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
div
161
000.573
-0.573
430
-750
3x3
/
430/-750=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
430750
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 750, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
430/-750=<div><neg><state>430750<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04300430<qmul>00000<rem>430<step>43004300<qmul>53750<rem>550<step>55005500<qmul>75250<rem>250<step>25002500<qmul>32250<rem>250<step>25002500<qmul>32250<rem>250<ans>000.573
div
159
000.261
-0.261
18
-69
2x2
/
18/-69=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
+-
train
018069
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 69, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
18/-69=<div><neg><state>018069<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00180018<qmul>00000<rem>018<step>01800180<qmul>20138<rem>042<step>04200420<qmul>60414<rem>006<step>00600060<qmul>00000<rem>060<step>06000600<qmul>80552<rem>048<ans>000.261
mul
120
386450
54683
-367
-149
3x3
*
-367*-149=
scratchpad-v3
positive
null
medium_column_sum
--
train
763941
[ { "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", ...
-367*-149=<mul><pos><state>763941<step>7963063<col>306<step>7428034<step>6954088<col>808<step>7107015<step>6424039<step>3927066<col>606<step>6106012<step>3412024<col>402<step>3103005<col>500<ans>386450
sub
42
7010
-107
817
924
3x3
-
817-924=
scratchpad-v3
negative
null
negative_result
++
train
429718
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 7, "serialized": "47071", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 0, "serialized": "21100", "subtrahend...
817-924=<sub><neg><state>429718<step>47071<step>21100<step>98010<ans>7010
mul
118
280797
797082
929
858
3x3
*
929*858=
scratchpad-v3
positive
null
high_column_sum
++
train
929858
[ { "a_digit": 9, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 72, "running_total": 72, "serialized": "9872072", "term_index": 0 }, { "carry_in": 0, "carry_out": 7, "column": 0, "column_sum": 72, "kind": "column", ...
929*858=<mul><pos><state>929858<step>9872072<col>207<step>9545052<step>2816068<col>806<step>9872078<step>2510088<step>9872160<col>016<step>2816032<step>9545077<col>707<step>9872079<col>907<ans>280797
sub
44
1100
11
-118
-129
3x3
-
-118--129=
scratchpad-v3
positive
null
no_borrow
--
train
921811
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 1, "serialized": "98010", "subtrahend_digit": 8 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 1, "serialized": "21010", "subtrahend...
-118--129=<sub><pos><state>921811<step>98010<step>21010<step>11000<ans>1100
mul
120
626787
787626
-798
-987
3x3
*
-798*-987=
scratchpad-v3
positive
null
high_column_sum
--
train
897789
[ { "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", ...
-798*-987=<mul><pos><state>897789<step>8756056<col>605<step>8864069<step>9763132<col>213<step>8972085<step>9872157<step>7749206<col>620<step>9981101<step>7856157<col>715<step>7963078<col>807<ans>626787
div
161
000.369
-0.369
257
-697
3x3
/
257/-697=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
+-
test
257697
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 697, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
257/-697=<div><neg><state>257697<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02570257<qmul>00000<rem>257<step>25702570<qmul>32091<rem>479<step>47904790<qmul>64182<rem>608<step>60806080<qmul>85576<rem>504<step>50405040<qmul>74879<rem>161<ans>000.369
sub
42
7220
-227
402
629
3x3
-
402-629=
scratchpad-v3
negative
null
negative_result
++
train
926204
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 7, "serialized": "92070", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 2, "serialized": "20020", "subtrahend...
402-629=<sub><neg><state>926204<step>92070<step>20020<step>64020<ans>7220
add
44
4290
-924
-596
-328
3x3
+
-596+-328=
scratchpad-v3
negative
null
multi_carry
--
train
695823
[ { "a_digit": 6, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 4, "serialized": "68041" }, { "a_digit": 9, "b_digit": 2, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "92121" }, { "a_digit":...
-596+-328=<add><neg><state>695823<step>68041<step>92121<step>53190<ans>4290
mul
118
932584
485239
769
631
3x3
*
769*631=
scratchpad-v3
positive
null
medium_column_sum
++
train
967136
[ { "a_digit": 9, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 9, "running_total": 9, "serialized": "9109009", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 9, "kind": "column", "o...
769*631=<mul><pos><state>967136<step>9109009<col>900<step>9327027<step>6106033<col>303<step>9654057<step>6318075<step>7107082<col>208<step>6636044<step>7321065<col>506<step>7642048<col>804<ans>932584
sub
43
5110
115
-88
-203
2x3
-
-88--203=
scratchpad-v3
positive
null
borrow_through_zero
--
train
302880
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 5, "serialized": "38051", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
-88--203=<sub><pos><state>302880<step>38051<step>08111<step>20110<ans>5110
div
160
005.000
5
770
154
3x3
/
770/154=
scratchpad-v3
positive
round-half-up
exact
++
train
770154
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 154, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
770/154=<div><pos><state>770154<step>00070007<qmul>00000<rem>007<step>00770077<qmul>00000<rem>077<step>07700770<qmul>50770<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>005.000
sub
44
5710
-175
-601
-426
3x3
-
-601--426=
scratchpad-v3
negative
null
negative_result
--
train
106624
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 5, "serialized": "16051", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 7, "serialized": "02171", "subtrahend...
-601--426=<sub><neg><state>106624<step>16051<step>02171<step>64110<ans>5710
add
43
2560
652
253
-399
3x3
-
253--399=
scratchpad-v3
positive
null
magnitude_addition
+-
train
352993
[ { "a_digit": 3, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "39021" }, { "a_digit": 5, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 5, "serialized": "59151" }, { "a_digit":...
253--399=<add><pos><state>352993<step>39021<step>59151<step>23160<ans>2560
mul
119
092087
-780290
-994
785
3x3
*
-994*785=
scratchpad-v3
negative
null
high_column_sum
-+
train
499587
[ { "a_digit": 4, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 20, "running_total": 20, "serialized": "4520020", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 20, "kind": "column", ...
-994*785=<mul><neg><state>499587<step>4520020<col>002<step>4832034<step>9545079<col>907<step>4728035<step>9872107<step>9545152<col>215<step>9763078<step>9872150<col>015<step>9763078<col>807<ans>092087
div
161
017.036
17.036
-477
-28
3x2
/
-477/-28=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
477028
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 28, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-477/-28=<div><pos><state>477028<step>00040004<qmul>00000<rem>004<step>00470047<qmul>10028<rem>019<step>01970197<qmul>70196<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>30084<rem>016<step>01600160<qmul>50140<rem>020<step>02000200<qmul>70196<rem>004<ans>017.036
div
158
000.216
0.216
19
88
2x2
/
19/88=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
019088
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 88, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
19/88=<div><pos><state>019088<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00190019<qmul>00000<rem>019<step>01900190<qmul>20176<rem>014<step>01400140<qmul>10088<rem>052<step>05200520<qmul>50440<rem>080<step>08000800<qmul>90792<rem>008<ans>000.216
sub
42
5350
535
958
423
3x3
-
958-423=
scratchpad-v3
positive
null
no_borrow
++
train
859324
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 8, "output_digit": 5, "serialized": "83050", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 5, "output_digit": 3, "serialized": "52030", "subtrahend...
958-423=<sub><pos><state>859324<step>83050<step>52030<step>94050<ans>5350
mul
118
422400
-4224
192
-22
3x2
*
192*-22=
scratchpad-v3
negative
null
repeated_digit
+-
train
291220
[ { "a_digit": 2, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 4, "running_total": 4, "serialized": "2204004", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 4, "kind": "column", "o...
192*-22=<mul><neg><state>291220<step>2204004<col>400<step>2204004<step>9218022<col>202<step>2000002<step>9218020<step>1202022<col>202<step>9000002<step>1202004<col>400<step>1000000<col>000<ans>422400
div
161
018.000
18
-810
-45
3x2
/
-810/-45=
scratchpad-v3
positive
round-half-up
exact
--
train
810045
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 45, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-810/-45=<div><pos><state>810045<step>00080008<qmul>00000<rem>008<step>00810081<qmul>10045<rem>036<step>03600360<qmul>80360<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>018.000
mul
119
174537
-735471
-759
969
3x3
*
-759*969=
scratchpad-v3
negative
null
high_column_sum
-+
train
957969
[ { "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", ...
-759*969=<mul><neg><state>957969<step>9981081<col>108<step>9654062<step>5945107<col>710<step>9981091<step>5630121<step>7963184<col>418<step>5945063<step>7642105<col>510<step>7963073<col>307<ans>174537
mul
119
831114
-411138
546
-753
3x3
*
546*-753=
scratchpad-v3
negative
null
medium_column_sum
+-
train
645357
[ { "a_digit": 6, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "6318018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
546*-753=<mul><neg><state>645357<step>6318018<col>801<step>6530031<step>4312043<col>304<step>6742046<step>4520066<step>5315081<col>108<step>4728036<step>5525061<col>106<step>5735041<col>104<ans>831114
sub
43
3520
253
727
-474
3x3
+
727+-474=
scratchpad-v3
positive
null
magnitude_subtraction
+-
train
727474
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 7, "output_digit": 3, "serialized": "74030", "subtrahend_digit": 4 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 5, "serialized": "27051", "subtrahend...
727+-474=<sub><pos><state>727474<step>74030<step>27051<step>74120<ans>3520
mul
119
094600
6490
-22
-295
2x3
*
-22*-295=
scratchpad-v3
positive
null
repeated_digit
--
train
220592
[ { "a_digit": 2, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 10, "running_total": 10, "serialized": "2510010", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 10, "kind": "column", ...
-22*-295=<mul><pos><state>220592<step>2510010<col>001<step>2918019<step>2510029<col>902<step>2204006<step>2918024<step>0500024<col>402<step>2204006<step>0900006<col>600<step>0200000<col>000<ans>094600
add
41
3850
-583
-583
0
3x1
+
-583+0=
scratchpad-v3
negative
null
identity
-+
train
385000
[ { "a_digit": 3, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "30030" }, { "a_digit": 8, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "80080" }, { "a_digit":...
-583+0=<add><neg><state>385000<step>30030<step>80080<step>50050<ans>3850
mul
120
678558
855876
-966
-886
3x3
*
-966*-886=
scratchpad-v3
positive
null
high_column_sum
--
train
669688
[ { "a_digit": 6, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "6636036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
-966*-886=<mul><pos><state>669688<step>6636036<col>603<step>6848051<step>6636087<col>708<step>6848056<step>6848104<step>9654158<col>815<step>6848063<step>9872135<col>513<step>9872085<col>508<ans>678558
mul
120
499048
840994
-946
-889
3x3
*
-946*-889=
scratchpad-v3
positive
null
high_column_sum
--
train
649988
[ { "a_digit": 6, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 54, "running_total": 54, "serialized": "6954054", "term_index": 0 }, { "carry_in": 0, "carry_out": 5, "column": 0, "column_sum": 54, "kind": "column", ...
-946*-889=<mul><pos><state>649988<step>6954054<col>405<step>6848053<step>4936089<col>908<step>6848056<step>4832088<step>9981169<col>916<step>4832048<step>9872120<col>012<step>9872084<col>408<ans>499048
sub
41
9520
259
305
46
3x2
-
305-46=
scratchpad-v3
positive
null
borrow_through_zero
++
train
503640
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 5, "output_digit": 9, "serialized": "56091", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 5, "serialized": "04151", "subtrahend...
305-46=<sub><pos><state>503640<step>56091<step>04151<step>30120<ans>9520
div
160
015.370
-15.37
707
-46
3x2
/
707/-46=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
707046
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 46, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
707/-46=<div><neg><state>707046<step>00070007<qmul>00000<rem>007<step>00700070<qmul>10046<rem>024<step>02470247<qmul>50230<rem>017<step>01700170<qmul>30138<rem>032<step>03200320<qmul>60276<rem>044<step>04400440<qmul>90414<rem>026<step>02600260<qmul>50230<rem>030<ans>015.370
mul
120
441266
662144
-739
-896
3x3
*
-739*-896=
scratchpad-v3
positive
null
high_column_sum
--
train
937698
[ { "a_digit": 9, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 54, "running_total": 54, "serialized": "9654054", "term_index": 0 }, { "carry_in": 0, "carry_out": 5, "column": 0, "column_sum": 54, "kind": "column", ...
-739*-896=<mul><pos><state>937698<step>9654054<col>405<step>9981086<step>3618104<col>410<step>9872082<step>3927109<step>7642151<col>115<step>3824039<step>7963102<col>210<step>7856066<col>606<ans>441266
div
160
003.600
-3.6
-342
95
3x2
/
-342/95=
scratchpad-v3
negative
round-half-up
exact
-+
train
342095
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 95, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-342/95=<div><neg><state>342095<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03420342<qmul>30285<rem>057<step>05700570<qmul>60570<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>003.600
mul
118
019710
-17910
-398
45
3x2
*
-398*45=
scratchpad-v3
negative
null
medium_column_sum
-+
train
893540
[ { "a_digit": 8, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 40, "running_total": 40, "serialized": "8540040", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 40, "kind": "column", ...
-398*45=<mul><neg><state>893540<step>8540040<col>004<step>8432036<step>9545081<col>108<step>8000008<step>9436044<step>3515059<col>905<step>9000005<step>3412017<col>701<step>3000001<col>100<ans>019710
mul
119
369350
53963
-593
-91
3x2
*
-593*-91=
scratchpad-v3
positive
null
medium_column_sum
--
train
395190
[ { "a_digit": 3, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 3, "running_total": 3, "serialized": "3103003", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 3, "kind": "column", "o...
-593*-91=<mul><pos><state>395190<step>3103003<col>300<step>3927027<step>9109036<col>603<step>3000003<step>9981084<step>5105089<col>908<step>9000008<step>5945053<col>305<step>5000005<col>500<ans>369350
mul
120
077358
853770
-894
-955
3x3
*
-894*-955=
scratchpad-v3
positive
null
medium_column_sum
--
train
498559
[ { "a_digit": 4, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 20, "running_total": 20, "serialized": "4520020", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 20, "kind": "column", ...
-894*-955=<mul><pos><state>498559<step>4520020<col>002<step>4520022<step>9545067<col>706<step>4936042<step>9545087<step>8540127<col>712<step>9981093<step>8540133<col>313<step>8972085<col>508<ans>077358
div
160
006.000
-6
252
-42
3x2
/
252/-42=
scratchpad-v3
negative
round-half-up
exact
+-
train
252042
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 42, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
252/-42=<div><neg><state>252042<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02520252<qmul>60252<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>006.000
add
44
1301
-1031
-786
-245
3x3
+
-786+-245=
scratchpad-v3
negative
null
cascading_carry
--
test
687542
[ { "a_digit": 6, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "65011" }, { "a_digit": 8, "b_digit": 4, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "84131" }, { "a_digit":...
-786+-245=<add><neg><state>687542<step>65011<step>84131<step>72101<ans>1301
add
44
1231
-1321
-414
-907
3x3
+
-414+-907=
scratchpad-v3
negative
null
overflow
--
train
414709
[ { "a_digit": 4, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "47011" }, { "a_digit": 1, "b_digit": 0, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "10120" }, { "a_digit":...
-414+-907=<add><neg><state>414709<step>47011<step>10120<step>49031<ans>1231
div
159
007.679
7.679
645
84
3x2
/
645/84=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
train
645084
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 84, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
645/84=<div><pos><state>645084<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06450645<qmul>70588<rem>057<step>05700570<qmul>60504<rem>066<step>06600660<qmul>70588<rem>072<step>07200720<qmul>80672<rem>048<step>04800480<qmul>50420<rem>060<ans>007.679
div
161
001.031
-1.031
901
-874
3x3
/
901/-874=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
901874
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 874, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
901/-874=<div><neg><state>901874<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09010901<qmul>10874<rem>027<step>02700270<qmul>00000<rem>270<step>27002700<qmul>32622<rem>078<step>07800780<qmul>00000<rem>780<step>78007800<qmul>86992<rem>808<ans>001.031
add
42
2190
912
585
327
3x3
+
585+327=
scratchpad-v3
positive
null
multi_carry
++
train
585723
[ { "a_digit": 5, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "57021" }, { "a_digit": 8, "b_digit": 2, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "82111" }, { "a_digit":...
585+327=<add><pos><state>585723<step>57021<step>82111<step>53190<ans>2190
add
42
7790
977
535
442
3x3
+
535+442=
scratchpad-v3
positive
null
no_carry
++
train
535244
[ { "a_digit": 5, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "52070" }, { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "34070" }, { "a_digit":...
535+442=<add><pos><state>535244<step>52070<step>34070<step>54090<ans>7790
div
159
008.929
8.929
875
98
3x2
/
875/98=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
train
875098
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 98, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
875/98=<div><pos><state>875098<step>00080008<qmul>00000<rem>008<step>00870087<qmul>00000<rem>087<step>08750875<qmul>80784<rem>091<step>09100910<qmul>90882<rem>028<step>02800280<qmul>20196<rem>084<step>08400840<qmul>80784<rem>056<step>05600560<qmul>50490<rem>070<ans>008.929
sub
44
5300
-35
-892
-857
3x3
-
-892--857=
scratchpad-v3
negative
null
negative_result
--
train
298758
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 5, "serialized": "27051", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 3, "serialized": "95130", "subtrahend...
-892--857=<sub><neg><state>298758<step>27051<step>95130<step>88000<ans>5300
mul
118
070501
105070
395
266
3x3
*
395*266=
scratchpad-v3
positive
null
medium_column_sum
++
train
593662
[ { "a_digit": 5, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 30, "running_total": 30, "serialized": "5630030", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 30, "kind": "column", ...
395*266=<mul><pos><state>593662<step>5630030<col>003<step>5630033<step>9654087<col>708<step>5210018<step>9654072<step>3618090<col>009<step>9218027<step>3618045<col>504<step>3206010<col>001<ans>070501
mul
119
229809
-908922
-969
938
3x3
*
-969*938=
scratchpad-v3
negative
null
high_column_sum
-+
train
969839
[ { "a_digit": 9, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 72, "running_total": 72, "serialized": "9872072", "term_index": 0 }, { "carry_in": 0, "carry_out": 7, "column": 0, "column_sum": 72, "kind": "column", ...
-969*938=<mul><neg><state>969839<step>9872072<col>207<step>9327034<step>6848082<col>208<step>9981089<step>6318107<step>9872179<col>917<step>6954071<step>9327098<col>809<step>9981090<col>009<ans>229809
sub
44
4630
364
-247
-611
3x3
-
-247--611=
scratchpad-v3
positive
null
multi_borrow
--
train
116742
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 4, "serialized": "17041", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 6, "serialized": "14161", "subtrahend...
-247--611=<sub><pos><state>116742<step>17041<step>14161<step>62130<ans>4630
sub
43
2300
-32
-668
636
3x3
+
-668+636=
scratchpad-v3
negative
null
magnitude_subtraction
-+
train
866636
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 8, "output_digit": 2, "serialized": "86020", "subtrahend_digit": 6 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 6, "output_digit": 3, "serialized": "63030", "subtrahend...
-668+636=<sub><neg><state>866636<step>86020<step>63030<step>66000<ans>2300
add
41
0310
130
4
-126
1x3
-
4--126=
scratchpad-v3
positive
null
magnitude_addition
+-
train
400621
[ { "a_digit": 4, "b_digit": 6, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "46001" }, { "a_digit": 0, "b_digit": 2, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "02130" }, { "a_digit":...
4--126=<add><pos><state>400621<step>46001<step>02130<step>01010<ans>0310
sub
42
5430
345
942
597
3x3
-
942-597=
scratchpad-v3
positive
null
multi_borrow
++
train
249795
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 5, "serialized": "27051", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 4, "serialized": "49141", "subtrahend...
942-597=<sub><pos><state>249795<step>27051<step>49141<step>95130<ans>5430
sub
44
0550
550
-253
-803
3x3
-
-253--803=
scratchpad-v3
positive
null
single_borrow
--
train
308352
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 3, "output_digit": 0, "serialized": "33000", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 5, "serialized": "05051", "subtrahend...
-253--803=<sub><pos><state>308352<step>33000<step>05051<step>82150<ans>0550
mul
119
912429
-924219
927
-997
3x3
*
927*-997=
scratchpad-v3
negative
null
high_column_sum
+-
train
729799
[ { "a_digit": 7, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 49, "running_total": 49, "serialized": "7749049", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 49, "kind": "column", ...
927*-997=<mul><neg><state>729799<step>7749049<col>904<step>7963067<step>2714081<col>108<step>7963071<step>2918089<step>9763152<col>215<step>2918033<step>9981114<col>411<step>9981092<col>209<ans>912429
mul
120
225328
823522
-997
-826
3x3
*
-997*-826=
scratchpad-v3
positive
null
medium_column_sum
--
train
799628
[ { "a_digit": 7, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 42, "running_total": 42, "serialized": "7642042", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 42, "kind": "column", ...
-997*-826=<mul><pos><state>799628<step>7642042<col>204<step>7214018<step>9654072<col>207<step>7856063<step>9218081<step>9654135<col>513<step>9872085<step>9218103<col>310<step>9872082<col>208<ans>225328
mul
119
420801
-108024
168
-643
3x3
*
168*-643=
scratchpad-v3
negative
null
medium_column_sum
+-
test
861346
[ { "a_digit": 8, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 24, "running_total": 24, "serialized": "8324024", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 24, "kind": "column", ...
168*-643=<mul><neg><state>861346<step>8324024<col>402<step>8432034<step>6318052<col>205<step>8648053<step>6424077<step>1303080<col>008<step>6636044<step>1404048<col>804<step>1606010<col>001<ans>420801
div
160
061.333
61.333
-368
-6
3x1
/
-368/-6=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
368006
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-368/-6=<div><pos><state>368006<step>00030003<qmul>00000<rem>003<step>00360036<qmul>60036<rem>000<step>00080008<qmul>10006<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>061.333
mul
118
219637
736912
848
869
3x3
*
848*869=
scratchpad-v3
positive
null
high_column_sum
++
train
848968
[ { "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", ...
848*869=<mul><pos><state>848968<step>8972072<col>207<step>8648055<step>4936091<col>109<step>8864073<step>4624097<step>8972169<col>916<step>4832048<step>8648096<col>609<step>8864073<col>307<ans>219637
sub
42
3000
-3
-76
-73
2x2
-
-76--73=
scratchpad-v3
negative
null
negative_result
--
train
670370
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 6, "output_digit": 3, "serialized": "63030", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 0, "serialized": "77000", "subtrahend...
-76--73=<sub><neg><state>670370<step>63030<step>77000<step>00000<ans>3000
sub
44
2200
22
-135
-157
3x3
-
-135--157=
scratchpad-v3
positive
null
no_borrow
--
val
751531
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 7, "output_digit": 2, "serialized": "75020", "subtrahend_digit": 5 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 5, "output_digit": 2, "serialized": "53020", "subtrahend...
-135--157=<sub><pos><state>751531<step>75020<step>53020<step>11000<ans>2200
mul
119
097533
-335790
585
-574
3x3
*
585*-574=
scratchpad-v3
negative
null
medium_column_sum
+-
train
585475
[ { "a_digit": 5, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 20, "running_total": 20, "serialized": "5420020", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 20, "kind": "column", ...
585*-574=<mul><neg><state>585475<step>5420020<col>002<step>5735037<step>8432069<col>906<step>5525031<step>8756087<step>5420107<col>710<step>8540050<step>5735085<col>508<step>5525033<col>303<ans>097533
div
162
000.384
0.384
-274
-714
3x3
/
-274/-714=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
274714
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 714, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-274/-714=<div><pos><state>274714<step>00020002<qmul>00000<rem>002<step>00270027<qmul>00000<rem>027<step>02740274<qmul>00000<rem>274<step>27402740<qmul>32142<rem>598<step>59805980<qmul>85712<rem>268<step>26802680<qmul>32142<rem>538<step>53805380<qmul>74998<rem>382<ans>000.384
mul
118
046530
-35640
440
-81
3x2
*
440*-81=
scratchpad-v3
negative
null
contains_zero_digit
+-
test
044180
[ { "a_digit": 0, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0100000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
440*-81=<mul><neg><state>044180<step>0100000<col>000<step>0800000<step>4104004<col>400<step>0000000<step>4832032<step>4104036<col>603<step>4000003<step>4832035<col>503<step>4000003<col>300<ans>046530
sub
40
7200
27
41
14
2x2
-
41-14=
scratchpad-v3
positive
null
single_borrow
++
val
140410
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 7, "serialized": "14071", "subtrahend_digit": 4 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 4, "output_digit": 2, "serialized": "41120", "subtrahend...
41-14=<sub><pos><state>140410<step>14071<step>41120<step>00000<ans>7200
sub
44
6510
-156
-362
-206
3x3
-
-362--206=
scratchpad-v3
negative
null
negative_result
--
train
263602
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 6, "serialized": "26061", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 6, "output_digit": 5, "serialized": "60150", "subtrahend...
-362--206=<sub><neg><state>263602<step>26061<step>60150<step>32010<ans>6510
div
19
<nan>
NAN
-41
0
2x1
/
-41/0=
scratchpad-v3
positive
round-half-up
nan
-+
train
041000
[]
-41/0=<div><pos><state>041000<ans><nan>
sub
40
2200
-22
19
41
2x2
-
19-41=
scratchpad-v3
negative
null
negative_result
++
train
140910
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 2, "serialized": "19021", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 4, "output_digit": 2, "serialized": "41120", "subtrahend...
19-41=<sub><neg><state>140910<step>19021<step>41120<step>00000<ans>2200
add
44
0250
-520
-210
-310
3x3
+
-210+-310=
scratchpad-v3
negative
null
no_carry
--
train
012013
[ { "a_digit": 0, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 0, "serialized": "00000" }, { "a_digit": 1, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "11020" }, { "a_digit":...
-210+-310=<add><neg><state>012013<step>00000<step>11020<step>23050<ans>0250
div
159
000.949
-0.949
-75
79
2x2
/
-75/79=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
075079
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 79, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-75/79=<div><neg><state>075079<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07500750<qmul>90711<rem>039<step>03900390<qmul>40316<rem>074<step>07400740<qmul>90711<rem>029<step>02900290<qmul>30237<rem>053<ans>000.949
add
44
3021
-1203
-844
-359
3x3
+
-844+-359=
scratchpad-v3
negative
null
cascading_carry
--
train
448953
[ { "a_digit": 4, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "49031" }, { "a_digit": 4, "b_digit": 5, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "45101" }, { "a_digit":...
-844+-359=<add><neg><state>448953<step>49031<step>45101<step>83121<ans>3021
mul
119
359695
-596953
749
-797
3x3
*
749*-797=
scratchpad-v3
negative
null
high_column_sum
+-
train
947797
[ { "a_digit": 9, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 63, "running_total": 63, "serialized": "9763063", "term_index": 0 }, { "carry_in": 0, "carry_out": 6, "column": 0, "column_sum": 63, "kind": "column", ...
749*-797=<mul><neg><state>947797<step>9763063<col>306<step>9981087<step>4728115<col>511<step>9763074<step>4936110<step>7749159<col>915<step>4728043<step>7963106<col>610<step>7749059<col>905<ans>359695
div
159
001.500
1.5
129
86
3x2
/
129/86=
scratchpad-v3
positive
round-half-up
exact
++
train
129086
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 86, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
129/86=<div><pos><state>129086<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01290129<qmul>10086<rem>043<step>04300430<qmul>50430<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.500
div
162
004.059
4.059
-759
-187
3x3
/
-759/-187=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
759187
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 187, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-759/-187=<div><pos><state>759187<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07590759<qmul>40748<rem>011<step>01100110<qmul>00000<rem>110<step>11001100<qmul>50935<rem>165<step>16501650<qmul>81496<rem>154<step>15401540<qmul>81496<rem>044<ans>004.059
mul
119
365266
-662563
-737
899
3x3
*
-737*899=
scratchpad-v3
negative
null
high_column_sum
-+
train
737998
[ { "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", ...
-737*899=<mul><neg><state>737998<step>7963063<col>306<step>7963069<step>3927096<col>609<step>7856065<step>3927092<step>7963155<col>515<step>3824039<step>7963102<col>210<step>7856066<col>606<ans>365266
div
159
000.098
0.098
84
861
2x3
/
84/861=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
test
084861
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 861, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
84/861=<div><pos><state>084861<step>00000000<qmul>00000<rem>000<step>00080008<qmul>00000<rem>008<step>00840084<qmul>00000<rem>084<step>08400840<qmul>00000<rem>840<step>84008400<qmul>97749<rem>651<step>65106510<qmul>76027<rem>483<step>48304830<qmul>54305<rem>525<ans>000.098
div
161
001.004
-1.004
-700
697
3x3
/
-700/697=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
700697
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 697, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-700/697=<div><neg><state>700697<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>10697<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>00000<rem>300<step>30003000<qmul>42788<rem>212<step>21202120<qmul>32091<rem>029<ans>001.004
mul
119
335337
-733533
-969
757
3x3
*
-969*757=
scratchpad-v3
negative
null
high_column_sum
-+
train
969757
[ { "a_digit": 9, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 63, "running_total": 63, "serialized": "9763063", "term_index": 0 }, { "carry_in": 0, "carry_out": 6, "column": 0, "column_sum": 63, "kind": "column", ...
-969*757=<mul><neg><state>969757<step>9763063<col>306<step>9545051<step>6742093<col>309<step>9763072<step>6530102<step>9763165<col>516<step>6742058<step>9545103<col>310<step>9763073<col>307<ans>335337
add
41
9310
139
55
-84
2x2
-
55--84=
scratchpad-v3
positive
null
magnitude_addition
+-
train
550480
[ { "a_digit": 5, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 9, "serialized": "54090" }, { "a_digit": 5, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "58031" }, { "a_digit":...
55--84=<add><pos><state>550480<step>54090<step>58031<step>00110<ans>9310
div
162
001.209
1.209
-936
-774
3x3
/
-936/-774=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
936774
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 774, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-936/-774=<div><pos><state>936774<step>00090009<qmul>00000<rem>009<step>00930093<qmul>00000<rem>093<step>09360936<qmul>10774<rem>162<step>16201620<qmul>21548<rem>072<step>07200720<qmul>00000<rem>720<step>72007200<qmul>96966<rem>234<step>23402340<qmul>32322<rem>018<ans>001.209
mul
118
549347
743945
779
955
3x3
*
779*955=
scratchpad-v3
positive
null
high_column_sum
++
train
977559
[ { "a_digit": 9, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 45, "running_total": 45, "serialized": "9545045", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 45, "kind": "column", ...
779*955=<mul><pos><state>977559<step>9545045<col>504<step>9545049<step>7535084<col>408<step>9981089<step>7535124<step>7535159<col>915<step>7963078<step>7535113<col>311<step>7963074<col>407<ans>549347
div
157
000.010
0.01
1
99
1x2
/
1/99=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
001099
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 99, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
1/99=<div><pos><state>001099<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>10099<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>10099<rem>001<ans>000.010
mul
117
825000
-528
22
-24
2x2
*
22*-24=
scratchpad-v3
negative
null
repeated_digit
+-
test
220420
[ { "a_digit": 2, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 8, "running_total": 8, "serialized": "2408008", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 8, "kind": "column", "o...
22*-24=<mul><neg><state>220420<step>2408008<col>800<step>2204004<step>2408012<col>201<step>2000001<step>2204005<step>0400005<col>500<step>2000000<step>0200000<col>000<step>0000000<col>000<ans>825000
div
159
000.053
0.053
-1
-19
1x2
/
-1/-19=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
001019
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 19, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-1/-19=<div><pos><state>001019<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>50095<rem>005<step>00500050<qmul>20038<rem>012<step>01200120<qmul>60114<rem>006<ans>000.053
mul
120
270192
291072
-758
-384
3x3
*
-758*-384=
scratchpad-v3
positive
null
medium_column_sum
--
train
857483
[ { "a_digit": 8, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 32, "running_total": 32, "serialized": "8432032", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 32, "kind": "column", ...
-758*-384=<mul><pos><state>857483<step>8432032<col>203<step>8864067<step>5420087<col>708<step>8324032<step>5840072<step>7428100<col>010<step>5315025<step>7856081<col>108<step>7321029<col>902<ans>270192
sub
43
8020
208
-98
-306
2x3
-
-98--306=
scratchpad-v3
positive
null
borrow_through_zero
--
train
603890
[ { "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": 0, "serialized": "09101", "subtrahend...
-98--306=<sub><pos><state>603890<step>68081<step>09101<step>30120<ans>8020
add
44
5260
-625
-398
-227
3x3
+
-398+-227=
scratchpad-v3
negative
null
multi_carry
--
train
893722
[ { "a_digit": 8, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "87051" }, { "a_digit": 9, "b_digit": 2, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "92121" }, { "a_digit":...
-398+-227=<add><neg><state>893722<step>87051<step>92121<step>32160<ans>5260
div
160
003.966
-3.966
234
-59
3x2
/
234/-59=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
234059
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 59, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
234/-59=<div><neg><state>234059<step>00020002<qmul>00000<rem>002<step>00230023<qmul>00000<rem>023<step>02340234<qmul>30177<rem>057<step>05700570<qmul>90531<rem>039<step>03900390<qmul>60354<rem>036<step>03600360<qmul>60354<rem>006<step>00600060<qmul>10059<rem>001<ans>003.966
div
161
001.790
-1.79
-829
463
3x3
/
-829/463=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
val
829463
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 463, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-829/463=<div><neg><state>829463<step>00080008<qmul>00000<rem>008<step>00820082<qmul>00000<rem>082<step>08290829<qmul>10463<rem>366<step>36603660<qmul>73241<rem>419<step>41904190<qmul>94167<rem>023<step>02300230<qmul>00000<rem>230<step>23002300<qmul>41852<rem>448<ans>001.790
add
42
5701
1075
448
627
3x3
+
448+627=
scratchpad-v3
positive
null
overflow
++
train
844726
[ { "a_digit": 8, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "87051" }, { "a_digit": 4, "b_digit": 2, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "42170" }, { "a_digit":...
448+627=<add><pos><state>844726<step>87051<step>42170<step>46001<ans>5701
mul
120
227898
898722
-918
-979
3x3
*
-918*-979=
scratchpad-v3
positive
null
high_column_sum
--
train
819979
[ { "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", ...
-918*-979=<mul><pos><state>819979<step>8972072<col>207<step>8756063<step>1909072<col>207<step>8972079<step>1707086<step>9981167<col>716<step>1909025<step>9763088<col>808<step>9981089<col>908<ans>227898
mul
117
279000
-972
1
-972
1x3
*
1*-972=
scratchpad-v3
negative
null
identity
+-
train
100279
[ { "a_digit": 1, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 2, "running_total": 2, "serialized": "1202002", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 2, "kind": "column", "o...
1*-972=<mul><neg><state>100279<step>1202002<col>200<step>1707007<step>0200007<col>700<step>1909009<step>0700009<step>0200009<col>900<step>0900000<step>0700000<col>000<step>0900000<col>000<ans>279000
div
159
000.468
0.468
51
109
2x3
/
51/109=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
051109
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 109, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
51/109=<div><pos><state>051109<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00510051<qmul>00000<rem>051<step>05100510<qmul>40436<rem>074<step>07400740<qmul>60654<rem>086<step>08600860<qmul>70763<rem>097<step>09700970<qmul>80872<rem>098<ans>000.468
mul
120
264767
767462
-769
-998
3x3
*
-769*-998=
scratchpad-v3
positive
null
high_column_sum
--
train
967899
[ { "a_digit": 9, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 72, "running_total": 72, "serialized": "9872072", "term_index": 0 }, { "carry_in": 0, "carry_out": 7, "column": 0, "column_sum": 72, "kind": "column", ...
-769*-998=<mul><pos><state>967899<step>9872072<col>207<step>9981088<step>6848136<col>613<step>9981094<step>6954148<step>7856204<col>420<step>6954074<step>7963137<col>713<step>7963076<col>607<ans>264767
add
43
7060
-607
-570
-37
3x2
+
-570+-37=
scratchpad-v3
negative
null
single_carry
--
train
075730
[ { "a_digit": 0, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "07070" }, { "a_digit": 7, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "73001" }, { "a_digit":...
-570+-37=<add><neg><state>075730<step>07070<step>73001<step>50160<ans>7060
div
162
001.379
1.379
-793
-575
3x3
/
-793/-575=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
793575
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 575, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-793/-575=<div><pos><state>793575<step>00070007<qmul>00000<rem>007<step>00790079<qmul>00000<rem>079<step>07930793<qmul>10575<rem>218<step>21802180<qmul>31725<rem>455<step>45504550<qmul>74025<rem>525<step>52505250<qmul>95175<rem>075<step>07500750<qmul>10575<rem>175<ans>001.379
div
159
131.143
-131.143
918
-7
3x1
/
918/-7=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
918007
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 7, "kind": "quotient_product", "position": 0, "quotient_digit": 1, "quotient_product": 7, "serialized": "10007" }, { "kind": ...
918/-7=<div><neg><state>918007<step>00090009<qmul>10007<rem>002<step>00210021<qmul>30021<rem>000<step>00080008<qmul>10007<rem>001<step>00100010<qmul>10007<rem>003<step>00300030<qmul>40028<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<ans>131.143
add
44
5121
-1215
-969
-246
3x3
+
-969+-246=
scratchpad-v3
negative
null
overflow
--
train
969642
[ { "a_digit": 9, "b_digit": 6, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "96051" }, { "a_digit": 6, "b_digit": 4, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "64111" }, { "a_digit":...
-969+-246=<add><neg><state>969642<step>96051<step>64111<step>92121<ans>5121
mul
118
036465
564630
885
638
3x3
*
885*638=
scratchpad-v3
positive
null
medium_column_sum
++
test
588836
[ { "a_digit": 5, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 40, "running_total": 40, "serialized": "5840040", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 40, "kind": "column", ...
885*638=<mul><pos><state>588836<step>5840040<col>004<step>5315019<step>8864083<col>308<step>5630038<step>8324062<step>8864126<col>612<step>8648060<step>8324084<col>408<step>8648056<col>605<ans>036465
sub
42
0000
0
308
308
3x3
-
308-308=
scratchpad-v3
positive
null
identity
++
train
803803
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 8, "output_digit": 0, "serialized": "88000", "subtrahend_digit": 8 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 0, "output_digit": 0, "serialized": "00000", "subtrahend...
308-308=<sub><pos><state>803803<step>88000<step>00000<step>33000<ans>0000
div
158
004.167
-4.167
25
-6
2x1
/
25/-6=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
025006
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
25/-6=<div><neg><state>025006<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00250025<qmul>40024<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>004.167
mul
118
709200
2907
-57
-51
2x2
*
-57*-51=
scratchpad-v3
positive
null
low_column_sum
--
train
750150
[ { "a_digit": 7, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 7, "running_total": 7, "serialized": "7107007", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 7, "kind": "column", "o...
-57*-51=<mul><pos><state>750150<step>7107007<col>700<step>7535035<step>5105040<col>004<step>7000004<step>5525029<step>0100029<col>902<step>5000002<step>0500002<col>200<step>0000000<col>000<ans>709200
mul
116
578000
875
25
35
2x2
*
25*35=
scratchpad-v3
positive
null
low_column_sum
++
train
520530
[ { "a_digit": 5, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 25, "running_total": 25, "serialized": "5525025", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 25, "kind": "column", ...
25*35=<mul><pos><state>520530<step>5525025<col>502<step>5315017<step>2510027<col>702<step>5000002<step>2306008<step>0500008<col>800<step>2000000<step>0300000<col>000<step>0000000<col>000<ans>578000