006"
},
{
"kind": ... | -799/-6=<div><pos><state>799006<step>00070007<qmul>10006<rem>001<step>00190019<qmul>30018<rem>001<step>00190019<qmul>30018<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>133.167 |
mul | 118 | 100980 | -89001 | 957 | -93 | 3x2 | * | 957*-93= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 759390 | [
{
"a_digit": 7,
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"serialized": "7321021",
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},
{
"carry_in": 0,
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"kind": "column",
... | 957*-93=<mul><neg><state>759390<step>7321021<col>102<step>7963065<step>5315080<col>008<step>7000008<step>5945053<step>9327080<col>008<step>5000008<step>9981089<col>908<step>9000008<col>800<ans>100980 |
mul | 120 | 300938 | 839003 | -979 | -857 | 3x3 | * | -979*-857= | scratchpad-v3 | positive | null | high_column_sum | -- | train | 979758 | [
{
"a_digit": 9,
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},
{
"carry_in": 0,
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"kind": "column",
... | -979*-857=<mul><pos><state>979758<step>9763063<col>306<step>9545051<step>7749100<col>010<step>9872082<step>7535117<step>9763180<col>018<step>7856074<step>9545119<col>911<step>9872083<col>308<ans>300938 |
sub | 42 | 3820 | -283 | 212 | 495 | 3x3 | - | 212-495= | scratchpad-v3 | negative | null | negative_result | ++ | train | 594212 | [
{
"borrow_in": 0,
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},
{
"borrow_in": 0,
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"column": 1,
"minuend_digit": 9,
"output_digit": 8,
"serialized": "91080",
"subtrahend... | 212-495=<sub><neg><state>594212<step>52030<step>91080<step>42020<ans>3820 |
sub | 41 | 1700 | 71 | 148 | 77 | 3x2 | - | 148-77= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 841770 | [
{
"borrow_in": 0,
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"output_digit": 1,
"serialized": "87010",
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},
{
"borrow_in": 0,
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"column": 1,
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"serialized": "47071",
"subtrahend... | 148-77=<sub><pos><state>841770<step>87010<step>47071<step>10100<ans>1700 |
add | 44 | 0080 | -800 | -469 | -331 | 3x3 | + | -469+-331= | scratchpad-v3 | negative | null | cascading_carry | -- | test | 964133 | [
{
"a_digit": 9,
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},
{
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"serialized": "63101"
},
{
"a_digit":... | -469+-331=<add><neg><state>964133<step>91001<step>63101<step>43180<ans>0080 |
mul | 119 | 580247 | -742085 | -769 | 965 | 3x3 | * | -769*965= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 967569 | [
{
"a_digit": 9,
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},
{
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... | -769*965=<mul><neg><state>967569<step>9545045<col>504<step>9654058<step>6530088<col>808<step>9981089<step>6636125<step>7535160<col>016<step>6954070<step>7642112<col>211<step>7963074<col>407<ans>580247 |
mul | 119 | 488577 | -775884 | -779 | 996 | 3x3 | * | -779*996= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 977699 | [
{
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},
{
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... | -779*996=<mul><neg><state>977699<step>9654054<col>405<step>9981086<step>7642128<col>812<step>9981093<step>7963156<step>7642198<col>819<step>7963082<step>7963145<col>514<step>7963077<col>707<ans>488577 |
div | 159 | 084.333 | -84.333 | 506 | -6 | 3x1 | / | 506/-6= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 506006 | [
{
"incoming_digit": 5,
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},
{
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"serialized": "00000"
},
{
"kind": ... | 506/-6=<div><neg><state>506006<step>00050005<qmul>00000<rem>005<step>00500050<qmul>80048<rem>002<step>00260026<qmul>40024<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<ans>084.333 |
mul | 117 | 974100 | -1479 | -29 | 51 | 2x2 | * | -29*51= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 920150 | [
{
"a_digit": 9,
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},
{
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"o... | -29*51=<mul><neg><state>920150<step>9109009<col>900<step>9545045<step>2102047<col>704<step>9000004<step>2510014<step>0100014<col>401<step>2000001<step>0500001<col>100<step>0000000<col>000<ans>974100 |
mul | 120 | 388611 | 116883 | -999 | -117 | 3x3 | * | -999*-117= | scratchpad-v3 | positive | null | repeated_digit | -- | train | 999711 | [
{
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
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"kind": "column",
... | -999*-117=<mul><pos><state>999711<step>9763063<col>306<step>9109015<step>9763078<col>807<step>9109016<step>9109025<step>9763088<col>808<step>9109017<step>9109026<col>602<step>9109011<col>101<ans>388611 |
add | 41 | 0860 | -680 | 0 | -680 | 1x3 | + | 0+-680= | scratchpad-v3 | negative | null | identity | +- | train | 000086 | [
{
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{
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"serialized": "08080"
},
{
"a_digit":... | 0+-680=<add><neg><state>000086<step>00000<step>08080<step>06060<ans>0860 |
add | 42 | 6370 | 736 | 158 | 578 | 3x3 | + | 158+578= | scratchpad-v3 | positive | null | multi_carry | ++ | val | 851875 | [
{
"a_digit": 8,
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"column": 0,
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},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "57131"
},
{
"a_digit":... | 158+578=<add><pos><state>851875<step>88061<step>57131<step>15170<ans>6370 |
div | 160 | 000.487 | 0.487 | 384 | 789 | 3x3 | / | 384/789= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 384789 | [
{
"incoming_digit": 3,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 384/789=<div><pos><state>384789<step>00030003<qmul>00000<rem>003<step>00380038<qmul>00000<rem>038<step>03840384<qmul>00000<rem>384<step>38403840<qmul>43156<rem>684<step>68406840<qmul>86312<rem>528<step>52805280<qmul>64734<rem>546<step>54605460<qmul>64734<rem>726<ans>000.487 |
mul | 116 | 000000 | 0 | 0 | 230 | 1x3 | * | 0*230= | scratchpad-v3 | positive | null | identity | ++ | train | 000032 | [
{
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{
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"o... | 0*230=<mul><pos><state>000032<step>0000000<col>000<step>0300000<step>0000000<col>000<step>0200000<step>0300000<step>0000000<col>000<step>0200000<step>0300000<col>000<step>0200000<col>000<ans>000000 |
sub | 42 | 5740 | 475 | 954 | 479 | 3x3 | - | 954-479= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 459974 | [
{
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{
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"column": 1,
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"output_digit": 7,
"serialized": "57171",
"subtrahend... | 954-479=<sub><pos><state>459974<step>49051<step>57171<step>94140<ans>5740 |
add | 44 | 1490 | -941 | -269 | -672 | 3x3 | + | -269+-672= | scratchpad-v3 | negative | null | multi_carry | -- | train | 962276 | [
{
"a_digit": 9,
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},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "67141"
},
{
"a_digit":... | -269+-672=<add><neg><state>962276<step>92011<step>67141<step>26190<ans>1490 |
add | 42 | 6231 | 1326 | 823 | 503 | 3x3 | + | 823+503= | scratchpad-v3 | positive | null | overflow | ++ | train | 328305 | [
{
"a_digit": 3,
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},
{
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"column": 1,
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"serialized": "20020"
},
{
"a_digit":... | 823+503=<add><pos><state>328305<step>33060<step>20020<step>85031<ans>6231 |
div | 160 | 006.685 | -6.685 | 361 | -54 | 3x2 | / | 361/-54= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 361054 | [
{
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind":... | 361/-54=<div><neg><state>361054<step>00030003<qmul>00000<rem>003<step>00360036<qmul>00000<rem>036<step>03610361<qmul>60324<rem>037<step>03700370<qmul>60324<rem>046<step>04600460<qmul>80432<rem>028<step>02800280<qmul>50270<rem>010<step>01000100<qmul>10054<rem>046<ans>006.685 |
mul | 118 | 099460 | -64990 | -670 | 97 | 3x2 | * | -670*97= | scratchpad-v3 | negative | null | contains_zero_digit | -+ | train | 076790 | [
{
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},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | -670*97=<mul><neg><state>076790<step>0700000<col>000<step>0900000<step>7749049<col>904<step>0000004<step>7963067<step>6742109<col>910<step>7000010<step>6954064<col>406<step>6000006<col>600<ans>099460 |
div | 159 | 097.667 | -97.667 | 293 | -3 | 3x1 | / | 293/-3= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 293003 | [
{
"incoming_digit": 2,
"kind": "partial",
"partial": 2,
"position": 0,
"remainder_in": 0,
"serialized": "00020002"
},
{
"divisor": 3,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 293/-3=<div><neg><state>293003<step>00020002<qmul>00000<rem>002<step>00290029<qmul>90027<rem>002<step>00230023<qmul>70021<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>097.667 |
sub | 41 | 9810 | -189 | 17 | 206 | 2x3 | - | 17-206= | scratchpad-v3 | negative | null | negative_result | ++ | train | 602710 | [
{
"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": 8,
"serialized": "01181",
"subtrahend... | 17-206=<sub><neg><state>602710<step>67091<step>01181<step>20110<ans>9810 |
sub | 44 | 2300 | 32 | -693 | -725 | 3x3 | - | -693--725= | scratchpad-v3 | positive | null | single_borrow | -- | train | 527396 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 5,
"output_digit": 2,
"serialized": "53020",
"subtrahend_digit": 3
},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 3,
"serialized": "29031",
"subtrahend... | -693--725=<sub><pos><state>527396<step>53020<step>29031<step>76100<ans>2300 |
sub | 44 | 7440 | 447 | -476 | -923 | 3x3 | - | -476--923= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 329674 | [
{
"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": 2,
"output_digit": 4,
"serialized": "27141",
"subtrahend... | -476--923=<sub><pos><state>329674<step>36071<step>27141<step>94140<ans>7440 |
mul | 118 | 095400 | -4590 | -17 | 270 | 2x3 | * | -17*270= | scratchpad-v3 | negative | null | contains_zero_digit | -+ | train | 710072 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 0,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 0,
"running_total": 0,
"serialized": "7000000",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | -17*270=<mul><neg><state>710072<step>7000000<col>000<step>7749049<step>1000049<col>904<step>7214018<step>1707025<step>0000025<col>502<step>1202004<step>0700004<col>400<step>0200000<col>000<ans>095400 |
add | 42 | 2780 | 872 | 321 | 551 | 3x3 | + | 321+551= | scratchpad-v3 | positive | null | no_carry | ++ | train | 123155 | [
{
"a_digit": 1,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 2,
"serialized": "11020"
},
{
"a_digit": 2,
"b_digit": 5,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "25070"
},
{
"a_digit":... | 321+551=<add><pos><state>123155<step>11020<step>25070<step>35080<ans>2780 |
div | 158 | 000.873 | 0.873 | 62 | 71 | 2x2 | / | 62/71= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | train | 062071 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 71,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 62/71=<div><pos><state>062071<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06200620<qmul>80568<rem>052<step>05200520<qmul>70497<rem>023<step>02300230<qmul>30213<rem>017<step>01700170<qmul>20142<rem>028<ans>000.873 |
sub | 44 | 0000 | 0 | -479 | -479 | 3x3 | - | -479--479= | scratchpad-v3 | positive | null | identity | -- | train | 974974 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 9,
"output_digit": 0,
"serialized": "99000",
"subtrahend_digit": 9
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 7,
"output_digit": 0,
"serialized": "77000",
"subtrahend... | -479--479=<sub><pos><state>974974<step>99000<step>77000<step>44000<ans>0000 |
mul | 118 | 383570 | -75383 | 847 | -89 | 3x2 | * | 847*-89= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 748980 | [
{
"a_digit": 7,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 63,
"running_total": 63,
"serialized": "7963063",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 6,
"column": 0,
"column_sum": 63,
"kind": "column",
... | 847*-89=<mul><neg><state>748980<step>7963063<col>306<step>7856062<step>4936098<col>809<step>7000009<step>4832041<step>8972113<col>311<step>4000011<step>8864075<col>507<step>8000007<col>700<ans>383570 |
add | 42 | 0081 | 1800 | 988 | 812 | 3x3 | + | 988+812= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 889218 | [
{
"a_digit": 8,
"b_digit": 2,
"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 0,
"serialized": "82001"
},
{
"a_digit": 8,
"b_digit": 1,
"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "81101"
},
{
"a_digit":... | 988+812=<add><pos><state>889218<step>82001<step>81101<step>98181<ans>0081 |
mul | 120 | 346872 | 278643 | -951 | -293 | 3x3 | * | -951*-293= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 159392 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 3,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 3,
"running_total": 3,
"serialized": "1303003",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 3,
"kind": "column",
"o... | -951*-293=<mul><pos><state>159392<step>1303003<col>300<step>1909009<step>5315024<col>402<step>1202004<step>5945049<step>9327076<col>607<step>5210017<step>9981098<col>809<step>9218027<col>702<ans>346872 |
div | 161 | 001.010 | -1.01 | -490 | 485 | 3x3 | / | -490/485= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 490485 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 485,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -490/485=<div><neg><state>490485<step>00040004<qmul>00000<rem>004<step>00490049<qmul>00000<rem>049<step>04900490<qmul>10485<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>10485<rem>015<step>01500150<qmul>00000<rem>150<step>15001500<qmul>31455<rem>045<ans>001.010 |
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