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 | 117 | 146200 | 2641 | 139 | 19 | 3x2 | * | 139*19= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 931910 | [
{
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"serialized": "9981081",
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},
{
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"kind": "column",
... | 139*19=<mul><pos><state>931910<step>9981081<col>108<step>9109017<step>3927044<col>404<step>9000004<step>3103007<step>1909016<col>601<step>3000001<step>1101002<col>200<step>1000000<col>000<ans>146200 |
div | 161 | 001.309 | -1.309 | -305 | 233 | 3x3 | / | -305/233= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 305233 | [
{
"incoming_digit": 3,
"kind": "partial",
"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -305/233=<div><neg><state>305233<step>00030003<qmul>00000<rem>003<step>00300030<qmul>00000<rem>030<step>03050305<qmul>10233<rem>072<step>07200720<qmul>30699<rem>021<step>02100210<qmul>00000<rem>210<step>21002100<qmul>92097<rem>003<step>00300030<qmul>00000<rem>030<ans>001.309 |
div | 157 | 000.000 | 0 | 0 | 37 | 1x2 | / | 0/37= | scratchpad-v3 | positive | round-half-up | zero_numerator | ++ | train | 000037 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 37,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 0/37=<div><pos><state>000037<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 |
mul | 117 | 509700 | -7905 | 93 | -85 | 2x2 | * | 93*-85= | scratchpad-v3 | negative | null | low_column_sum | +- | train | 390580 | [
{
"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,
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"column_sum": 15,
"kind": "column",
... | 93*-85=<mul><neg><state>390580<step>3515015<col>501<step>3824025<step>9545070<col>007<step>3000007<step>9872079<step>0500079<col>907<step>9000007<step>0800007<col>700<step>0000000<col>000<ans>509700 |
mul | 119 | 815161 | -161518 | 973 | -166 | 3x3 | * | 973*-166= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 379661 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 6,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 18,
"running_total": 18,
"serialized": "3618018",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 1,
"column": 0,
"column_sum": 18,
"kind": "column",
... | 973*-166=<mul><neg><state>379661<step>3618018<col>801<step>3618019<step>7642061<col>106<step>3103009<step>7642051<step>9654105<col>510<step>7107017<step>9654071<col>107<step>9109016<col>601<ans>815161 |
mul | 118 | 191418 | 814191 | 959 | 849 | 3x3 | * | 959*849= | scratchpad-v3 | positive | null | high_column_sum | ++ | train | 959948 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 9,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 81,
"running_total": 81,
"serialized": "9981081",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 8,
"column": 0,
"column_sum": 81,
"kind": "column",
... | 959*849=<mul><pos><state>959948<step>9981081<col>108<step>9436044<step>5945089<col>908<step>9872080<step>5420100<step>9981181<col>118<step>5840058<step>9436094<col>409<step>9872081<col>108<ans>191418 |
add | 44 | 7780 | -877 | -633 | -244 | 3x3 | + | -633+-244= | scratchpad-v3 | negative | null | no_carry | -- | train | 336442 | [
{
"a_digit": 3,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "34070"
},
{
"a_digit": 3,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "34070"
},
{
"a_digit":... | -633+-244=<add><neg><state>336442<step>34070<step>34070<step>62080<ans>7780 |
mul | 118 | 211310 | -13112 | 44 | -298 | 2x3 | * | 44*-298= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 440892 | [
{
"a_digit": 4,
"a_index": 0,
"b_digit": 8,
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"column": 0,
"kind": "term",
"product": 32,
"running_total": 32,
"serialized": "4832032",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 32,
"kind": "column",
... | 44*-298=<mul><neg><state>440892<step>4832032<col>203<step>4936039<step>4832071<col>107<step>4208015<step>4936051<step>0800051<col>105<step>4208013<step>0900013<col>301<step>0200001<col>100<ans>211310 |
div | 162 | 000.500 | 0.5 | -403 | -806 | 3x3 | / | -403/-806= | scratchpad-v3 | positive | round-half-up | exact | -- | train | 403806 | [
{
"incoming_digit": 4,
"kind": "partial",
"partial": 4,
"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
"divisor": 806,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -403/-806=<div><pos><state>403806<step>00040004<qmul>00000<rem>004<step>00400040<qmul>00000<rem>040<step>04030403<qmul>00000<rem>403<step>40304030<qmul>54030<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>000.500 |
add | 43 | 8820 | -288 | -54 | -234 | 2x3 | + | -54+-234= | scratchpad-v3 | negative | null | no_carry | -- | train | 450432 | [
{
"a_digit": 4,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 8,
"serialized": "44080"
},
{
"a_digit": 5,
"b_digit": 3,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 8,
"serialized": "53080"
},
{
"a_digit":... | -54+-234=<add><neg><state>450432<step>44080<step>53080<step>02020<ans>8820 |
mul | 119 | 390397 | -793093 | 827 | -959 | 3x3 | * | 827*-959= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 728959 | [
{
"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",
... | 827*-959=<mul><neg><state>728959<step>7963063<col>306<step>7535041<step>2918059<col>905<step>7963068<step>2510078<step>8972150<col>015<step>2918033<step>8540073<col>307<step>8972079<col>907<ans>390397 |
mul | 120 | 825552 | 255528 | -338 | -756 | 3x3 | * | -338*-756= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 833657 | [
{
"a_digit": 8,
"a_index": 0,
"b_digit": 6,
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"column": 0,
"kind": "term",
"product": 48,
"running_total": 48,
"serialized": "8648048",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 48,
"kind": "column",
... | -338*-756=<mul><pos><state>833657<step>8648048<col>804<step>8540044<step>3618062<col>206<step>8756062<step>3515077<step>3618095<col>509<step>3721030<step>3515045<col>504<step>3721025<col>502<ans>825552 |
sub | 44 | 3610 | -163 | -965 | -802 | 3x3 | - | -965--802= | scratchpad-v3 | negative | null | negative_result | -- | val | 569208 | [
{
"borrow_in": 0,
"borrow_out": 0,
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"output_digit": 3,
"serialized": "52030",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 6,
"serialized": "60060",
"subtrahend... | -965--802=<sub><neg><state>569208<step>52030<step>60060<step>98010<ans>3610 |
div | 161 | 000.908 | -0.908 | -554 | 610 | 3x3 | / | -554/610= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | -+ | train | 554610 | [
{
"incoming_digit": 5,
"kind": "partial",
"partial": 5,
"position": 0,
"remainder_in": 0,
"serialized": "00050005"
},
{
"divisor": 610,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -554/610=<div><neg><state>554610<step>00050005<qmul>00000<rem>005<step>00550055<qmul>00000<rem>055<step>05540554<qmul>00000<rem>554<step>55405540<qmul>95490<rem>050<step>05000500<qmul>00000<rem>500<step>50005000<qmul>84880<rem>120<step>12001200<qmul>10610<rem>590<ans>000.908 |
sub | 41 | 9070 | 709 | 804 | 95 | 3x2 | - | 804-95= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 408590 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 9,
"serialized": "45091",
"subtrahend_digit": 5
},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 0,
"serialized": "09101",
"subtrahend... | 804-95=<sub><pos><state>408590<step>45091<step>09101<step>80170<ans>9070 |
sub | 41 | 5160 | 615 | 700 | 85 | 3x2 | - | 700-85= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | test | 007580 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
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"output_digit": 5,
"serialized": "05051",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | 700-85=<sub><pos><state>007580<step>05051<step>08111<step>70160<ans>5160 |
div | 161 | 000.191 | 0.191 | -43 | -225 | 2x3 | / | -43/-225= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | -- | train | 043225 | [
{
"incoming_digit": 0,
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"serialized": "00000000"
},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -43/-225=<div><pos><state>043225<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04300430<qmul>10225<rem>205<step>20502050<qmul>92025<rem>025<step>02500250<qmul>10225<rem>025<step>02500250<qmul>10225<rem>025<ans>000.191 |
add | 40 | 5980 | 895 | 890 | 5 | 3x1 | + | 890+5= | scratchpad-v3 | positive | null | no_carry | ++ | train | 098500 | [
{
"a_digit": 0,
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"column": 0,
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"serialized": "05050"
},
{
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"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "90090"
},
{
"a_digit":... | 890+5=<add><pos><state>098500<step>05050<step>90090<step>80080<ans>5980 |
div | 160 | 000.470 | 0.47 | 435 | 925 | 3x3 | / | 435/925= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | train | 435925 | [
{
"incoming_digit": 4,
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"position": 0,
"remainder_in": 0,
"serialized": "00040004"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 435/925=<div><pos><state>435925<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04350435<qmul>00000<rem>435<step>43504350<qmul>43700<rem>650<step>65006500<qmul>76475<rem>025<step>02500250<qmul>00000<rem>250<step>25002500<qmul>21850<rem>650<ans>000.470 |
sub | 42 | 8710 | 178 | 947 | 769 | 3x3 | - | 947-769= | scratchpad-v3 | positive | null | multi_borrow | ++ | train | 749967 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 7,
"output_digit": 8,
"serialized": "79081",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 4,
"output_digit": 7,
"serialized": "46171",
"subtrahend... | 947-769=<sub><pos><state>749967<step>79081<step>46171<step>97110<ans>8710 |
sub | 41 | 6610 | 166 | 204 | 38 | 3x2 | - | 204-38= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 402830 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 4,
"output_digit": 6,
"serialized": "48061",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 6,
"serialized": "03161",
"subtrahend... | 204-38=<sub><pos><state>402830<step>48061<step>03161<step>20110<ans>6610 |
add | 42 | 4101 | 1014 | 565 | 449 | 3x3 | + | 565+449= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 565944 | [
{
"a_digit": 5,
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"carry_in": 0,
"carry_out": 1,
"column": 0,
"output_digit": 4,
"serialized": "59041"
},
{
"a_digit": 6,
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"carry_in": 1,
"carry_out": 1,
"column": 1,
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"serialized": "64111"
},
{
"a_digit":... | 565+449=<add><pos><state>565944<step>59041<step>64111<step>54101<ans>4101 |
mul | 116 | 234200 | 2432 | 76 | 32 | 2x2 | * | 76*32= | scratchpad-v3 | positive | null | low_column_sum | ++ | train | 670230 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 2,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 12,
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"serialized": "6212012",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 12,
"kind": "column",
... | 76*32=<mul><pos><state>670230<step>6212012<col>201<step>6318019<step>7214033<col>303<step>6000003<step>7321024<step>0200024<col>402<step>7000002<step>0300002<col>200<step>0000000<col>000<ans>234200 |
div | 162 | 000.533 | 0.533 | -319 | -599 | 3x3 | / | -319/-599= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 319599 | [
{
"incoming_digit": 3,
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"partial": 3,
"position": 0,
"remainder_in": 0,
"serialized": "00030003"
},
{
"divisor": 599,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -319/-599=<div><pos><state>319599<step>00030003<qmul>00000<rem>003<step>00310031<qmul>00000<rem>031<step>03190319<qmul>00000<rem>319<step>31903190<qmul>52995<rem>195<step>19501950<qmul>31797<rem>153<step>15301530<qmul>21198<rem>332<step>33203320<qmul>52995<rem>325<ans>000.533 |
mul | 119 | 331479 | -974133 | -981 | 993 | 3x3 | * | -981*993= | scratchpad-v3 | negative | null | high_column_sum | -+ | train | 189399 | [
{
"a_digit": 1,
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},
{
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"column": 0,
"column_sum": 3,
"kind": "column",
"o... | -981*993=<mul><neg><state>189399<step>1303003<col>300<step>1909009<step>8324033<col>303<step>1909012<step>8972084<step>9327111<col>111<step>8972083<step>9981164<col>416<step>9981097<col>709<ans>331479 |
mul | 119 | 844650 | 56448 | -882 | -64 | 3x2 | * | -882*-64= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 288460 | [
{
"a_digit": 2,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 8,
"kind": "column",
"o... | -882*-64=<mul><pos><state>288460<step>2408008<col>800<step>2612012<step>8432044<col>404<step>2000004<step>8648052<step>8432084<col>408<step>8000008<step>8648056<col>605<step>8000005<col>500<ans>844650 |
div | 159 | 000.143 | 0.143 | -4 | -28 | 1x2 | / | -4/-28= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 004028 | [
{
"incoming_digit": 0,
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},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | -4/-28=<div><pos><state>004028<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00400040<qmul>10028<rem>012<step>01200120<qmul>40112<rem>008<step>00800080<qmul>20056<rem>024<step>02400240<qmul>80224<rem>016<ans>000.143 |
div | 159 | 149.500 | -149.5 | -897 | 6 | 3x1 | / | -897/6= | scratchpad-v3 | negative | round-half-up | exact | -+ | train | 897006 | [
{
"incoming_digit": 8,
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"position": 0,
"remainder_in": 0,
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},
{
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"position": 0,
"quotient_digit": 1,
"quotient_product": 6,
"serialized": "10006"
},
{
"kind": ... | -897/6=<div><neg><state>897006<step>00080008<qmul>10006<rem>002<step>00290029<qmul>40024<rem>005<step>00570057<qmul>90054<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<ans>149.500 |
mul | 117 | 053200 | -2350 | -25 | 94 | 2x2 | * | -25*94= | scratchpad-v3 | negative | null | low_column_sum | -+ | train | 520490 | [
{
"a_digit": 5,
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{
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... | -25*94=<mul><neg><state>520490<step>5420020<col>002<step>5945047<step>2408055<col>505<step>5000005<step>2918023<step>0400023<col>302<step>2000002<step>0900002<col>200<step>0000000<col>000<ans>053200 |
add | 42 | 2040 | 402 | 318 | -84 | 3x2 | - | 318--84= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 813480 | [
{
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},
{
"a_digit":... | 318--84=<add><pos><state>813480<step>84021<step>18101<step>30140<ans>2040 |
div | 159 | 000.947 | -0.947 | 36 | -38 | 2x2 | / | 36/-38= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 036038 | [
{
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{
"kind":... | 36/-38=<div><neg><state>036038<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00360036<qmul>00000<rem>036<step>03600360<qmul>90342<rem>018<step>01800180<qmul>40152<rem>028<step>02800280<qmul>70266<rem>014<step>01400140<qmul>30114<rem>026<ans>000.947 |
div | 159 | 014.429 | -14.429 | -101 | 7 | 3x1 | / | -101/7= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | -+ | train | 101007 | [
{
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{
"kind": ... | -101/7=<div><neg><state>101007<step>00010001<qmul>00000<rem>001<step>00100010<qmul>10007<rem>003<step>00310031<qmul>40028<rem>003<step>00300030<qmul>40028<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<step>00400040<qmul>50035<rem>005<ans>014.429 |
add | 42 | 1021 | 1201 | 557 | 644 | 3x3 | + | 557+644= | scratchpad-v3 | positive | null | cascading_carry | ++ | train | 755446 | [
{
"a_digit": 7,
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{
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"serialized": "54101"
},
{
"a_digit":... | 557+644=<add><pos><state>755446<step>74011<step>54101<step>56121<ans>1021 |
div | 159 | 000.652 | -0.652 | 45 | -69 | 2x2 | / | 45/-69= | scratchpad-v3 | negative | round-half-up | rounded_below_one_down | +- | train | 045069 | [
{
"incoming_digit": 0,
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},
{
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"serialized": "00000"
},
{
"kind":... | 45/-69=<div><neg><state>045069<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00450045<qmul>00000<rem>045<step>04500450<qmul>60414<rem>036<step>03600360<qmul>50345<rem>015<step>01500150<qmul>20138<rem>012<step>01200120<qmul>10069<rem>051<ans>000.652 |
div | 161 | 001.800 | -1.8 | 727 | -404 | 3x3 | / | 727/-404= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | train | 727404 | [
{
"incoming_digit": 7,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 727/-404=<div><neg><state>727404<step>00070007<qmul>00000<rem>007<step>00720072<qmul>00000<rem>072<step>07270727<qmul>10404<rem>323<step>32303230<qmul>72828<rem>402<step>40204020<qmul>93636<rem>384<step>38403840<qmul>93636<rem>204<step>20402040<qmul>52020<rem>020<ans>001.800 |
add | 43 | 8051 | -1508 | -695 | 813 | 3x3 | - | -695-813= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 596318 | [
{
"a_digit": 5,
"b_digit": 3,
"carry_in": 0,
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},
{
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"serialized": "91001"
},
{
"a_digit":... | -695-813=<add><neg><state>596318<step>53080<step>91001<step>68151<ans>8051 |
add | 43 | 7680 | 867 | 543 | -324 | 3x3 | - | 543--324= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 345423 | [
{
"a_digit": 3,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
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},
{
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"carry_out": 0,
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"serialized": "42060"
},
{
"a_digit":... | 543--324=<add><pos><state>345423<step>34070<step>42060<step>53080<ans>7680 |
add | 42 | 5760 | 675 | 379 | 296 | 3x3 | + | 379+296= | scratchpad-v3 | positive | null | multi_carry | ++ | train | 973692 | [
{
"a_digit": 9,
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"carry_in": 0,
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},
{
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"serialized": "79171"
},
{
"a_digit":... | 379+296=<add><pos><state>973692<step>96051<step>79171<step>32160<ans>5760 |
mul | 118 | 407220 | -22704 | 44 | -516 | 2x3 | * | 44*-516= | scratchpad-v3 | negative | null | repeated_digit | +- | train | 440615 | [
{
"a_digit": 4,
"a_index": 0,
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},
{
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"kind": "column",
... | 44*-516=<mul><neg><state>440615<step>4624024<col>402<step>4104006<step>4624030<col>003<step>4520023<step>4104027<step>0600027<col>702<step>4520022<step>0100022<col>202<step>0500002<col>200<ans>407220 |
add | 43 | 6070 | -706 | -436 | 270 | 3x3 | - | -436-270= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 634072 | [
{
"a_digit": 6,
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"serialized": "60060"
},
{
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"carry_out": 1,
"column": 1,
"output_digit": 0,
"serialized": "37001"
},
{
"a_digit":... | -436-270=<add><neg><state>634072<step>60060<step>37001<step>42170<ans>6070 |
mul | 119 | 030030 | 30030 | -385 | -78 | 3x2 | * | -385*-78= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 583870 | [
{
"a_digit": 5,
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},
{
"carry_in": 0,
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"column": 0,
"column_sum": 40,
"kind": "column",
... | -385*-78=<mul><pos><state>583870<step>5840040<col>004<step>5735039<step>8864103<col>310<step>5000010<step>8756066<step>3824090<col>009<step>8000009<step>3721030<col>003<step>3000003<col>300<ans>030030 |
sub | 43 | 5840 | 485 | -18 | -503 | 2x3 | - | -18--503= | scratchpad-v3 | positive | null | borrow_through_zero | -- | train | 305810 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
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"serialized": "38051",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 8,
"serialized": "01181",
"subtrahend... | -18--503=<sub><pos><state>305810<step>38051<step>01181<step>50140<ans>5840 |
div | 161 | 000.068 | 0.068 | -25 | -370 | 2x3 | / | -25/-370= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | -- | train | 025370 | [
{
"incoming_digit": 0,
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"partial": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | -25/-370=<div><pos><state>025370<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02500250<qmul>00000<rem>250<step>25002500<qmul>62220<rem>280<step>28002800<qmul>72590<rem>210<step>21002100<qmul>51850<rem>250<ans>000.068 |
add | 41 | 4310 | -134 | -9 | 125 | 1x3 | - | -9-125= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 900521 | [
{
"a_digit": 9,
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"carry_in": 0,
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},
{
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"column": 1,
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"serialized": "02130"
},
{
"a_digit":... | -9-125=<add><neg><state>900521<step>95041<step>02130<step>01010<ans>4310 |
mul | 118 | 526270 | -72625 | 875 | -83 | 3x2 | * | 875*-83= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 578380 | [
{
"a_digit": 5,
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},
{
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"kind": "column",
... | 875*-83=<mul><neg><state>578380<step>5315015<col>501<step>5840041<step>7321062<col>206<step>5000006<step>7856062<step>8324086<col>608<step>7000008<step>8864072<col>207<step>8000007<col>700<ans>526270 |
mul | 119 | 695220 | 22596 | -269 | -84 | 3x2 | * | -269*-84= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 962480 | [
{
"a_digit": 9,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
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"kind": "column",
... | -269*-84=<mul><pos><state>962480<step>9436036<col>603<step>9872075<step>6424099<col>909<step>9000009<step>6848057<step>2408065<col>506<step>6000006<step>2816022<col>202<step>2000002<col>200<ans>695220 |
add | 42 | 9730 | 379 | 322 | -57 | 3x2 | - | 322--57= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 223750 | [
{
"a_digit": 2,
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},
{
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"column": 1,
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"serialized": "25070"
},
{
"a_digit":... | 322--57=<add><pos><state>223750<step>27090<step>25070<step>30030<ans>9730 |
sub | 40 | 5100 | 15 | 62 | 47 | 2x2 | - | 62-47= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 260740 | [
{
"borrow_in": 0,
"borrow_out": 1,
"column": 0,
"minuend_digit": 2,
"output_digit": 5,
"serialized": "27051",
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},
{
"borrow_in": 1,
"borrow_out": 0,
"column": 1,
"minuend_digit": 6,
"output_digit": 1,
"serialized": "64110",
"subtrahend... | 62-47=<sub><pos><state>260740<step>27051<step>64110<step>00000<ans>5100 |
sub | 41 | 1120 | -211 | 1 | -212 | 1x3 | + | 1+-212= | scratchpad-v3 | negative | null | magnitude_subtraction | +- | test | 212100 | [
{
"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": 1,
"output_digit": 1,
"serialized": "10010",
"subtrahend... | 1+-212=<sub><neg><state>212100<step>21010<step>10010<step>20020<ans>1120 |
div | 160 | 011.691 | -11.691 | 795 | -68 | 3x2 | / | 795/-68= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 795068 | [
{
"incoming_digit": 7,
"kind": "partial",
"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
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"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 795/-68=<div><neg><state>795068<step>00070007<qmul>00000<rem>007<step>00790079<qmul>10068<rem>011<step>01150115<qmul>10068<rem>047<step>04700470<qmul>60408<rem>062<step>06200620<qmul>90612<rem>008<step>00800080<qmul>10068<rem>012<step>01200120<qmul>10068<rem>052<ans>011.691 |
sub | 41 | 6170 | 716 | 802 | 86 | 3x2 | - | 802-86= | scratchpad-v3 | positive | null | borrow_through_zero | ++ | train | 208680 | [
{
"borrow_in": 0,
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"column": 0,
"minuend_digit": 2,
"output_digit": 6,
"serialized": "26061",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 0,
"output_digit": 1,
"serialized": "08111",
"subtrahend... | 802-86=<sub><pos><state>208680<step>26061<step>08111<step>80170<ans>6170 |
mul | 117 | 713000 | -317 | 1 | -317 | 1x3 | * | 1*-317= | scratchpad-v3 | negative | null | identity | +- | train | 100713 | [
{
"a_digit": 1,
"a_index": 0,
"b_digit": 7,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 7,
"kind": "column",
"o... | 1*-317=<mul><neg><state>100713<step>1707007<col>700<step>1101001<step>0700001<col>100<step>1303003<step>0100003<step>0700003<col>300<step>0300000<step>0100000<col>000<step>0300000<col>000<ans>713000 |
mul | 119 | 654687 | -786456 | 993 | -792 | 3x3 | * | 993*-792= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 399297 | [
{
"a_digit": 3,
"a_index": 0,
"b_digit": 2,
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"column": 0,
"kind": "term",
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"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 6,
"kind": "column",
"o... | 993*-792=<mul><neg><state>399297<step>3206006<col>600<step>3927027<step>9218045<col>504<step>3721025<step>9981106<step>9218124<col>412<step>9763075<step>9981156<col>615<step>9763078<col>807<ans>654687 |
div | 161 | 001.135 | -1.135 | 999 | -880 | 3x3 | / | 999/-880= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 999880 | [
{
"incoming_digit": 9,
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"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind"... | 999/-880=<div><neg><state>999880<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09990999<qmul>10880<rem>119<step>11901190<qmul>10880<rem>310<step>31003100<qmul>32640<rem>460<step>46004600<qmul>54400<rem>200<step>20002000<qmul>21760<rem>240<ans>001.135 |
sub | 42 | 2710 | 172 | 637 | 465 | 3x3 | - | 637-465= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 736564 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 7,
"output_digit": 2,
"serialized": "75020",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 7,
"serialized": "36071",
"subtrahend... | 637-465=<sub><pos><state>736564<step>75020<step>36071<step>64110<ans>2710 |
div | 159 | 000.592 | 0.592 | 71 | 120 | 2x3 | / | 71/120= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 071120 | [
{
"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"... | 71/120=<div><pos><state>071120<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00710071<qmul>00000<rem>071<step>07100710<qmul>50600<rem>110<step>11001100<qmul>91080<rem>020<step>02000200<qmul>10120<rem>080<step>08000800<qmul>60720<rem>080<ans>000.592 |
mul | 117 | 500500 | -5005 | -77 | 65 | 2x2 | * | -77*65= | scratchpad-v3 | negative | null | repeated_digit | -+ | val | 770560 | [
{
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"term_index": 0
},
{
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"kind": "column",
... | -77*65=<mul><neg><state>770560<step>7535035<col>503<step>7642045<step>7535080<col>008<step>7000008<step>7642050<step>0500050<col>005<step>7000005<step>0600005<col>500<step>0000000<col>000<ans>500500 |
sub | 42 | 5100 | 15 | -31 | -46 | 2x2 | - | -31--46= | scratchpad-v3 | positive | null | no_borrow | -- | train | 640130 | [
{
"borrow_in": 0,
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"minuend_digit": 6,
"output_digit": 5,
"serialized": "61050",
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},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 4,
"output_digit": 1,
"serialized": "43010",
"subtrahend... | -31--46=<sub><pos><state>640130<step>61050<step>43010<step>00000<ans>5100 |
add | 44 | 2270 | -722 | -224 | -498 | 3x3 | + | -224+-498= | scratchpad-v3 | negative | null | multi_carry | -- | train | 422894 | [
{
"a_digit": 4,
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},
{
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"serialized": "29121"
},
{
"a_digit":... | -224+-498=<add><neg><state>422894<step>48021<step>29121<step>24170<ans>2270 |
mul | 119 | 312629 | -926213 | 997 | -929 | 3x3 | * | 997*-929= | scratchpad-v3 | negative | null | high_column_sum | +- | train | 799929 | [
{
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},
{
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... | 997*-929=<mul><neg><state>799929<step>7963063<col>306<step>7214020<step>9981101<col>110<step>7963073<step>9218091<step>9981172<col>217<step>9981098<step>9218116<col>611<step>9981092<col>209<ans>312629 |
sub | 41 | 6700 | -76 | -79 | -3 | 2x1 | - | -79--3= | scratchpad-v3 | negative | null | negative_result | -- | train | 970300 | [
{
"borrow_in": 0,
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"serialized": "93060",
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},
{
"borrow_in": 0,
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"output_digit": 7,
"serialized": "70070",
"subtrahend... | -79--3=<sub><neg><state>970300<step>93060<step>70070<step>00000<ans>6700 |
div | 159 | 000.455 | -0.455 | 30 | -66 | 2x2 | / | 30/-66= | scratchpad-v3 | negative | round-half-up | rounded_below_one_up | +- | train | 030066 | [
{
"incoming_digit": 0,
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{
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{
"kind":... | 30/-66=<div><neg><state>030066<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>40264<rem>036<step>03600360<qmul>50330<rem>030<step>03000300<qmul>40264<rem>036<step>03600360<qmul>50330<rem>030<ans>000.455 |
mul | 118 | 911000 | 119 | -1 | -119 | 1x3 | * | -1*-119= | scratchpad-v3 | positive | null | identity | -- | train | 100911 | [
{
"a_digit": 1,
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},
{
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"o... | -1*-119=<mul><pos><state>100911<step>1909009<col>900<step>1101001<step>0900001<col>100<step>1101001<step>0100001<step>0900001<col>100<step>0100000<step>0100000<col>000<step>0100000<col>000<ans>911000 |
mul | 117 | 221830 | 38122 | 778 | 49 | 3x2 | * | 778*49= | scratchpad-v3 | positive | null | medium_column_sum | ++ | train | 877940 | [
{
"a_digit": 8,
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"term_index": 0
},
{
"carry_in": 0,
"carry_out": 7,
"column": 0,
"column_sum": 72,
"kind": "column",
... | 778*49=<mul><pos><state>877940<step>8972072<col>207<step>8432039<step>7963102<col>210<step>8000010<step>7428038<step>7963101<col>110<step>7000010<step>7428038<col>803<step>7000003<col>300<ans>221830 |
div | 160 | 064.000 | 64 | -576 | -9 | 3x1 | / | -576/-9= | scratchpad-v3 | positive | round-half-up | exact | -- | train | 576009 | [
{
"incoming_digit": 5,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind": ... | -576/-9=<div><pos><state>576009<step>00050005<qmul>00000<rem>005<step>00570057<qmul>60054<rem>003<step>00360036<qmul>40036<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>064.000 |
div | 161 | 001.216 | -1.216 | 755 | -621 | 3x3 | / | 755/-621= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_up | +- | test | 755621 | [
{
"incoming_digit": 7,
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"remainder_in": 0,
"serialized": "00070007"
},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | 755/-621=<div><neg><state>755621<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07550755<qmul>10621<rem>134<step>13401340<qmul>21242<rem>098<step>09800980<qmul>10621<rem>359<step>35903590<qmul>53105<rem>485<step>48504850<qmul>74347<rem>503<ans>001.216 |
mul | 118 | 235560 | -65532 | 762 | -86 | 3x2 | * | 762*-86= | scratchpad-v3 | negative | null | medium_column_sum | +- | train | 267680 | [
{
"a_digit": 2,
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"term_index": 0
},
{
"carry_in": 0,
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"kind": "column",
... | 762*-86=<mul><neg><state>267680<step>2612012<col>201<step>2816017<step>6636053<col>305<step>2000005<step>6848053<step>7642095<col>509<step>6000009<step>7856065<col>506<step>7000006<col>600<ans>235560 |
div | 160 | 000.663 | 0.663 | 629 | 949 | 3x3 | / | 629/949= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 629949 | [
{
"incoming_digit": 6,
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"position": 0,
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"serialized": "00060006"
},
{
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"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | 629/949=<div><pos><state>629949<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06290629<qmul>00000<rem>629<step>62906290<qmul>65694<rem>596<step>59605960<qmul>65694<rem>266<step>26602660<qmul>21898<rem>762<step>76207620<qmul>87592<rem>028<ans>000.663 |
div | 160 | 074.444 | 74.444 | -670 | -9 | 3x1 | / | -670/-9= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 670009 | [
{
"incoming_digit": 6,
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"remainder_in": 0,
"serialized": "00060006"
},
{
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"serialized": "00000"
},
{
"kind": ... | -670/-9=<div><pos><state>670009<step>00060006<qmul>00000<rem>006<step>00670067<qmul>70063<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<ans>074.444 |
add | 42 | 2590 | 952 | 132 | 820 | 3x3 | + | 132+820= | scratchpad-v3 | positive | null | no_carry | ++ | train | 231028 | [
{
"a_digit": 2,
"b_digit": 0,
"carry_in": 0,
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"serialized": "20020"
},
{
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"carry_in": 0,
"carry_out": 0,
"column": 1,
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"serialized": "32050"
},
{
"a_digit":... | 132+820=<add><pos><state>231028<step>20020<step>32050<step>18090<ans>2590 |
div | 162 | 006.257 | 6.257 | -707 | -113 | 3x3 | / | -707/-113= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 707113 | [
{
"incoming_digit": 7,
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"partial": 7,
"position": 0,
"remainder_in": 0,
"serialized": "00070007"
},
{
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"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -707/-113=<div><pos><state>707113<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07070707<qmul>60678<rem>029<step>02900290<qmul>20226<rem>064<step>06400640<qmul>50565<rem>075<step>07500750<qmul>60678<rem>072<step>07200720<qmul>60678<rem>042<ans>006.257 |
add | 43 | 2860 | 682 | 121 | -561 | 3x3 | - | 121--561= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 121165 | [
{
"a_digit": 1,
"b_digit": 1,
"carry_in": 0,
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"column": 0,
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"serialized": "11020"
},
{
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"serialized": "26080"
},
{
"a_digit":... | 121--561=<add><pos><state>121165<step>11020<step>26080<step>15060<ans>2860 |
div | 161 | 001.568 | -1.568 | 690 | -440 | 3x3 | / | 690/-440= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | +- | train | 690440 | [
{
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},
{
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"kind": "quotient_product",
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"serialized": "00000"
},
{
"kind"... | 690/-440=<div><neg><state>690440<step>00060006<qmul>00000<rem>006<step>00690069<qmul>00000<rem>069<step>06900690<qmul>10440<rem>250<step>25002500<qmul>52200<rem>300<step>30003000<qmul>62640<rem>360<step>36003600<qmul>83520<rem>080<step>08000800<qmul>10440<rem>360<ans>001.568 |
mul | 119 | 881850 | 58188 | -746 | -78 | 3x2 | * | -746*-78= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 647870 | [
{
"a_digit": 6,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 48,
"kind": "column",
... | -746*-78=<mul><pos><state>647870<step>6848048<col>804<step>6742046<step>4832078<col>807<step>6000007<step>4728035<step>7856091<col>109<step>4000009<step>7749058<col>805<step>7000005<col>500<ans>881850 |
mul | 120 | 460824 | 428064 | -624 | -686 | 3x3 | * | -624*-686= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 426686 | [
{
"a_digit": 4,
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"kind": "term",
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"serialized": "4624024",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 24,
"kind": "column",
... | -624*-686=<mul><pos><state>426686<step>4624024<col>402<step>4832034<step>2612046<col>604<step>4624028<step>2816044<step>6636080<col>008<step>2612020<step>6848068<col>806<step>6636042<col>204<ans>460824 |
mul | 118 | 832000 | 238 | -14 | -17 | 2x2 | * | -14*-17= | scratchpad-v3 | positive | null | low_column_sum | -- | train | 410710 | [
{
"a_digit": 4,
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"column": 0,
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"serialized": "4728028",
"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 28,
"kind": "column",
... | -14*-17=<mul><pos><state>410710<step>4728028<col>802<step>4104006<step>1707013<col>301<step>4000001<step>1101002<step>0700002<col>200<step>1000000<step>0100000<col>000<step>0000000<col>000<ans>832000 |
add | 42 | 7170 | 717 | 649 | -68 | 3x2 | - | 649--68= | scratchpad-v3 | positive | null | magnitude_addition | +- | train | 946860 | [
{
"a_digit": 9,
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"serialized": "98071"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "46111"
},
{
"a_digit":... | 649--68=<add><pos><state>946860<step>98071<step>46111<step>60170<ans>7170 |
sub | 42 | 7840 | 487 | 819 | 332 | 3x3 | - | 819-332= | scratchpad-v3 | positive | null | single_borrow | ++ | train | 918233 | [
{
"borrow_in": 0,
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"minuend_digit": 9,
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"serialized": "92070",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 1,
"output_digit": 8,
"serialized": "13081",
"subtrahend... | 819-332=<sub><pos><state>918233<step>92070<step>13081<step>83140<ans>7840 |
mul | 116 | 672100 | 1276 | 29 | 44 | 2x2 | * | 29*44= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 920440 | [
{
"a_digit": 9,
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"column": 0,
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"term_index": 0
},
{
"carry_in": 0,
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"column": 0,
"column_sum": 36,
"kind": "column",
... | 29*44=<mul><pos><state>920440<step>9436036<col>603<step>9436039<step>2408047<col>704<step>9000004<step>2408012<step>0400012<col>201<step>2000001<step>0400001<col>100<step>0000000<col>000<ans>672100 |
div | 162 | 001.512 | 1.512 | -700 | -463 | 3x3 | / | -700/-463= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 700463 | [
{
"incoming_digit": 7,
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"position": 0,
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},
{
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"kind": "quotient_product",
"position": 0,
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"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -700/-463=<div><pos><state>700463<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>10463<rem>237<step>23702370<qmul>52315<rem>055<step>05500550<qmul>10463<rem>087<step>08700870<qmul>10463<rem>407<step>40704070<qmul>83704<rem>366<ans>001.512 |
add | 43 | 1831 | -1381 | -880 | 501 | 3x3 | - | -880-501= | scratchpad-v3 | negative | null | magnitude_addition | -+ | train | 088105 | [
{
"a_digit": 0,
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},
{
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"column": 1,
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"serialized": "80080"
},
{
"a_digit":... | -880-501=<add><neg><state>088105<step>01010<step>80080<step>85031<ans>1831 |
sub | 44 | 2320 | 232 | -193 | -425 | 3x3 | - | -193--425= | scratchpad-v3 | positive | null | single_borrow | -- | train | 524391 | [
{
"borrow_in": 0,
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"output_digit": 2,
"serialized": "53020",
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},
{
"borrow_in": 0,
"borrow_out": 1,
"column": 1,
"minuend_digit": 2,
"output_digit": 3,
"serialized": "29031",
"subtrahend... | -193--425=<sub><pos><state>524391<step>53020<step>29031<step>41120<ans>2320 |
div | 158 | 000.000 | 0 | 0 | 351 | 1x3 | / | 0/351= | scratchpad-v3 | positive | round-half-up | zero_numerator | ++ | train | 000351 | [
{
"incoming_digit": 0,
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},
{
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"kind": "quotient_product",
"position": 0,
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"serialized": "00000"
},
{
"kind"... | 0/351=<div><pos><state>000351<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>000.000 |
add | 44 | 2360 | -632 | -339 | -293 | 3x3 | + | -339+-293= | scratchpad-v3 | negative | null | multi_carry | -- | train | 933392 | [
{
"a_digit": 9,
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"column": 0,
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"serialized": "93021"
},
{
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"carry_in": 1,
"carry_out": 1,
"column": 1,
"output_digit": 3,
"serialized": "39131"
},
{
"a_digit":... | -339+-293=<add><neg><state>933392<step>93021<step>39131<step>32160<ans>2360 |
div | 162 | 001.013 | 1.013 | -940 | -928 | 3x3 | / | -940/-928= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | -- | train | 940928 | [
{
"incoming_digit": 9,
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"position": 0,
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},
{
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"position": 0,
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"serialized": "00000"
},
{
"kind"... | -940/-928=<div><pos><state>940928<step>00090009<qmul>00000<rem>009<step>00940094<qmul>00000<rem>094<step>09400940<qmul>10928<rem>012<step>01200120<qmul>00000<rem>120<step>12001200<qmul>10928<rem>272<step>27202720<qmul>21856<rem>864<step>86408640<qmul>98352<rem>288<ans>001.013 |
sub | 44 | 6730 | 376 | -157 | -533 | 3x3 | - | -157--533= | scratchpad-v3 | positive | null | multi_borrow | -- | train | 335751 | [
{
"borrow_in": 0,
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"minuend_digit": 3,
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"serialized": "37061",
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},
{
"borrow_in": 1,
"borrow_out": 1,
"column": 1,
"minuend_digit": 3,
"output_digit": 7,
"serialized": "35171",
"subtrahend... | -157--533=<sub><pos><state>335751<step>37061<step>35171<step>51130<ans>6730 |
mul | 118 | 687312 | 213786 | 222 | 963 | 3x3 | * | 222*963= | scratchpad-v3 | positive | null | repeated_digit | ++ | train | 222369 | [
{
"a_digit": 2,
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"column": 0,
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"term_index": 0
},
{
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"kind": "column",
"o... | 222*963=<mul><pos><state>222369<step>2306006<col>600<step>2612012<step>2306018<col>801<step>2918019<step>2612031<step>2306037<col>703<step>2918021<step>2612033<col>303<step>2918021<col>102<ans>687312 |
div | 157 | 010.333 | 10.333 | 31 | 3 | 2x1 | / | 31/3= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | ++ | train | 031003 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 3,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind": ... | 31/3=<div><pos><state>031003<step>00000000<qmul>00000<rem>000<step>00030003<qmul>10003<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<ans>010.333 |
add | 41 | 2770 | -772 | -772 | 0 | 3x1 | - | -772-0= | scratchpad-v3 | negative | null | identity | -+ | train | 277000 | [
{
"a_digit": 2,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 2,
"serialized": "20020"
},
{
"a_digit": 7,
"b_digit": 0,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "70070"
},
{
"a_digit":... | -772-0=<add><neg><state>277000<step>20020<step>70070<step>70070<ans>2770 |
mul | 118 | 029730 | -37920 | 79 | -480 | 2x3 | * | 79*-480= | scratchpad-v3 | negative | null | contains_zero_digit | +- | train | 970084 | [
{
"a_digit": 9,
"a_index": 0,
"b_digit": 0,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 0,
"running_total": 0,
"serialized": "9000000",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 0,
"column": 0,
"column_sum": 0,
"kind": "column",
"o... | 79*-480=<mul><neg><state>970084<step>9000000<col>000<step>9872072<step>7000072<col>207<step>9436043<step>7856099<step>0000099<col>909<step>7428037<step>0800037<col>703<step>0400003<col>300<ans>029730 |
add | 43 | 4980 | -894 | -802 | -92 | 3x2 | + | -802+-92= | scratchpad-v3 | negative | null | no_carry | -- | train | 208290 | [
{
"a_digit": 2,
"b_digit": 2,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 4,
"serialized": "22040"
},
{
"a_digit": 0,
"b_digit": 9,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 9,
"serialized": "09090"
},
{
"a_digit":... | -802+-92=<add><neg><state>208290<step>22040<step>09090<step>80080<ans>4980 |
mul | 119 | 865470 | 74568 | -956 | -78 | 3x2 | * | -956*-78= | scratchpad-v3 | positive | null | medium_column_sum | -- | train | 659870 | [
{
"a_digit": 6,
"a_index": 0,
"b_digit": 8,
"b_index": 0,
"column": 0,
"kind": "term",
"product": 48,
"running_total": 48,
"serialized": "6848048",
"term_index": 0
},
{
"carry_in": 0,
"carry_out": 4,
"column": 0,
"column_sum": 48,
"kind": "column",
... | -956*-78=<mul><pos><state>659870<step>6848048<col>804<step>6742046<step>5840086<col>608<step>6000008<step>5735043<step>9872115<col>511<step>5000011<step>9763074<col>407<step>9000007<col>700<ans>865470 |
div | 159 | 008.729 | 8.729 | 611 | 70 | 3x2 | / | 611/70= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_up | ++ | val | 611070 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 70,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 611/70=<div><pos><state>611070<step>00060006<qmul>00000<rem>006<step>00610061<qmul>00000<rem>061<step>06110611<qmul>80560<rem>051<step>05100510<qmul>70490<rem>020<step>02000200<qmul>20140<rem>060<step>06000600<qmul>80560<rem>040<step>04000400<qmul>50350<rem>050<ans>008.729 |
div | 161 | 001.124 | -1.124 | -697 | 620 | 3x3 | / | -697/620= | scratchpad-v3 | negative | round-half-up | rounded_ge_one_down | -+ | train | 697620 | [
{
"incoming_digit": 6,
"kind": "partial",
"partial": 6,
"position": 0,
"remainder_in": 0,
"serialized": "00060006"
},
{
"divisor": 620,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -697/620=<div><neg><state>697620<step>00060006<qmul>00000<rem>006<step>00690069<qmul>00000<rem>069<step>06970697<qmul>10620<rem>077<step>07700770<qmul>10620<rem>150<step>15001500<qmul>21240<rem>260<step>26002600<qmul>42480<rem>120<step>12001200<qmul>10620<rem>580<ans>001.124 |
div | 158 | 000.815 | 0.815 | 22 | 27 | 2x2 | / | 22/27= | scratchpad-v3 | positive | round-half-up | rounded_below_one_up | ++ | train | 022027 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 27,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 22/27=<div><pos><state>022027<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02200220<qmul>80216<rem>004<step>00400040<qmul>10027<rem>013<step>01300130<qmul>40108<rem>022<step>02200220<qmul>80216<rem>004<ans>000.815 |
div | 158 | 000.774 | 0.774 | 24 | 31 | 2x2 | / | 24/31= | scratchpad-v3 | positive | round-half-up | rounded_below_one_down | ++ | train | 024031 | [
{
"incoming_digit": 0,
"kind": "partial",
"partial": 0,
"position": 0,
"remainder_in": 0,
"serialized": "00000000"
},
{
"divisor": 31,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind":... | 24/31=<div><pos><state>024031<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00240024<qmul>00000<rem>024<step>02400240<qmul>70217<rem>023<step>02300230<qmul>70217<rem>013<step>01300130<qmul>40124<rem>006<step>00600060<qmul>10031<rem>029<ans>000.774 |
div | 162 | 002.464 | 2.464 | -902 | -366 | 3x3 | / | -902/-366= | scratchpad-v3 | positive | round-half-up | rounded_ge_one_down | -- | train | 902366 | [
{
"incoming_digit": 9,
"kind": "partial",
"partial": 9,
"position": 0,
"remainder_in": 0,
"serialized": "00090009"
},
{
"divisor": 366,
"kind": "quotient_product",
"position": 0,
"quotient_digit": 0,
"quotient_product": 0,
"serialized": "00000"
},
{
"kind"... | -902/-366=<div><pos><state>902366<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09020902<qmul>20732<rem>170<step>17001700<qmul>41464<rem>236<step>23602360<qmul>62196<rem>164<step>16401640<qmul>41464<rem>176<step>17601760<qmul>41464<rem>296<ans>002.464 |
add | 44 | 7121 | -1217 | -390 | -827 | 3x3 | + | -390+-827= | scratchpad-v3 | negative | null | overflow | -- | train | 093728 | [
{
"a_digit": 0,
"b_digit": 7,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "07070"
},
{
"a_digit": 9,
"b_digit": 2,
"carry_in": 0,
"carry_out": 1,
"column": 1,
"output_digit": 1,
"serialized": "92011"
},
{
"a_digit":... | -390+-827=<add><neg><state>093728<step>07070<step>92011<step>38121<ans>7121 |
sub | 40 | 4300 | 34 | 36 | -2 | 2x1 | + | 36+-2= | scratchpad-v3 | positive | null | magnitude_subtraction | +- | train | 630200 | [
{
"borrow_in": 0,
"borrow_out": 0,
"column": 0,
"minuend_digit": 6,
"output_digit": 4,
"serialized": "62040",
"subtrahend_digit": 2
},
{
"borrow_in": 0,
"borrow_out": 0,
"column": 1,
"minuend_digit": 3,
"output_digit": 3,
"serialized": "30030",
"subtrahend... | 36+-2=<sub><pos><state>630200<step>62040<step>30030<step>00000<ans>4300 |
add | 43 | 7720 | -277 | -263 | -14 | 3x2 | + | -263+-14= | scratchpad-v3 | negative | null | no_carry | -- | train | 362410 | [
{
"a_digit": 3,
"b_digit": 4,
"carry_in": 0,
"carry_out": 0,
"column": 0,
"output_digit": 7,
"serialized": "34070"
},
{
"a_digit": 6,
"b_digit": 1,
"carry_in": 0,
"carry_out": 0,
"column": 1,
"output_digit": 7,
"serialized": "61070"
},
{
"a_digit":... | -263+-14=<add><neg><state>362410<step>34070<step>61070<step>20020<ans>7720 |
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