effective_operation
stringclasses
4 values
encoded_tokens
int64
17
162
internal_answer
stringlengths
4
7
natural_answer
stringlengths
1
8
operand_a
int64
-999
999
operand_b
int64
-999
999
operand_digits
stringclasses
9 values
operation
stringclasses
4 values
prompt
stringlengths
4
10
representation
stringclasses
1 value
result_sign
stringclasses
2 values
rounding
stringclasses
1 value
scenario
stringclasses
25 values
sign_pattern
stringclasses
4 values
split
stringclasses
3 values
state
stringlengths
6
6
steps
listlengths
0
21
text
stringlengths
37
276
sub
41
7080
807
903
96
3x2
-
903-96=
scratchpad-v3
positive
null
borrow_through_zero
++
train
309690
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 7, "serialized": "36071", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 0, "serialized": "09101", "subtrahend...
903-96=<sub><pos><state>309690<step>36071<step>09101<step>90180<ans>7080
sub
44
9010
-109
-773
-664
3x3
-
-773--664=
scratchpad-v3
negative
null
negative_result
--
train
377466
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 9, "serialized": "34091", "subtrahend_digit": 4 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 0, "serialized": "76100", "subtrahend...
-773--664=<sub><neg><state>377466<step>34091<step>76100<step>76010<ans>9010
add
43
7211
1127
857
-270
3x3
-
857--270=
scratchpad-v3
positive
null
magnitude_addition
+-
train
758072
[ { "a_digit": 7, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "70070" }, { "a_digit": 5, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "57021" }, { "a_digit":...
857--270=<add><pos><state>758072<step>70070<step>57021<step>82111<ans>7211
add
42
4411
1144
603
541
3x3
+
603+541=
scratchpad-v3
positive
null
overflow
++
train
306145
[ { "a_digit": 3, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 4, "serialized": "31040" }, { "a_digit": 0, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 4, "serialized": "04040" }, { "a_digit":...
603+541=<add><pos><state>306145<step>31040<step>04040<step>65011<ans>4411
sub
43
4700
-74
-145
-71
3x2
-
-145--71=
scratchpad-v3
negative
null
negative_result
--
train
541170
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 4, "serialized": "51040", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 7, "serialized": "47071", "subtrahend...
-145--71=<sub><neg><state>541170<step>51040<step>47071<step>10100<ans>4700
add
42
0361
1630
709
921
3x3
+
709+921=
scratchpad-v3
positive
null
overflow
++
train
907129
[ { "a_digit": 9, "b_digit": 1, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "91001" }, { "a_digit": 0, "b_digit": 2, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "02130" }, { "a_digit":...
709+921=<add><pos><state>907129<step>91001<step>02130<step>79061<ans>0361
mul
117
692100
-1296
54
-24
2x2
*
54*-24=
scratchpad-v3
negative
null
low_column_sum
+-
train
450420
[ { "a_digit": 4, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 16, "running_total": 16, "serialized": "4416016", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 16, "kind": "column", ...
54*-24=<mul><neg><state>450420<step>4416016<col>601<step>4208009<step>5420029<col>902<step>4000002<step>5210012<step>0400012<col>201<step>5000001<step>0200001<col>100<step>0000000<col>000<ans>692100
sub
43
8670
768
-37
-805
2x3
-
-37--805=
scratchpad-v3
positive
null
borrow_through_zero
--
train
508730
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 5, "output_digit": 8, "serialized": "57081", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 6, "serialized": "03161", "subtrahend...
-37--805=<sub><pos><state>508730<step>57081<step>03161<step>80170<ans>8670
div
160
000.786
0.786
-22
-28
2x2
/
-22/-28=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
022028
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 28, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-22/-28=<div><pos><state>022028<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02200220<qmul>70196<rem>024<step>02400240<qmul>80224<rem>016<step>01600160<qmul>50140<rem>020<step>02000200<qmul>70196<rem>004<ans>000.786
div
160
020.500
-20.5
-574
28
3x2
/
-574/28=
scratchpad-v3
negative
round-half-up
exact
-+
train
574028
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 28, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-574/28=<div><neg><state>574028<step>00050005<qmul>00000<rem>005<step>00570057<qmul>20056<rem>001<step>00140014<qmul>00000<rem>014<step>01400140<qmul>50140<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>020.500
sub
41
1200
21
-28
49
2x2
+
-28+49=
scratchpad-v3
positive
null
magnitude_subtraction
-+
train
940820
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 1, "serialized": "98010", "subtrahend_digit": 8 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 4, "output_digit": 2, "serialized": "42020", "subtrahend...
-28+49=<sub><pos><state>940820<step>98010<step>42020<step>00000<ans>1200
sub
43
7710
177
-29
-206
2x3
-
-29--206=
scratchpad-v3
positive
null
borrow_through_zero
--
train
602920
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 7, "serialized": "69071", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 7, "serialized": "02171", "subtrahend...
-29--206=<sub><pos><state>602920<step>69071<step>02171<step>20110<ans>7710
add
42
1860
681
210
471
3x3
+
210+471=
scratchpad-v3
positive
null
no_carry
++
train
012174
[ { "a_digit": 0, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 1, "serialized": "01010" }, { "a_digit": 1, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "17080" }, { "a_digit":...
210+471=<add><pos><state>012174<step>01010<step>17080<step>24060<ans>1860
div
160
001.000
1
649
649
3x3
/
649/649=
scratchpad-v3
positive
round-half-up
exact
++
train
649649
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 649, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
649/649=<div><pos><state>649649<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06490649<qmul>10649<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.000
mul
117
000000
0
0
-848
1x3
*
0*-848=
scratchpad-v3
negative
null
identity
+-
train
000848
[ { "a_digit": 0, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0800000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
0*-848=<mul><neg><state>000848<step>0800000<col>000<step>0400000<step>0800000<col>000<step>0800000<step>0400000<step>0800000<col>000<step>0800000<step>0400000<col>000<step>0800000<col>000<ans>000000
div
159
009.426
9.426
575
61
3x2
/
575/61=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
575061
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 61, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
575/61=<div><pos><state>575061<step>00050005<qmul>00000<rem>005<step>00570057<qmul>00000<rem>057<step>05750575<qmul>90549<rem>026<step>02600260<qmul>40244<rem>016<step>01600160<qmul>20122<rem>038<step>03800380<qmul>60366<rem>014<step>01400140<qmul>20122<rem>018<ans>009.426
mul
118
597252
252795
285
887
3x3
*
285*887=
scratchpad-v3
positive
null
medium_column_sum
++
train
582788
[ { "a_digit": 5, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 35, "running_total": 35, "serialized": "5735035", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 35, "kind": "column", ...
285*887=<mul><pos><state>582788<step>5735035<col>503<step>5840043<step>8756099<col>909<step>5840049<step>8864113<step>2714127<col>712<step>8864076<step>2816092<col>209<step>2816025<col>502<ans>597252
mul
120
699060
60996
-204
-299
3x3
*
-204*-299=
scratchpad-v3
positive
null
contains_zero_digit
--
train
402992
[ { "a_digit": 4, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "4936036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
-204*-299=<mul><pos><state>402992<step>4936036<col>603<step>4936039<step>0900039<col>903<step>4208011<step>0900011<step>2918029<col>902<step>0200002<step>2918020<col>002<step>2204006<col>600<ans>699060
mul
120
462917
719264
-728
-988
3x3
*
-728*-988=
scratchpad-v3
positive
null
high_column_sum
--
train
827889
[ { "a_digit": 8, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 64, "running_total": 64, "serialized": "8864064", "term_index": 0 }, { "carry_in": 0, "carry_out": 6, "column": 0, "column_sum": 64, "kind": "column", ...
-728*-988=<mul><pos><state>827889<step>8864064<col>406<step>8864070<step>2816086<col>608<step>8972080<step>2816096<step>7856152<col>215<step>2918033<step>7856089<col>908<step>7963071<col>107<ans>462917
sub
43
9680
869
-37
-906
2x3
-
-37--906=
scratchpad-v3
positive
null
borrow_through_zero
--
test
609730
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 9, "serialized": "67091", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 6, "serialized": "03161", "subtrahend...
-37--906=<sub><pos><state>609730<step>67091<step>03161<step>90180<ans>9680
add
42
5170
-715
-681
34
3x2
-
-681-34=
scratchpad-v3
negative
null
magnitude_addition
-+
train
186430
[ { "a_digit": 1, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "14050" }, { "a_digit": 8, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "83011" }, { "a_digit":...
-681-34=<add><neg><state>186430<step>14050<step>83011<step>60170<ans>5170
mul
117
882750
57288
682
84
3x2
*
682*84=
scratchpad-v3
positive
null
medium_column_sum
++
train
286480
[ { "a_digit": 2, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 8, "running_total": 8, "serialized": "2408008", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 8, "kind": "column", "o...
682*84=<mul><pos><state>286480<step>2408008<col>800<step>2816016<step>8432048<col>804<step>2000004<step>8864068<step>6424092<col>209<step>8000009<step>6848057<col>705<step>6000005<col>500<ans>882750
sub
40
1500
51
91
40
2x2
-
91-40=
scratchpad-v3
positive
null
no_borrow
++
train
190040
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 1, "output_digit": 1, "serialized": "10010", "subtrahend_digit": 0 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 5, "serialized": "94050", "subtrahend...
91-40=<sub><pos><state>190040<step>10010<step>94050<step>00000<ans>1500
add
44
4650
-564
-432
-132
3x3
+
-432+-132=
scratchpad-v3
negative
null
no_carry
--
train
234231
[ { "a_digit": 2, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 4, "serialized": "22040" }, { "a_digit": 3, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "33060" }, { "a_digit":...
-432+-132=<add><neg><state>234231<step>22040<step>33060<step>41050<ans>4650
add
42
5550
555
297
258
3x3
+
297+258=
scratchpad-v3
positive
null
multi_carry
++
train
792852
[ { "a_digit": 7, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "78051" }, { "a_digit": 9, "b_digit": 5, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 5, "serialized": "95151" }, { "a_digit":...
297+258=<add><pos><state>792852<step>78051<step>95151<step>22150<ans>5550
div
159
002.652
-2.652
-61
23
2x2
/
-61/23=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
test
061023
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 23, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-61/23=<div><neg><state>061023<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00610061<qmul>20046<rem>015<step>01500150<qmul>60138<rem>012<step>01200120<qmul>50115<rem>005<step>00500050<qmul>20046<rem>004<step>00400040<qmul>10023<rem>017<ans>002.652
div
160
001.478
1.478
263
178
3x3
/
263/178=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
train
263178
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 178, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
263/178=<div><pos><state>263178<step>00020002<qmul>00000<rem>002<step>00260026<qmul>00000<rem>026<step>02630263<qmul>10178<rem>085<step>08500850<qmul>40712<rem>138<step>13801380<qmul>71246<rem>134<step>13401340<qmul>71246<rem>094<step>09400940<qmul>50890<rem>050<ans>001.478
sub
41
7100
-17
-24
-7
2x1
-
-24--7=
scratchpad-v3
negative
null
negative_result
--
train
420700
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 7, "serialized": "47071", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 1, "serialized": "20110", "subtrahend...
-24--7=<sub><neg><state>420700<step>47071<step>20110<step>00000<ans>7100
div
162
001.127
1.127
-799
-709
3x3
/
-799/-709=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
799709
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 709, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-799/-709=<div><pos><state>799709<step>00070007<qmul>00000<rem>007<step>00790079<qmul>00000<rem>079<step>07990799<qmul>10709<rem>090<step>09000900<qmul>10709<rem>191<step>19101910<qmul>21418<rem>492<step>49204920<qmul>64254<rem>666<step>66606660<qmul>96381<rem>279<ans>001.127
add
40
2470
742
3
739
1x3
+
3+739=
scratchpad-v3
positive
null
single_carry
++
train
300937
[ { "a_digit": 3, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "39021" }, { "a_digit": 0, "b_digit": 3, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 4, "serialized": "03140" }, { "a_digit":...
3+739=<add><pos><state>300937<step>39021<step>03140<step>07070<ans>2470
div
160
021.000
-21
-651
31
3x2
/
-651/31=
scratchpad-v3
negative
round-half-up
exact
-+
train
651031
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 31, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-651/31=<div><neg><state>651031<step>00060006<qmul>00000<rem>006<step>00650065<qmul>20062<rem>003<step>00310031<qmul>10031<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>021.000
div
160
000.791
0.791
-34
-43
2x2
/
-34/-43=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
034043
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 43, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-34/-43=<div><pos><state>034043<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03400340<qmul>70301<rem>039<step>03900390<qmul>90387<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>60258<rem>042<ans>000.791
mul
118
218397
793812
996
797
3x3
*
996*797=
scratchpad-v3
positive
null
high_column_sum
++
train
699797
[ { "a_digit": 6, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 42, "running_total": 42, "serialized": "6742042", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 42, "kind": "column", ...
996*797=<mul><pos><state>699797<step>6742042<col>204<step>6954058<step>9763121<col>112<step>6742054<step>9981135<step>9763198<col>819<step>9763082<step>9981163<col>316<step>9763079<col>907<ans>218397
div
161
001.920
-1.92
-649
338
3x3
/
-649/338=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
649338
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 338, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-649/338=<div><neg><state>649338<step>00060006<qmul>00000<rem>006<step>00640064<qmul>00000<rem>064<step>06490649<qmul>10338<rem>311<step>31103110<qmul>93042<rem>068<step>06800680<qmul>20676<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>10338<rem>062<ans>001.920
mul
117
497100
-1794
69
-26
2x2
*
69*-26=
scratchpad-v3
negative
null
low_column_sum
+-
train
960620
[ { "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", ...
69*-26=<mul><neg><state>960620<step>9654054<col>405<step>9218023<step>6636059<col>905<step>9000005<step>6212017<step>0600017<col>701<step>6000001<step>0200001<col>100<step>0000000<col>000<ans>497100
mul
119
693568
-865396
868
-997
3x3
*
868*-997=
scratchpad-v3
negative
null
high_column_sum
+-
train
868799
[ { "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", ...
868*-997=<mul><neg><state>868799<step>8756056<col>605<step>8972077<step>6742119<col>911<step>8972083<step>6954137<step>8756193<col>319<step>6954073<step>8972145<col>514<step>8972086<col>608<ans>693568
div
160
000.343
-0.343
70
-204
2x3
/
70/-204=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
070204
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 204, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
70/-204=<div><neg><state>070204<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>30612<rem>088<step>08800880<qmul>40816<rem>064<step>06400640<qmul>30612<rem>028<step>02800280<qmul>10204<rem>076<ans>000.343
sub
41
6280
-826
12
838
2x3
-
12-838=
scratchpad-v3
negative
null
negative_result
++
train
838210
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 8, "output_digit": 6, "serialized": "82060", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 3, "output_digit": 2, "serialized": "31020", "subtrahend...
12-838=<sub><neg><state>838210<step>82060<step>31020<step>80080<ans>6280
mul
118
857610
-16758
882
-19
3x2
*
882*-19=
scratchpad-v3
negative
null
medium_column_sum
+-
val
288910
[ { "a_digit": 2, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "2918018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
882*-19=<mul><neg><state>288910<step>2918018<col>801<step>2102003<step>8972075<col>507<step>2000007<step>8108015<step>8972087<col>708<step>8000008<step>8108016<col>601<step>8000001<col>100<ans>857610
mul
120
757603
306757
-353
-869
3x3
*
-353*-869=
scratchpad-v3
positive
null
medium_column_sum
--
val
353968
[ { "a_digit": 3, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 27, "running_total": 27, "serialized": "3927027", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 27, "kind": "column", ...
-353*-869=<mul><pos><state>353968<step>3927027<col>702<step>3618020<step>5945065<col>506<step>3824030<step>5630060<step>3927087<col>708<step>5840048<step>3618066<col>606<step>3824030<col>003<ans>757603
mul
117
048600
6840
38
180
2x3
*
38*180=
scratchpad-v3
positive
null
contains_zero_digit
++
train
830081
[ { "a_digit": 8, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "8000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
38*180=<mul><pos><state>830081<step>8000000<col>000<step>8864064<step>3000064<col>406<step>8108014<step>3824038<step>0000038<col>803<step>3103006<step>0800006<col>600<step>0100000<col>000<ans>048600
sub
43
8860
688
-17
-705
2x3
-
-17--705=
scratchpad-v3
positive
null
borrow_through_zero
--
train
507710
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 5, "output_digit": 8, "serialized": "57081", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 8, "serialized": "01181", "subtrahend...
-17--705=<sub><pos><state>507710<step>57081<step>01181<step>70160<ans>8860
div
160
000.447
-0.447
-68
152
2x3
/
-68/152=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
068152
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 152, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-68/152=<div><neg><state>068152<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00680068<qmul>00000<rem>068<step>06800680<qmul>40608<rem>072<step>07200720<qmul>40608<rem>112<step>11201120<qmul>71064<rem>056<step>05600560<qmul>30456<rem>104<ans>000.447
div
160
010.187
-10.187
-764
75
3x2
/
-764/75=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
764075
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 75, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-764/75=<div><neg><state>764075<step>00070007<qmul>00000<rem>007<step>00760076<qmul>10075<rem>001<step>00140014<qmul>00000<rem>014<step>01400140<qmul>10075<rem>065<step>06500650<qmul>80600<rem>050<step>05000500<qmul>60450<rem>050<step>05000500<qmul>60450<rem>050<ans>010.187
add
42
8960
698
316
382
3x3
+
316+382=
scratchpad-v3
positive
null
no_carry
++
train
613283
[ { "a_digit": 6, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 8, "serialized": "62080" }, { "a_digit": 1, "b_digit": 8, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "18090" }, { "a_digit":...
316+382=<add><pos><state>613283<step>62080<step>18090<step>33060<ans>8960
sub
40
9000
9
-8
17
1x2
+
-8+17=
scratchpad-v3
positive
null
magnitude_subtraction
-+
train
710800
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 7, "output_digit": 9, "serialized": "78091", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 0, "serialized": "10100", "subtrahend...
-8+17=<sub><pos><state>710800<step>78091<step>10100<step>00000<ans>9000
mul
118
084210
-12480
160
-78
3x2
*
160*-78=
scratchpad-v3
negative
null
contains_zero_digit
+-
train
061870
[ { "a_digit": 0, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0800000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
160*-78=<mul><neg><state>061870<step>0800000<col>000<step>0700000<step>6848048<col>804<step>0000004<step>6742046<step>1808054<col>405<step>6000005<step>1707012<col>201<step>1000001<col>100<ans>084210
div
162
001.169
1.169
-727
-622
3x3
/
-727/-622=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
727622
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 622, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-727/-622=<div><pos><state>727622<step>00070007<qmul>00000<rem>007<step>00720072<qmul>00000<rem>072<step>07270727<qmul>10622<rem>105<step>10501050<qmul>10622<rem>428<step>42804280<qmul>63732<rem>548<step>54805480<qmul>84976<rem>504<step>50405040<qmul>84976<rem>064<ans>001.169
div
158
002.667
2.667
-8
-3
1x1
/
-8/-3=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
008003
[ { "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": ...
-8/-3=<div><pos><state>008003<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00080008<qmul>20006<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<ans>002.667
mul
119
353727
-727353
-869
837
3x3
*
-869*837=
scratchpad-v3
negative
null
high_column_sum
-+
train
968738
[ { "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", ...
-869*837=<mul><neg><state>968738<step>9763063<col>306<step>9327033<step>6742075<col>507<step>9872079<step>6318097<step>8756153<col>315<step>6848063<step>8324087<col>708<step>8864072<col>207<ans>353727
div
161
001.000
-1
207
-207
3x3
/
207/-207=
scratchpad-v3
negative
round-half-up
exact
+-
train
207207
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 207, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
207/-207=<div><neg><state>207207<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02070207<qmul>10207<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.000
sub
42
4100
14
-41
-55
2x2
-
-41--55=
scratchpad-v3
positive
null
no_borrow
--
train
550140
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 4, "serialized": "51040", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 5, "output_digit": 1, "serialized": "54010", "subtrahend...
-41--55=<sub><pos><state>550140<step>51040<step>54010<step>00000<ans>4100
mul
116
570000
-75
-75
1
2x1
*
-75*1=
scratchpad-v3
negative
null
identity
-+
train
570100
[ { "a_digit": 5, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 5, "running_total": 5, "serialized": "5105005", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 5, "kind": "column", "o...
-75*1=<mul><neg><state>570100<step>5105005<col>500<step>5000000<step>7107007<col>700<step>5000000<step>7000000<step>0100000<col>000<step>7000000<step>0000000<col>000<step>0000000<col>000<ans>570000
add
44
3441
-1443
-549
-894
3x3
+
-549+-894=
scratchpad-v3
negative
null
overflow
--
train
945498
[ { "a_digit": 9, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "94031" }, { "a_digit": 4, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 4, "serialized": "49141" }, { "a_digit":...
-549+-894=<add><neg><state>945498<step>94031<step>49141<step>58141<ans>3441
div
157
000.127
0.127
9
71
1x2
/
9/71=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
009071
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 71, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
9/71=<div><pos><state>009071<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00090009<qmul>00000<rem>009<step>00900090<qmul>10071<rem>019<step>01900190<qmul>20142<rem>048<step>04800480<qmul>60426<rem>054<step>05400540<qmul>70497<rem>043<ans>000.127
mul
118
255360
-63552
-662
96
3x2
*
-662*96=
scratchpad-v3
negative
null
medium_column_sum
-+
train
266690
[ { "a_digit": 2, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 12, "running_total": 12, "serialized": "2612012", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 12, "kind": "column", ...
-662*96=<mul><neg><state>266690<step>2612012<col>201<step>2918019<step>6636055<col>505<step>2000005<step>6954059<step>6636095<col>509<step>6000009<step>6954063<col>306<step>6000006<col>600<ans>255360
mul
119
807860
68708
-772
-89
3x2
*
-772*-89=
scratchpad-v3
positive
null
medium_column_sum
--
train
277980
[ { "a_digit": 2, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "2918018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
-772*-89=<mul><pos><state>277980<step>2918018<col>801<step>2816017<step>7963080<col>008<step>2000008<step>7856064<step>7963127<col>712<step>7000012<step>7856068<col>806<step>7000006<col>600<ans>807860
div
161
000.814
-0.814
-320
393
3x3
/
-320/393=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
320393
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 393, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-320/393=<div><neg><state>320393<step>00030003<qmul>00000<rem>003<step>00320032<qmul>00000<rem>032<step>03200320<qmul>00000<rem>320<step>32003200<qmul>83144<rem>056<step>05600560<qmul>10393<rem>167<step>16701670<qmul>41572<rem>098<step>09800980<qmul>20786<rem>194<ans>000.814
mul
118
082940
-49280
-55
896
2x3
*
-55*896=
scratchpad-v3
negative
null
repeated_digit
-+
train
550698
[ { "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", ...
-55*896=<mul><neg><state>550698<step>5630030<col>003<step>5945048<step>5630078<col>807<step>5840047<step>5945092<step>0600092<col>209<step>5840049<step>0900049<col>904<step>0800004<col>400<ans>082940
div
161
000.348
-0.348
261
-749
3x3
/
261/-749=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
261749
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 749, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
261/-749=<div><neg><state>261749<step>00020002<qmul>00000<rem>002<step>00260026<qmul>00000<rem>026<step>02610261<qmul>00000<rem>261<step>26102610<qmul>32247<rem>363<step>36303630<qmul>42996<rem>634<step>63406340<qmul>85992<rem>348<step>34803480<qmul>42996<rem>484<ans>000.348
sub
43
1650
561
-39
-600
2x3
-
-39--600=
scratchpad-v3
positive
null
borrow_through_zero
--
train
006930
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 1, "serialized": "09011", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 6, "serialized": "03161", "subtrahend...
-39--600=<sub><pos><state>006930<step>09011<step>03161<step>60150<ans>1650
mul
118
653748
847356
879
964
3x3
*
879*964=
scratchpad-v3
positive
null
high_column_sum
++
train
978469
[ { "a_digit": 9, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "9436036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
879*964=<mul><pos><state>978469<step>9436036<col>603<step>9654057<step>7428085<col>508<step>9981089<step>7642131<step>8432163<col>316<step>7963079<step>8648127<col>712<step>8972084<col>408<ans>653748
sub
43
3110
113
811
-698
3x3
+
811+-698=
scratchpad-v3
positive
null
magnitude_subtraction
+-
train
118896
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 3, "serialized": "18031", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 1, "serialized": "19111", "subtrahend...
811+-698=<sub><pos><state>118896<step>18031<step>19111<step>86110<ans>3110
add
42
6011
1106
928
178
3x3
+
928+178=
scratchpad-v3
positive
null
cascading_carry
++
val
829871
[ { "a_digit": 8, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 6, "serialized": "88061" }, { "a_digit": 2, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "27101" }, { "a_digit":...
928+178=<add><pos><state>829871<step>88061<step>27101<step>91111<ans>6011
mul
118
689623
326986
334
979
3x3
*
334*979=
scratchpad-v3
positive
null
medium_column_sum
++
train
433979
[ { "a_digit": 4, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "4936036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
334*979=<mul><pos><state>433979<step>4936036<col>603<step>4728031<step>3927058<col>805<step>4936041<step>3721062<step>3927089<col>908<step>3927035<step>3721056<col>605<step>3927032<col>203<ans>689623
div
161
000.236
-0.236
-235
997
3x3
/
-235/997=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
-+
train
235997
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 997, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-235/997=<div><neg><state>235997<step>00020002<qmul>00000<rem>002<step>00230023<qmul>00000<rem>023<step>02350235<qmul>00000<rem>235<step>23502350<qmul>21994<rem>356<step>35603560<qmul>32991<rem>569<step>56905690<qmul>54985<rem>705<step>70507050<qmul>76979<rem>071<ans>000.236
mul
118
614033
330416
428
772
3x3
*
428*772=
scratchpad-v3
positive
null
medium_column_sum
++
train
824277
[ { "a_digit": 8, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 16, "running_total": 16, "serialized": "8216016", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 16, "kind": "column", ...
428*772=<mul><pos><state>824277<step>8216016<col>601<step>8756057<step>2204061<col>106<step>8756062<step>2714076<step>4208084<col>408<step>2714022<step>4728050<col>005<step>4728033<col>303<ans>614033
sub
42
6700
76
-17
-93
2x2
-
-17--93=
scratchpad-v3
positive
null
single_borrow
--
test
390710
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 6, "serialized": "37061", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 7, "serialized": "91170", "subtrahend...
-17--93=<sub><pos><state>390710<step>37061<step>91170<step>00000<ans>6700
sub
42
8230
328
810
482
3x3
-
810-482=
scratchpad-v3
positive
null
multi_borrow
++
train
018284
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 8, "serialized": "02081", "subtrahend_digit": 2 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 2, "serialized": "18121", "subtrahend...
810-482=<sub><pos><state>018284<step>02081<step>18121<step>84130<ans>8230
mul
119
221727
-727122
759
-958
3x3
*
759*-958=
scratchpad-v3
negative
null
high_column_sum
+-
val
957859
[ { "a_digit": 9, "a_index": 0, "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", ...
759*-958=<mul><neg><state>957859<step>9872072<col>207<step>9545052<step>5840092<col>209<step>9981090<step>5525115<step>7856171<col>117<step>5945062<step>7535097<col>709<step>7963072<col>207<ans>221727
add
42
3770
773
684
-89
3x2
-
684--89=
scratchpad-v3
positive
null
magnitude_addition
+-
train
486980
[ { "a_digit": 4, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "49031" }, { "a_digit": 8, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 7, "serialized": "88171" }, { "a_digit":...
684--89=<add><pos><state>486980<step>49031<step>88171<step>60170<ans>3770
div
160
024.758
-24.758
-817
33
3x2
/
-817/33=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
817033
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 33, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-817/33=<div><neg><state>817033<step>00080008<qmul>00000<rem>008<step>00810081<qmul>20066<rem>015<step>01570157<qmul>40132<rem>025<step>02500250<qmul>70231<rem>019<step>01900190<qmul>50165<rem>025<step>02500250<qmul>70231<rem>019<step>01900190<qmul>50165<rem>025<ans>024.758
add
44
1650
-561
-284
-277
3x3
+
-284+-277=
scratchpad-v3
negative
null
multi_carry
--
train
482772
[ { "a_digit": 4, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "47011" }, { "a_digit": 8, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 6, "serialized": "87161" }, { "a_digit":...
-284+-277=<add><neg><state>482772<step>47011<step>87161<step>22150<ans>1650
mul
119
211520
25112
-292
-86
3x2
*
-292*-86=
scratchpad-v3
positive
null
medium_column_sum
--
train
292680
[ { "a_digit": 2, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 12, "running_total": 12, "serialized": "2612012", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 12, "kind": "column", ...
-292*-86=<mul><pos><state>292680<step>2612012<col>201<step>2816017<step>9654071<col>107<step>2000007<step>9872079<step>2612091<col>109<step>9000009<step>2816025<col>502<step>2000002<col>200<ans>211520
mul
119
574771
-177475
229
-775
3x3
*
229*-775=
scratchpad-v3
negative
null
medium_column_sum
+-
train
922577
[ { "a_digit": 9, "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", ...
229*-775=<mul><neg><state>922577<step>9545045<col>504<step>9763067<step>2510077<col>707<step>9763070<step>2714084<step>2510094<col>409<step>2714023<step>2714037<col>703<step>2714017<col>701<ans>574771
div
162
000.264
0.264
-173
-655
3x3
/
-173/-655=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
173655
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 655, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-173/-655=<div><pos><state>173655<step>00010001<qmul>00000<rem>001<step>00170017<qmul>00000<rem>017<step>01730173<qmul>00000<rem>173<step>17301730<qmul>21310<rem>420<step>42004200<qmul>63930<rem>270<step>27002700<qmul>42620<rem>080<step>08000800<qmul>10655<rem>145<ans>000.264
mul
118
891654
456198
834
547
3x3
*
834*547=
scratchpad-v3
positive
null
medium_column_sum
++
train
438745
[ { "a_digit": 4, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 28, "running_total": 28, "serialized": "4728028", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 28, "kind": "column", ...
834*547=<mul><pos><state>438745<step>4728028<col>802<step>4416018<step>3721039<col>903<step>4520023<step>3412035<step>8756091<col>109<step>3515024<step>8432056<col>605<step>8540045<col>504<ans>891654
mul
119
651660
-66156
-149
444
3x3
*
-149*444=
scratchpad-v3
negative
null
repeated_digit
-+
train
941444
[ { "a_digit": 9, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "9436036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
-149*444=<mul><neg><state>941444<step>9436036<col>603<step>9436039<step>4416055<col>505<step>9436041<step>4416057<step>1404061<col>106<step>4416022<step>1404026<col>602<step>1404006<col>600<ans>651660
add
44
0450
-540
-362
-178
3x3
+
-362+-178=
scratchpad-v3
negative
null
multi_carry
--
val
263871
[ { "a_digit": 2, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "28001" }, { "a_digit": 6, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 4, "serialized": "67141" }, { "a_digit":...
-362+-178=<add><neg><state>263871<step>28001<step>67141<step>31150<ans>0450
add
44
3241
-1423
-693
-730
3x3
+
-693+-730=
scratchpad-v3
negative
null
overflow
--
val
396037
[ { "a_digit": 3, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "30030" }, { "a_digit": 9, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "93021" }, { "a_digit":...
-693+-730=<add><neg><state>396037<step>30030<step>93021<step>67141<ans>3241
div
160
004.809
-4.809
428
-89
3x2
/
428/-89=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
428089
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 89, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
428/-89=<div><neg><state>428089<step>00040004<qmul>00000<rem>004<step>00420042<qmul>00000<rem>042<step>04280428<qmul>40356<rem>072<step>07200720<qmul>80712<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>80712<rem>088<step>08800880<qmul>90801<rem>079<ans>004.809
div
161
001.241
-1.241
-840
677
3x3
/
-840/677=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
840677
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 677, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-840/677=<div><neg><state>840677<step>00080008<qmul>00000<rem>008<step>00840084<qmul>00000<rem>084<step>08400840<qmul>10677<rem>163<step>16301630<qmul>21354<rem>276<step>27602760<qmul>42708<rem>052<step>05200520<qmul>00000<rem>520<step>52005200<qmul>74739<rem>461<ans>001.241
add
42
3041
1403
705
698
3x3
+
705+698=
scratchpad-v3
positive
null
cascading_carry
++
train
507896
[ { "a_digit": 5, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "58031" }, { "a_digit": 0, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "09101" }, { "a_digit":...
705+698=<add><pos><state>507896<step>58031<step>09101<step>76141<ans>3041
mul
119
241191
-191142
666
-287
3x3
*
666*-287=
scratchpad-v3
negative
null
repeated_digit
+-
train
666782
[ { "a_digit": 6, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 42, "running_total": 42, "serialized": "6742042", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 42, "kind": "column", ...
666*-287=<mul><neg><state>666782<step>6742042<col>204<step>6848052<step>6742094<col>409<step>6212021<step>6848069<step>6742111<col>111<step>6212023<step>6848071<col>107<step>6212019<col>901<ans>241191
sub
44
1120
-211
-529
-318
3x3
-
-529--318=
scratchpad-v3
negative
null
negative_result
--
train
925813
[ { "borrow_in": 0, "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...
-529--318=<sub><neg><state>925813<step>98010<step>21010<step>53020<ans>1120
add
44
5031
-1305
-668
-637
3x3
+
-668+-637=
scratchpad-v3
negative
null
cascading_carry
--
train
866736
[ { "a_digit": 8, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "87051" }, { "a_digit": 6, "b_digit": 3, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "63101" }, { "a_digit":...
-668+-637=<add><neg><state>866736<step>87051<step>63101<step>66131<ans>5031
div
161
000.183
-0.183
176
-962
3x3
/
176/-962=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
+-
train
176962
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 962, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
176/-962=<div><neg><state>176962<step>00010001<qmul>00000<rem>001<step>00170017<qmul>00000<rem>017<step>01760176<qmul>00000<rem>176<step>17601760<qmul>10962<rem>798<step>79807980<qmul>87696<rem>284<step>28402840<qmul>21924<rem>916<step>91609160<qmul>98658<rem>502<ans>000.183
div
158
000.731
0.731
38
52
2x2
/
38/52=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
038052
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 52, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
38/52=<div><pos><state>038052<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00380038<qmul>00000<rem>038<step>03800380<qmul>70364<rem>016<step>01600160<qmul>30156<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>70364<rem>036<ans>000.731
mul
119
678358
-853876
-866
986
3x3
*
-866*986=
scratchpad-v3
negative
null
high_column_sum
-+
train
668689
[ { "a_digit": 6, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "6636036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
-866*986=<mul><neg><state>668689<step>6636036<col>603<step>6848051<step>6636087<col>708<step>6954062<step>6848110<step>8648158<col>815<step>6954069<step>8864133<col>313<step>8972085<col>508<ans>678358
sub
41
4680
864
903
39
3x2
-
903-39=
scratchpad-v3
positive
null
borrow_through_zero
++
train
309930
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 4, "serialized": "39041", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 6, "serialized": "03161", "subtrahend...
903-39=<sub><pos><state>309930<step>39041<step>03161<step>90180<ans>4680
add
42
1080
801
413
388
3x3
+
413+388=
scratchpad-v3
positive
null
cascading_carry
++
train
314883
[ { "a_digit": 3, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "38011" }, { "a_digit": 1, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "18101" }, { "a_digit":...
413+388=<add><pos><state>314883<step>38011<step>18101<step>43180<ans>1080
div
161
001.008
-1.008
995
-987
3x3
/
995/-987=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
995987
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 987, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
995/-987=<div><neg><state>995987<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09950995<qmul>10987<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>00000<rem>800<step>80008000<qmul>87896<rem>104<step>10401040<qmul>10987<rem>053<ans>001.008
div
158
000.488
0.488
20
41
2x2
/
20/41=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
val
020041
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 41, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
20/41=<div><pos><state>020041<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>40164<rem>036<step>03600360<qmul>80328<rem>032<step>03200320<qmul>70287<rem>033<step>03300330<qmul>80328<rem>002<ans>000.488
div
20
<nan>
NAN
-352
0
3x1
/
-352/0=
scratchpad-v3
positive
round-half-up
nan
-+
train
352000
[]
-352/0=<div><pos><state>352000<ans><nan>
div
162
001.280
1.28
-682
-533
3x3
/
-682/-533=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
682533
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 533, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-682/-533=<div><pos><state>682533<step>00060006<qmul>00000<rem>006<step>00680068<qmul>00000<rem>068<step>06820682<qmul>10533<rem>149<step>14901490<qmul>21066<rem>424<step>42404240<qmul>73731<rem>509<step>50905090<qmul>94797<rem>293<step>29302930<qmul>52665<rem>265<ans>001.280
add
42
4280
824
569
255
3x3
+
569+255=
scratchpad-v3
positive
null
multi_carry
++
train
965552
[ { "a_digit": 9, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 4, "serialized": "95041" }, { "a_digit": 6, "b_digit": 5, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "65121" }, { "a_digit":...
569+255=<add><pos><state>965552<step>95041<step>65121<step>52180<ans>4280
add
43
3160
-613
-41
-572
2x3
+
-41+-572=
scratchpad-v3
negative
null
single_carry
--
train
140275
[ { "a_digit": 1, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "12030" }, { "a_digit": 4, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "47011" }, { "a_digit":...
-41+-572=<add><neg><state>140275<step>12030<step>47011<step>05160<ans>3160
div
160
039.435
-39.435
-907
23
3x2
/
-907/23=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
907023
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 23, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-907/23=<div><neg><state>907023<step>00090009<qmul>00000<rem>009<step>00900090<qmul>30069<rem>021<step>02170217<qmul>90207<rem>010<step>01000100<qmul>40092<rem>008<step>00800080<qmul>30069<rem>011<step>01100110<qmul>40092<rem>018<step>01800180<qmul>70161<rem>019<ans>039.435
div
159
088.875
-88.875
711
-8
3x1
/
711/-8=
scratchpad-v3
negative
round-half-up
exact
+-
train
711008
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 8, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
711/-8=<div><neg><state>711008<step>00070007<qmul>00000<rem>007<step>00710071<qmul>80064<rem>007<step>00710071<qmul>80064<rem>007<step>00700070<qmul>80064<rem>006<step>00600060<qmul>70056<rem>004<step>00400040<qmul>50040<rem>000<step>00000000<qmul>00000<rem>000<ans>088.875
div
160
000.236
0.236
144
611
3x3
/
144/611=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
144611
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 611, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
144/611=<div><pos><state>144611<step>00010001<qmul>00000<rem>001<step>00140014<qmul>00000<rem>014<step>01440144<qmul>00000<rem>144<step>14401440<qmul>21222<rem>218<step>21802180<qmul>31833<rem>347<step>34703470<qmul>53055<rem>415<step>41504150<qmul>63666<rem>484<ans>000.236