effective_operation
stringclasses
4 values
encoded_tokens
int64
17
162
internal_answer
stringlengths
4
7
natural_answer
stringlengths
1
8
operand_a
int64
-999
999
operand_b
int64
-999
999
operand_digits
stringclasses
9 values
operation
stringclasses
4 values
prompt
stringlengths
4
10
representation
stringclasses
1 value
result_sign
stringclasses
2 values
rounding
stringclasses
1 value
scenario
stringclasses
25 values
sign_pattern
stringclasses
4 values
split
stringclasses
3 values
state
stringlengths
6
6
steps
listlengths
0
21
text
stringlengths
37
276
add
44
6341
-1436
-661
-775
3x3
+
-661+-775=
scratchpad-v3
negative
null
overflow
--
val
166577
[ { "a_digit": 1, "b_digit": 5, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "15060" }, { "a_digit": 6, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "67031" }, { "a_digit":...
-661+-775=<add><neg><state>166577<step>15060<step>67031<step>67141<ans>6341
add
41
3710
-173
-173
0
3x1
+
-173+0=
scratchpad-v3
negative
null
identity
-+
train
371000
[ { "a_digit": 3, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "30030" }, { "a_digit": 7, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "70070" }, { "a_digit":...
-173+0=<add><neg><state>371000<step>30030<step>70070<step>10010<ans>3710
mul
116
374400
4473
63
71
2x2
*
63*71=
scratchpad-v3
positive
null
low_column_sum
++
train
360170
[ { "a_digit": 3, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 3, "running_total": 3, "serialized": "3103003", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 3, "kind": "column", "o...
63*71=<mul><pos><state>360170<step>3103003<col>300<step>3721021<step>6106027<col>702<step>3000002<step>6742044<step>0100044<col>404<step>6000004<step>0700004<col>400<step>0000000<col>000<ans>374400
sub
42
5900
95
-9
-104
1x3
-
-9--104=
scratchpad-v3
positive
null
borrow_through_zero
--
train
401900
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 5, "serialized": "49051", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 9, "serialized": "00191", "subtrahend...
-9--104=<sub><pos><state>401900<step>49051<step>00191<step>10100<ans>5900
add
41
0380
-830
0
-830
1x3
+
0+-830=
scratchpad-v3
negative
null
identity
+-
train
000038
[ { "a_digit": 0, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 0, "serialized": "00000" }, { "a_digit": 0, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "03030" }, { "a_digit":...
0+-830=<add><neg><state>000038<step>00000<step>03030<step>08080<ans>0380
mul
117
018400
-4810
-74
65
2x2
*
-74*65=
scratchpad-v3
negative
null
low_column_sum
-+
train
470560
[ { "a_digit": 4, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 20, "running_total": 20, "serialized": "4520020", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 20, "kind": "column", ...
-74*65=<mul><neg><state>470560<step>4520020<col>002<step>4624026<step>7535061<col>106<step>4000006<step>7642048<step>0500048<col>804<step>7000004<step>0600004<col>400<step>0000000<col>000<ans>018400
mul
116
804000
408
24
17
2x2
*
24*17=
scratchpad-v3
positive
null
low_column_sum
++
val
420710
[ { "a_digit": 4, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 28, "running_total": 28, "serialized": "4728028", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 28, "kind": "column", ...
24*17=<mul><pos><state>420710<step>4728028<col>802<step>4104006<step>2714020<col>002<step>4000002<step>2102004<step>0700004<col>400<step>2000000<step>0100000<col>000<step>0000000<col>000<ans>804000
add
40
2310
132
0
132
1x3
+
0+132=
scratchpad-v3
positive
null
identity
++
train
000231
[ { "a_digit": 0, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "02020" }, { "a_digit": 0, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "03030" }, { "a_digit":...
0+132=<add><pos><state>000231<step>02020<step>03030<step>01010<ans>2310
div
161
002.266
-2.266
-963
425
3x3
/
-963/425=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
963425
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 425, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-963/425=<div><neg><state>963425<step>00090009<qmul>00000<rem>009<step>00960096<qmul>00000<rem>096<step>09630963<qmul>20850<rem>113<step>11301130<qmul>20850<rem>280<step>28002800<qmul>62550<rem>250<step>25002500<qmul>52125<rem>375<step>37503750<qmul>83400<rem>350<ans>002.266
div
159
000.179
-0.179
-12
67
2x2
/
-12/67=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
012067
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 67, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-12/67=<div><neg><state>012067<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01200120<qmul>10067<rem>053<step>05300530<qmul>70469<rem>061<step>06100610<qmul>90603<rem>007<step>00700070<qmul>10067<rem>003<ans>000.179
add
42
7881
1887
905
982
3x3
+
905+982=
scratchpad-v3
positive
null
overflow
++
train
509289
[ { "a_digit": 5, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "52070" }, { "a_digit": 0, "b_digit": 8, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "08080" }, { "a_digit":...
905+982=<add><pos><state>509289<step>52070<step>08080<step>99081<ans>7881
sub
42
5750
575
729
154
3x3
-
729-154=
scratchpad-v3
positive
null
single_borrow
++
train
927451
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 5, "serialized": "94050", "subtrahend_digit": 4 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 7, "serialized": "25071", "subtrahend...
729-154=<sub><pos><state>927451<step>94050<step>25071<step>71150<ans>5750
sub
43
1050
501
-21
-522
2x3
-
-21--522=
scratchpad-v3
positive
null
no_borrow
--
train
225120
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 2, "output_digit": 1, "serialized": "21010", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 0, "serialized": "22000", "subtrahend...
-21--522=<sub><pos><state>225120<step>21010<step>22000<step>50050<ans>1050
sub
42
8400
48
614
566
3x3
-
614-566=
scratchpad-v3
positive
null
multi_borrow
++
train
416665
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 8, "serialized": "46081", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 4, "serialized": "16141", "subtrahend...
614-566=<sub><pos><state>416665<step>46081<step>16141<step>65100<ans>8400
mul
118
580620
-26085
-555
47
3x2
*
-555*47=
scratchpad-v3
negative
null
repeated_digit
-+
train
555740
[ { "a_digit": 5, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 35, "running_total": 35, "serialized": "5735035", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 35, "kind": "column", ...
-555*47=<mul><neg><state>555740<step>5735035<col>503<step>5420023<step>5735058<col>805<step>5000005<step>5420025<step>5735060<col>006<step>5000006<step>5420026<col>602<step>5000002<col>200<ans>580620
mul
117
693000
-396
-11
36
2x2
*
-11*36=
scratchpad-v3
negative
null
repeated_digit
-+
train
110630
[ { "a_digit": 1, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 6, "running_total": 6, "serialized": "1606006", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 6, "kind": "column", "o...
-11*36=<mul><neg><state>110630<step>1606006<col>600<step>1303003<step>1606009<col>900<step>1000000<step>1303003<step>0600003<col>300<step>1000000<step>0300000<col>000<step>0000000<col>000<ans>693000
mul
117
552300
-3255
93
-35
2x2
*
93*-35=
scratchpad-v3
negative
null
low_column_sum
+-
train
390530
[ { "a_digit": 3, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 15, "running_total": 15, "serialized": "3515015", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 15, "kind": "column", ...
93*-35=<mul><neg><state>390530<step>3515015<col>501<step>3309010<step>9545055<col>505<step>3000005<step>9327032<step>0500032<col>203<step>9000003<step>0300003<col>300<step>0000000<col>000<ans>552300
sub
40
5100
15
92
77
2x2
-
92-77=
scratchpad-v3
positive
null
single_borrow
++
train
290770
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 5, "serialized": "27051", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 1, "serialized": "97110", "subtrahend...
92-77=<sub><pos><state>290770<step>27051<step>97110<step>00000<ans>5100
div
160
010.500
-10.5
546
-52
3x2
/
546/-52=
scratchpad-v3
negative
round-half-up
exact
+-
train
546052
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 52, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
546/-52=<div><neg><state>546052<step>00050005<qmul>00000<rem>005<step>00540054<qmul>10052<rem>002<step>00260026<qmul>00000<rem>026<step>02600260<qmul>50260<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>010.500
div
160
017.615
-17.615
-229
13
3x2
/
-229/13=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
229013
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 13, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-229/13=<div><neg><state>229013<step>00020002<qmul>00000<rem>002<step>00220022<qmul>10013<rem>009<step>00990099<qmul>70091<rem>008<step>00800080<qmul>60078<rem>002<step>00200020<qmul>10013<rem>007<step>00700070<qmul>50065<rem>005<step>00500050<qmul>30039<rem>011<ans>017.615
mul
119
563780
-87365
-505
173
3x3
*
-505*173=
scratchpad-v3
negative
null
contains_zero_digit
-+
train
505371
[ { "a_digit": 5, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 15, "running_total": 15, "serialized": "5315015", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 15, "kind": "column", ...
-505*173=<mul><neg><state>505371<step>5315015<col>501<step>5735036<step>0300036<col>603<step>5105008<step>0700008<step>5315023<col>302<step>0100002<step>5735037<col>703<step>5105008<col>800<ans>563780
div
160
005.979
-5.979
287
-48
3x2
/
287/-48=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
287048
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 48, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
287/-48=<div><neg><state>287048<step>00020002<qmul>00000<rem>002<step>00280028<qmul>00000<rem>028<step>02870287<qmul>50240<rem>047<step>04700470<qmul>90432<rem>038<step>03800380<qmul>70336<rem>044<step>04400440<qmul>90432<rem>008<step>00800080<qmul>10048<rem>032<ans>005.979
div
160
000.313
0.313
184
588
3x3
/
184/588=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
184588
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 588, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
184/588=<div><pos><state>184588<step>00010001<qmul>00000<rem>001<step>00180018<qmul>00000<rem>018<step>01840184<qmul>00000<rem>184<step>18401840<qmul>31764<rem>076<step>07600760<qmul>10588<rem>172<step>17201720<qmul>21176<rem>544<step>54405440<qmul>95292<rem>148<ans>000.313
sub
42
4540
-454
528
982
3x3
-
528-982=
scratchpad-v3
negative
null
negative_result
++
train
289825
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 4, "serialized": "28041", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 8, "output_digit": 5, "serialized": "82150", "subtrahend...
528-982=<sub><neg><state>289825<step>28041<step>82150<step>95040<ans>4540
div
162
000.916
0.916
-206
-225
3x3
/
-206/-225=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
206225
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 225, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-206/-225=<div><pos><state>206225<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02060206<qmul>00000<rem>206<step>20602060<qmul>92025<rem>035<step>03500350<qmul>10225<rem>125<step>12501250<qmul>51125<rem>125<step>12501250<qmul>51125<rem>125<ans>000.916
mul
119
476619
-916674
-946
969
3x3
*
-946*969=
scratchpad-v3
negative
null
high_column_sum
-+
train
649969
[ { "a_digit": 6, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 54, "running_total": 54, "serialized": "6954054", "term_index": 0 }, { "carry_in": 0, "carry_out": 5, "column": 0, "column_sum": 54, "kind": "column", ...
-946*969=<mul><neg><state>649969<step>6954054<col>405<step>6636041<step>4936077<col>707<step>6954061<step>4624085<step>9981166<col>616<step>4936052<step>9654106<col>610<step>9981091<col>109<ans>476619
div
159
051.000
-51
357
-7
3x1
/
357/-7=
scratchpad-v3
negative
round-half-up
exact
+-
train
357007
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 7, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
357/-7=<div><neg><state>357007<step>00030003<qmul>00000<rem>003<step>00350035<qmul>50035<rem>000<step>00070007<qmul>10007<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>051.000
sub
42
7810
187
329
142
3x3
-
329-142=
scratchpad-v3
positive
null
single_borrow
++
train
923241
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 7, "serialized": "92070", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 8, "serialized": "24081", "subtrahend...
329-142=<sub><pos><state>923241<step>92070<step>24081<step>31110<ans>7810
mul
119
011092
-290110
-866
335
3x3
*
-866*335=
scratchpad-v3
negative
null
medium_column_sum
-+
train
668533
[ { "a_digit": 6, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 30, "running_total": 30, "serialized": "6530030", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 30, "kind": "column", ...
-866*335=<mul><neg><state>668533<step>6530030<col>003<step>6318021<step>6530051<col>105<step>6318023<step>6318041<step>8540081<col>108<step>6318026<step>8324050<col>005<step>8324029<col>902<ans>011092
div
160
000.311
0.311
131
421
3x3
/
131/421=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
test
131421
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 421, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
131/421=<div><pos><state>131421<step>00010001<qmul>00000<rem>001<step>00130013<qmul>00000<rem>013<step>01310131<qmul>00000<rem>131<step>13101310<qmul>31263<rem>047<step>04700470<qmul>10421<rem>049<step>04900490<qmul>10421<rem>069<step>06900690<qmul>10421<rem>269<ans>000.311
add
41
5780
875
74
801
2x3
+
74+801=
scratchpad-v3
positive
null
no_carry
++
train
470108
[ { "a_digit": 4, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "41050" }, { "a_digit": 7, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "70070" }, { "a_digit":...
74+801=<add><pos><state>470108<step>41050<step>70070<step>08080<ans>5780
div
161
000.374
-0.374
161
-430
3x3
/
161/-430=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
161430
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 430, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
161/-430=<div><neg><state>161430<step>00010001<qmul>00000<rem>001<step>00160016<qmul>00000<rem>016<step>01610161<qmul>00000<rem>161<step>16101610<qmul>31290<rem>320<step>32003200<qmul>73010<rem>190<step>19001900<qmul>41720<rem>180<step>18001800<qmul>41720<rem>080<ans>000.374
div
160
000.970
0.97
-32
-33
2x2
/
-32/-33=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
032033
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 33, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-32/-33=<div><pos><state>032033<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00320032<qmul>00000<rem>032<step>03200320<qmul>90297<rem>023<step>02300230<qmul>60198<rem>032<step>03200320<qmul>90297<rem>023<step>02300230<qmul>60198<rem>032<ans>000.970
sub
44
9900
99
-447
-546
3x3
-
-447--546=
scratchpad-v3
positive
null
multi_borrow
--
train
645744
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 9, "serialized": "67091", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 9, "serialized": "44191", "subtrahend...
-447--546=<sub><pos><state>645744<step>67091<step>44191<step>54100<ans>9900
add
40
8750
578
0
578
1x3
+
0+578=
scratchpad-v3
positive
null
identity
++
train
000875
[ { "a_digit": 0, "b_digit": 8, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 8, "serialized": "08080" }, { "a_digit": 0, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "07070" }, { "a_digit":...
0+578=<add><pos><state>000875<step>08080<step>07070<step>05050<ans>8750
div
159
007.167
7.167
-43
-6
2x1
/
-43/-6=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
043006
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-43/-6=<div><pos><state>043006<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00430043<qmul>70042<rem>001<step>00100010<qmul>10006<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<ans>007.167
sub
43
6870
786
-14
-800
2x3
-
-14--800=
scratchpad-v3
positive
null
borrow_through_zero
--
test
008410
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 6, "serialized": "04061", "subtrahend_digit": 4 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 8, "serialized": "01181", "subtrahend...
-14--800=<sub><pos><state>008410<step>04061<step>01181<step>80170<ans>6870
mul
119
021297
-792120
920
-861
3x3
*
920*-861=
scratchpad-v3
negative
null
contains_zero_digit
+-
train
029168
[ { "a_digit": 0, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0100000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
920*-861=<mul><neg><state>029168<step>0100000<col>000<step>0600000<step>2102002<col>200<step>0800000<step>2612012<step>9109021<col>102<step>2816018<step>9654072<col>207<step>9872079<col>907<ans>021297
div
161
001.096
-1.096
934
-852
3x3
/
934/-852=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
934852
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 852, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
934/-852=<div><neg><state>934852<step>00090009<qmul>00000<rem>009<step>00930093<qmul>00000<rem>093<step>09340934<qmul>10852<rem>082<step>08200820<qmul>00000<rem>820<step>82008200<qmul>97668<rem>532<step>53205320<qmul>65112<rem>208<step>20802080<qmul>21704<rem>376<ans>001.096
add
42
4071
1704
868
836
3x3
+
868+836=
scratchpad-v3
positive
null
cascading_carry
++
train
868638
[ { "a_digit": 8, "b_digit": 6, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 4, "serialized": "86041" }, { "a_digit": 6, "b_digit": 3, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "63101" }, { "a_digit":...
868+836=<add><pos><state>868638<step>86041<step>63101<step>88171<ans>4071
add
42
6170
716
439
277
3x3
+
439+277=
scratchpad-v3
positive
null
multi_carry
++
train
934772
[ { "a_digit": 9, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 6, "serialized": "97061" }, { "a_digit": 3, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "37111" }, { "a_digit":...
439+277=<add><pos><state>934772<step>97061<step>37111<step>42170<ans>6170
mul
117
885000
-588
12
-49
2x2
*
12*-49=
scratchpad-v3
negative
null
low_column_sum
+-
train
210940
[ { "a_digit": 2, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "2918018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
12*-49=<mul><neg><state>210940<step>2918018<col>801<step>2408009<step>1909018<col>801<step>2000001<step>1404005<step>0900005<col>500<step>1000000<step>0400000<col>000<step>0000000<col>000<ans>885000
sub
42
2570
-752
188
940
3x3
-
188-940=
scratchpad-v3
negative
null
negative_result
++
train
049881
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 2, "serialized": "08021", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 5, "serialized": "48151", "subtrahend...
188-940=<sub><neg><state>049881<step>08021<step>48151<step>91170<ans>2570
add
42
1190
911
522
389
3x3
+
522+389=
scratchpad-v3
positive
null
multi_carry
++
train
225983
[ { "a_digit": 2, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "29011" }, { "a_digit": 2, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "28111" }, { "a_digit":...
522+389=<add><pos><state>225983<step>29011<step>28111<step>53190<ans>1190
div
160
103.800
103.8
-519
-5
3x1
/
-519/-5=
scratchpad-v3
positive
round-half-up
exact
--
train
519005
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 5, "kind": "quotient_product", "position": 0, "quotient_digit": 1, "quotient_product": 5, "serialized": "10005" }, { "kind": ...
-519/-5=<div><pos><state>519005<step>00050005<qmul>10005<rem>000<step>00010001<qmul>00000<rem>001<step>00190019<qmul>30015<rem>004<step>00400040<qmul>80040<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>103.800
mul
116
639000
936
26
36
2x2
*
26*36=
scratchpad-v3
positive
null
low_column_sum
++
train
620630
[ { "a_digit": 6, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "6636036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
26*36=<mul><pos><state>620630<step>6636036<col>603<step>6318021<step>2612033<col>303<step>6000003<step>2306009<step>0600009<col>900<step>2000000<step>0300000<col>000<step>0000000<col>000<ans>639000
mul
117
084000
-480
1
-480
1x3
*
1*-480=
scratchpad-v3
negative
null
identity
+-
train
100084
[ { "a_digit": 1, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "1000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
1*-480=<mul><neg><state>100084<step>1000000<col>000<step>1808008<step>0000008<col>800<step>1404004<step>0800004<step>0000004<col>400<step>0400000<step>0800000<col>000<step>0400000<col>000<ans>084000
div
162
000.635
0.635
-195
-307
3x3
/
-195/-307=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
195307
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 307, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-195/-307=<div><pos><state>195307<step>00010001<qmul>00000<rem>001<step>00190019<qmul>00000<rem>019<step>01950195<qmul>00000<rem>195<step>19501950<qmul>61842<rem>108<step>10801080<qmul>30921<rem>159<step>15901590<qmul>51535<rem>055<step>05500550<qmul>10307<rem>243<ans>000.635
add
44
3570
-753
-463
-290
3x3
+
-463+-290=
scratchpad-v3
negative
null
single_carry
--
train
364092
[ { "a_digit": 3, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "30030" }, { "a_digit": 6, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 5, "serialized": "69051" }, { "a_digit":...
-463+-290=<add><neg><state>364092<step>30030<step>69051<step>42170<ans>3570
div
159
001.797
1.797
124
69
3x2
/
124/69=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
124069
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 69, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
124/69=<div><pos><state>124069<step>00010001<qmul>00000<rem>001<step>00120012<qmul>00000<rem>012<step>01240124<qmul>10069<rem>055<step>05500550<qmul>70483<rem>067<step>06700670<qmul>90621<rem>049<step>04900490<qmul>70483<rem>007<step>00700070<qmul>10069<rem>001<ans>001.797
div
159
032.556
-32.556
-293
9
3x1
/
-293/9=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
293009
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 9, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-293/9=<div><neg><state>293009<step>00020002<qmul>00000<rem>002<step>00290029<qmul>30027<rem>002<step>00230023<qmul>20018<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<step>00500050<qmul>50045<rem>005<ans>032.556
add
44
5640
-465
-253
-212
3x3
+
-253+-212=
scratchpad-v3
negative
null
no_carry
--
train
352212
[ { "a_digit": 3, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "32050" }, { "a_digit": 5, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "51060" }, { "a_digit":...
-253+-212=<add><neg><state>352212<step>32050<step>51060<step>22040<ans>5640
add
41
7960
697
670
27
3x2
+
670+27=
scratchpad-v3
positive
null
no_carry
++
train
076720
[ { "a_digit": 0, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "07070" }, { "a_digit": 7, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "72090" }, { "a_digit":...
670+27=<add><pos><state>076720<step>07070<step>72090<step>60060<ans>7960
add
44
7311
-1137
-824
-313
3x3
+
-824+-313=
scratchpad-v3
negative
null
overflow
--
val
428313
[ { "a_digit": 4, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "43070" }, { "a_digit": 2, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "21030" }, { "a_digit":...
-824+-313=<add><neg><state>428313<step>43070<step>21030<step>83011<ans>7311
div
157
000.000
0
0
94
1x2
/
0/94=
scratchpad-v3
positive
round-half-up
zero_numerator
++
train
000094
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 94, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
0/94=<div><pos><state>000094<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>000.000
div
160
000.678
0.678
-59
-87
2x2
/
-59/-87=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
059087
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 87, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-59/-87=<div><pos><state>059087<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00590059<qmul>00000<rem>059<step>05900590<qmul>60522<rem>068<step>06800680<qmul>70609<rem>071<step>07100710<qmul>80696<rem>014<step>01400140<qmul>10087<rem>053<ans>000.678
mul
119
311412
-214113
479
-447
3x3
*
479*-447=
scratchpad-v3
negative
null
medium_column_sum
+-
val
974744
[ { "a_digit": 9, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 63, "running_total": 63, "serialized": "9763063", "term_index": 0 }, { "carry_in": 0, "carry_out": 6, "column": 0, "column_sum": 63, "kind": "column", ...
479*-447=<mul><neg><state>974744<step>9763063<col>306<step>9436042<step>7749091<col>109<step>9436045<step>7428073<step>4728101<col>110<step>7428038<step>4416054<col>405<step>4416021<col>102<ans>311412
sub
44
3400
43
-182
-225
3x3
-
-182--225=
scratchpad-v3
positive
null
single_borrow
--
train
522281
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 3, "serialized": "52030", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 4, "serialized": "28041", "subtrahend...
-182--225=<sub><pos><state>522281<step>52030<step>28041<step>21100<ans>3400
sub
43
3000
-3
-414
411
3x3
+
-414+411=
scratchpad-v3
negative
null
magnitude_subtraction
-+
train
414114
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 4, "output_digit": 3, "serialized": "41030", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 0, "serialized": "11000", "subtrahend...
-414+411=<sub><neg><state>414114<step>41030<step>11000<step>44000<ans>3000
mul
118
329084
480923
811
593
3x3
*
811*593=
scratchpad-v3
positive
null
medium_column_sum
++
val
118395
[ { "a_digit": 1, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 3, "running_total": 3, "serialized": "1303003", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 3, "kind": "column", "o...
811*593=<mul><pos><state>118395<step>1303003<col>300<step>1909009<step>1303012<col>201<step>1505006<step>1909015<step>8324039<col>903<step>1505008<step>8972080<col>008<step>8540048<col>804<ans>329084
div
161
001.066
-1.066
-963
903
3x3
/
-963/903=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
963903
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 903, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-963/903=<div><neg><state>963903<step>00090009<qmul>00000<rem>009<step>00960096<qmul>00000<rem>096<step>09630963<qmul>10903<rem>060<step>06000600<qmul>00000<rem>600<step>60006000<qmul>65418<rem>582<step>58205820<qmul>65418<rem>402<step>40204020<qmul>43612<rem>408<ans>001.066
add
44
0911
-1190
-417
-773
3x3
+
-417+-773=
scratchpad-v3
negative
null
overflow
--
train
714377
[ { "a_digit": 7, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "73001" }, { "a_digit": 1, "b_digit": 7, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "17190" }, { "a_digit":...
-417+-773=<add><neg><state>714377<step>73001<step>17190<step>47011<ans>0911
mul
116
546100
1645
47
35
2x2
*
47*35=
scratchpad-v3
positive
null
low_column_sum
++
train
740530
[ { "a_digit": 7, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 35, "running_total": 35, "serialized": "7535035", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 35, "kind": "column", ...
47*35=<mul><pos><state>740530<step>7535035<col>503<step>7321024<step>4520044<col>404<step>7000004<step>4312016<step>0500016<col>601<step>4000001<step>0300001<col>100<step>0000000<col>000<ans>546100
div
161
001.000
-1
-622
622
3x3
/
-622/622=
scratchpad-v3
negative
round-half-up
exact
-+
train
622622
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 622, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-622/622=<div><neg><state>622622<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06220622<qmul>10622<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.000
add
43
6770
776
370
-406
3x3
-
370--406=
scratchpad-v3
positive
null
magnitude_addition
+-
train
073604
[ { "a_digit": 0, "b_digit": 6, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "06060" }, { "a_digit": 7, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "70070" }, { "a_digit":...
370--406=<add><pos><state>073604<step>06060<step>70070<step>34070<ans>6770
div
158
000.490
0.49
48
98
2x2
/
48/98=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
048098
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 98, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
48/98=<div><pos><state>048098<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00480048<qmul>00000<rem>048<step>04800480<qmul>40392<rem>088<step>08800880<qmul>80784<rem>096<step>09600960<qmul>90882<rem>078<step>07800780<qmul>70686<rem>094<ans>000.490
add
42
5280
-825
-24
801
2x3
-
-24-801=
scratchpad-v3
negative
null
magnitude_addition
-+
train
420108
[ { "a_digit": 4, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "41050" }, { "a_digit": 2, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "20020" }, { "a_digit":...
-24-801=<add><neg><state>420108<step>41050<step>20020<step>08080<ans>5280
div
159
000.357
-0.357
-15
42
2x2
/
-15/42=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
015042
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 42, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-15/42=<div><neg><state>015042<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00150015<qmul>00000<rem>015<step>01500150<qmul>30126<rem>024<step>02400240<qmul>50210<rem>030<step>03000300<qmul>70294<rem>006<step>00600060<qmul>10042<rem>018<ans>000.357
div
161
001.543
-1.543
-466
302
3x3
/
-466/302=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
466302
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 302, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-466/302=<div><neg><state>466302<step>00040004<qmul>00000<rem>004<step>00460046<qmul>00000<rem>046<step>04660466<qmul>10302<rem>164<step>16401640<qmul>51510<rem>130<step>13001300<qmul>41208<rem>092<step>09200920<qmul>30906<rem>014<step>01400140<qmul>00000<rem>140<ans>001.543
add
42
9950
599
475
124
3x3
+
475+124=
scratchpad-v3
positive
null
no_carry
++
train
574421
[ { "a_digit": 5, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 9, "serialized": "54090" }, { "a_digit": 7, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "72090" }, { "a_digit":...
475+124=<add><pos><state>574421<step>54090<step>72090<step>41050<ans>9950
sub
41
8100
18
103
85
3x2
-
103-85=
scratchpad-v3
positive
null
borrow_through_zero
++
train
301580
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 8, "serialized": "35081", "subtrahend_digit": 5 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
103-85=<sub><pos><state>301580<step>35081<step>08111<step>10100<ans>8100
div
160
002.398
-2.398
223
-93
3x2
/
223/-93=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
223093
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 93, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
223/-93=<div><neg><state>223093<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02230223<qmul>20186<rem>037<step>03700370<qmul>30279<rem>091<step>09100910<qmul>90837<rem>073<step>07300730<qmul>70651<rem>079<step>07900790<qmul>80744<rem>046<ans>002.398
sub
40
7000
-7
10
17
2x2
-
10-17=
scratchpad-v3
negative
null
negative_result
++
train
710010
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 7, "output_digit": 7, "serialized": "70070", "subtrahend_digit": 0 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 0, "serialized": "11000", "subtrahend...
10-17=<sub><neg><state>710010<step>70070<step>11000<step>00000<ans>7000
sub
40
2000
-2
81
83
2x2
-
81-83=
scratchpad-v3
negative
null
negative_result
++
train
380180
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 3, "output_digit": 2, "serialized": "31020", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 8, "output_digit": 0, "serialized": "88000", "subtrahend...
81-83=<sub><neg><state>380180<step>31020<step>88000<step>00000<ans>2000
div
161
005.361
5.361
-445
-83
3x2
/
-445/-83=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
test
445083
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 83, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-445/-83=<div><pos><state>445083<step>00040004<qmul>00000<rem>004<step>00440044<qmul>00000<rem>044<step>04450445<qmul>50415<rem>030<step>03000300<qmul>30249<rem>051<step>05100510<qmul>60498<rem>012<step>01200120<qmul>10083<rem>037<step>03700370<qmul>40332<rem>038<ans>005.361
sub
42
5190
915
999
-84
3x2
+
999+-84=
scratchpad-v3
positive
null
magnitude_subtraction
+-
train
999480
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 5, "serialized": "94050", "subtrahend_digit": 4 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 1, "serialized": "98010", "subtrahend...
999+-84=<sub><pos><state>999480<step>94050<step>98010<step>90090<ans>5190
sub
43
8160
618
-89
-707
2x3
-
-89--707=
scratchpad-v3
positive
null
borrow_through_zero
--
train
707980
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 7, "output_digit": 8, "serialized": "79081", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
-89--707=<sub><pos><state>707980<step>79081<step>08111<step>70160<ans>8160
div
161
001.000
-1
894
-894
3x3
/
894/-894=
scratchpad-v3
negative
round-half-up
exact
+-
train
894894
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 894, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
894/-894=<div><neg><state>894894<step>00080008<qmul>00000<rem>008<step>00890089<qmul>00000<rem>089<step>08940894<qmul>10894<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>001.000
mul
118
033100
1330
-95
-14
2x2
*
-95*-14=
scratchpad-v3
positive
null
low_column_sum
--
train
590410
[ { "a_digit": 5, "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", ...
-95*-14=<mul><pos><state>590410<step>5420020<col>002<step>5105007<step>9436043<col>304<step>5000004<step>9109013<step>0400013<col>301<step>9000001<step>0100001<col>100<step>0000000<col>000<ans>033100
add
44
6311
-1136
-190
-946
3x3
+
-190+-946=
scratchpad-v3
negative
null
overflow
--
train
091649
[ { "a_digit": 0, "b_digit": 6, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "06060" }, { "a_digit": 9, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "94031" }, { "a_digit":...
-190+-946=<add><neg><state>091649<step>06060<step>94031<step>19111<ans>6311
mul
116
239100
1932
21
92
2x2
*
21*92=
scratchpad-v3
positive
null
low_column_sum
++
train
120290
[ { "a_digit": 1, "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...
21*92=<mul><pos><state>120290<step>1202002<col>200<step>1909009<step>2204013<col>301<step>1000001<step>2918019<step>0200019<col>901<step>2000001<step>0900001<col>100<step>0000000<col>000<ans>239100
mul
119
638638
-836836
-847
988
3x3
*
-847*988=
scratchpad-v3
negative
null
high_column_sum
-+
train
748889
[ { "a_digit": 7, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 56, "running_total": 56, "serialized": "7856056", "term_index": 0 }, { "carry_in": 0, "carry_out": 5, "column": 0, "column_sum": 56, "kind": "column", ...
-847*988=<mul><neg><state>748889<step>7856056<col>605<step>7856061<step>4832093<col>309<step>7963072<step>4832104<step>8864168<col>816<step>4936052<step>8864116<col>611<step>8972083<col>308<ans>638638
div
158
045.000
45
270
6
3x1
/
270/6=
scratchpad-v3
positive
round-half-up
exact
++
train
270006
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
270/6=<div><pos><state>270006<step>00020002<qmul>00000<rem>002<step>00270027<qmul>40024<rem>003<step>00300030<qmul>50030<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>045.000
div
160
000.588
-0.588
-80
136
2x3
/
-80/136=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
080136
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 136, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-80/136=<div><neg><state>080136<step>00000000<qmul>00000<rem>000<step>00080008<qmul>00000<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>50680<rem>120<step>12001200<qmul>81088<rem>112<step>11201120<qmul>81088<rem>032<step>03200320<qmul>20272<rem>048<ans>000.588
div
160
001.977
1.977
957
484
3x3
/
957/484=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
957484
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 484, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
957/484=<div><pos><state>957484<step>00090009<qmul>00000<rem>009<step>00950095<qmul>00000<rem>095<step>09570957<qmul>10484<rem>473<step>47304730<qmul>94356<rem>374<step>37403740<qmul>73388<rem>352<step>35203520<qmul>73388<rem>132<step>13201320<qmul>20968<rem>352<ans>001.977
add
42
1320
-231
-89
142
2x3
-
-89-142=
scratchpad-v3
negative
null
magnitude_addition
-+
train
980241
[ { "a_digit": 9, "b_digit": 2, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "92011" }, { "a_digit": 8, "b_digit": 4, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "84131" }, { "a_digit":...
-89-142=<add><neg><state>980241<step>92011<step>84131<step>01120<ans>1320
div
158
000.222
0.222
10
45
2x2
/
10/45=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
010045
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 45, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
10/45=<div><pos><state>010045<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<step>01000100<qmul>20090<rem>010<ans>000.222
div
158
077.833
77.833
467
6
3x1
/
467/6=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
test
467006
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
467/6=<div><pos><state>467006<step>00040004<qmul>00000<rem>004<step>00460046<qmul>70042<rem>004<step>00470047<qmul>70042<rem>005<step>00500050<qmul>80048<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<ans>077.833
div
161
002.824
-2.824
-768
272
3x3
/
-768/272=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
768272
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 272, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-768/272=<div><neg><state>768272<step>00070007<qmul>00000<rem>007<step>00760076<qmul>00000<rem>076<step>07680768<qmul>20544<rem>224<step>22402240<qmul>82176<rem>064<step>06400640<qmul>20544<rem>096<step>09600960<qmul>30816<rem>144<step>14401440<qmul>51360<rem>080<ans>002.824
mul
119
525098
-890525
-895
995
3x3
*
-895*995=
scratchpad-v3
negative
null
high_column_sum
-+
train
598599
[ { "a_digit": 5, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 25, "running_total": 25, "serialized": "5525025", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 25, "kind": "column", ...
-895*995=<mul><neg><state>598599<step>5525025<col>502<step>5945047<step>9545092<col>209<step>5945054<step>9981135<step>8540175<col>517<step>9981098<step>8972170<col>017<step>8972089<col>908<ans>525098
add
42
3790
973
485
488
3x3
+
485+488=
scratchpad-v3
positive
null
multi_carry
++
train
584884
[ { "a_digit": 5, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "58031" }, { "a_digit": 8, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 7, "serialized": "88171" }, { "a_digit":...
485+488=<add><pos><state>584884<step>58031<step>88171<step>44190<ans>3790
mul
120
165792
297561
-781
-381
3x3
*
-781*-381=
scratchpad-v3
positive
null
medium_column_sum
--
train
187183
[ { "a_digit": 1, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 1, "running_total": 1, "serialized": "1101001", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 1, "kind": "column", "o...
-781*-381=<mul><pos><state>187183<step>1101001<col>100<step>1808008<step>8108016<col>601<step>1303004<step>8864068<step>7107075<col>507<step>8324031<step>7856087<col>708<step>7321029<col>902<ans>165792
mul
118
241243
342142
347
986
3x3
*
347*986=
scratchpad-v3
positive
null
medium_column_sum
++
val
743689
[ { "a_digit": 7, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 42, "running_total": 42, "serialized": "7642042", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 42, "kind": "column", ...
347*986=<mul><pos><state>743689<step>7642042<col>204<step>7856060<step>4624084<col>408<step>7963071<step>4832103<step>3618121<col>112<step>4936048<step>3824072<col>207<step>3927034<col>403<ans>241243
mul
118
467100
1764
-49
-36
2x2
*
-49*-36=
scratchpad-v3
positive
null
low_column_sum
--
train
940630
[ { "a_digit": 9, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 54, "running_total": 54, "serialized": "9654054", "term_index": 0 }, { "carry_in": 0, "carry_out": 5, "column": 0, "column_sum": 54, "kind": "column", ...
-49*-36=<mul><pos><state>940630<step>9654054<col>405<step>9327032<step>4624056<col>605<step>9000005<step>4312017<step>0600017<col>701<step>4000001<step>0300001<col>100<step>0000000<col>000<ans>467100
add
43
3580
-853
-461
392
3x3
-
-461-392=
scratchpad-v3
negative
null
magnitude_addition
-+
train
164293
[ { "a_digit": 1, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "12030" }, { "a_digit": 6, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 5, "serialized": "69051" }, { "a_digit":...
-461-392=<add><neg><state>164293<step>12030<step>69051<step>43180<ans>3580
add
42
1180
-811
-71
740
2x3
-
-71-740=
scratchpad-v3
negative
null
magnitude_addition
-+
train
170047
[ { "a_digit": 1, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 1, "serialized": "10010" }, { "a_digit": 7, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "74011" }, { "a_digit":...
-71-740=<add><neg><state>170047<step>10010<step>74011<step>07180<ans>1180
add
42
1761
1671
877
794
3x3
+
877+794=
scratchpad-v3
positive
null
overflow
++
train
778497
[ { "a_digit": 7, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "74011" }, { "a_digit": 7, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 7, "serialized": "79171" }, { "a_digit":...
877+794=<add><pos><state>778497<step>74011<step>79171<step>87161<ans>1761
add
41
9540
-459
-459
0
3x1
+
-459+0=
scratchpad-v3
negative
null
identity
-+
train
954000
[ { "a_digit": 9, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 9, "serialized": "90090" }, { "a_digit": 5, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 5, "serialized": "50050" }, { "a_digit":...
-459+0=<add><neg><state>954000<step>90090<step>50050<step>40040<ans>9540
add
42
2301
1032
771
261
3x3
+
771+261=
scratchpad-v3
positive
null
cascading_carry
++
train
177162
[ { "a_digit": 1, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "11020" }, { "a_digit": 7, "b_digit": 6, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "76031" }, { "a_digit":...
771+261=<add><pos><state>177162<step>11020<step>76031<step>72101<ans>2301
sub
42
8740
478
532
-54
3x2
+
532+-54=
scratchpad-v3
positive
null
magnitude_subtraction
+-
train
235450
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 8, "serialized": "24081", "subtrahend_digit": 4 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 3, "output_digit": 7, "serialized": "35171", "subtrahend...
532+-54=<sub><pos><state>235450<step>24081<step>35171<step>50140<ans>8740