effective_operation
stringclasses
4 values
encoded_tokens
int64
17
162
internal_answer
stringlengths
4
7
natural_answer
stringlengths
1
8
operand_a
int64
-999
999
operand_b
int64
-999
999
operand_digits
stringclasses
9 values
operation
stringclasses
4 values
prompt
stringlengths
4
10
representation
stringclasses
1 value
result_sign
stringclasses
2 values
rounding
stringclasses
1 value
scenario
stringclasses
25 values
sign_pattern
stringclasses
4 values
split
stringclasses
3 values
state
stringlengths
6
6
steps
listlengths
0
21
text
stringlengths
37
276
div
158
080.500
80.5
483
6
3x1
/
483/6=
scratchpad-v3
positive
round-half-up
exact
++
train
483006
[ { "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": ...
483/6=<div><pos><state>483006<step>00040004<qmul>00000<rem>004<step>00480048<qmul>80048<rem>000<step>00030003<qmul>00000<rem>003<step>00300030<qmul>50030<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>080.500
mul
119
684867
-768486
974
-789
3x3
*
974*-789=
scratchpad-v3
negative
null
high_column_sum
+-
train
479987
[ { "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", ...
974*-789=<mul><neg><state>479987<step>4936036<col>603<step>4832035<step>7963098<col>809<step>4728037<step>7856093<step>9981174<col>417<step>7749066<step>9872138<col>813<step>9763076<col>607<ans>684867
mul
118
431029
920134
982
937
3x3
*
982*937=
scratchpad-v3
positive
null
medium_column_sum
++
train
289739
[ { "a_digit": 2, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 14, "running_total": 14, "serialized": "2714014", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 14, "kind": "column", ...
982*937=<mul><pos><state>289739<step>2714014<col>401<step>2306007<step>8756063<col>306<step>2918024<step>8324048<step>9763111<col>111<step>8972083<step>9327110<col>011<step>9981092<col>209<ans>431029
sub
41
7230
327
406
79
3x2
-
406-79=
scratchpad-v3
positive
null
borrow_through_zero
++
train
604970
[ { "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": 2, "serialized": "07121", "subtrahend...
406-79=<sub><pos><state>604970<step>69071<step>07121<step>40130<ans>7230
sub
42
8960
-698
32
-730
2x3
+
32+-730=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
037230
[ { "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": 3, "output_digit": 9, "serialized": "33191", "subtrahend...
32+-730=<sub><neg><state>037230<step>02081<step>33191<step>70160<ans>8960
add
44
1231
-1321
-543
-778
3x3
+
-543+-778=
scratchpad-v3
negative
null
overflow
--
train
345877
[ { "a_digit": 3, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "38011" }, { "a_digit": 4, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "47121" }, { "a_digit":...
-543+-778=<add><neg><state>345877<step>38011<step>47121<step>57131<ans>1231
sub
43
6530
356
-47
-403
2x3
-
-47--403=
scratchpad-v3
positive
null
borrow_through_zero
--
test
304740
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 6, "serialized": "37061", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 5, "serialized": "04151", "subtrahend...
-47--403=<sub><pos><state>304740<step>37061<step>04151<step>40130<ans>6530
add
40
4040
404
404
0
3x1
-
404-0=
scratchpad-v3
positive
null
identity
++
train
404000
[ { "a_digit": 4, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 4, "serialized": "40040" }, { "a_digit": 0, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 0, "serialized": "00000" }, { "a_digit":...
404-0=<add><pos><state>404000<step>40040<step>00000<step>40040<ans>4040
div
159
027.000
27
567
21
3x2
/
567/21=
scratchpad-v3
positive
round-half-up
exact
++
train
567021
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 21, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
567/21=<div><pos><state>567021<step>00050005<qmul>00000<rem>005<step>00560056<qmul>20042<rem>014<step>01470147<qmul>70147<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>027.000
sub
44
5710
175
-398
-573
3x3
-
-398--573=
scratchpad-v3
positive
null
multi_borrow
--
val
375893
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 5, "serialized": "38051", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 7, "output_digit": 7, "serialized": "79171", "subtrahend...
-398--573=<sub><pos><state>375893<step>38051<step>79171<step>53110<ans>5710
add
41
2610
162
35
127
2x3
+
35+127=
scratchpad-v3
positive
null
single_carry
++
train
530721
[ { "a_digit": 5, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "57021" }, { "a_digit": 3, "b_digit": 2, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "32160" }, { "a_digit":...
35+127=<add><pos><state>530721<step>57021<step>32160<step>01010<ans>2610
div
159
005.667
5.667
-51
-9
2x1
/
-51/-9=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
051009
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 9, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-51/-9=<div><pos><state>051009<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00510051<qmul>50045<rem>006<step>00600060<qmul>60054<rem>006<step>00600060<qmul>60054<rem>006<step>00600060<qmul>60054<rem>006<step>00600060<qmul>60054<rem>006<ans>005.667
sub
43
5320
235
-94
-329
2x3
-
-94--329=
scratchpad-v3
positive
null
single_borrow
--
train
923490
[ { "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": 3, "serialized": "29031", "subtrahend...
-94--329=<sub><pos><state>923490<step>94050<step>29031<step>30120<ans>5320
div
158
000.899
0.899
80
89
2x2
/
80/89=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
080089
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 89, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
80/89=<div><pos><state>080089<step>00000000<qmul>00000<rem>000<step>00080008<qmul>00000<rem>008<step>00800080<qmul>00000<rem>080<step>08000800<qmul>80712<rem>088<step>08800880<qmul>90801<rem>079<step>07900790<qmul>80712<rem>078<step>07800780<qmul>80712<rem>068<ans>000.899
mul
120
258505
505852
-692
-731
3x3
*
-692*-731=
scratchpad-v3
positive
null
medium_column_sum
--
train
296137
[ { "a_digit": 2, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 2, "running_total": 2, "serialized": "2102002", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 2, "kind": "column", "o...
-692*-731=<mul><pos><state>296137<step>2102002<col>200<step>2306006<step>9109015<col>501<step>2714015<step>9327042<step>6106048<col>804<step>9763067<step>6318085<col>508<step>6742050<col>005<ans>258505
mul
117
050750
57050
70
815
2x3
*
70*815=
scratchpad-v3
positive
null
contains_zero_digit
++
train
070518
[ { "a_digit": 0, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0500000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
70*815=<mul><pos><state>070518<step>0500000<col>000<step>0100000<step>7535035<col>503<step>0800003<step>7107010<step>0500010<col>001<step>7856057<step>0100057<col>705<step>0800005<col>500<ans>050750
add
43
5380
-835
-51
-784
2x3
+
-51+-784=
scratchpad-v3
negative
null
single_carry
--
val
150487
[ { "a_digit": 1, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "14050" }, { "a_digit": 5, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "58031" }, { "a_digit":...
-51+-784=<add><neg><state>150487<step>14050<step>58031<step>07180<ans>5380
add
44
1801
-1081
-788
-293
3x3
+
-788+-293=
scratchpad-v3
negative
null
cascading_carry
--
val
887392
[ { "a_digit": 8, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "83011" }, { "a_digit": 8, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 8, "serialized": "89181" }, { "a_digit":...
-788+-293=<add><neg><state>887392<step>83011<step>89181<step>72101<ans>1801
mul
116
844200
2448
36
68
2x2
*
36*68=
scratchpad-v3
positive
null
low_column_sum
++
train
630860
[ { "a_digit": 6, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 48, "running_total": 48, "serialized": "6848048", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 48, "kind": "column", ...
36*68=<mul><pos><state>630860<step>6848048<col>804<step>6636040<step>3824064<col>406<step>6000006<step>3618024<step>0800024<col>402<step>3000002<step>0600002<col>200<step>0000000<col>000<ans>844200
mul
119
616858
-858616
968
-887
3x3
*
968*-887=
scratchpad-v3
negative
null
high_column_sum
+-
train
869788
[ { "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", ...
968*-887=<mul><neg><state>869788<step>8756056<col>605<step>8864069<step>6742111<col>111<step>8864075<step>6848123<step>9763186<col>618<step>6848066<step>9872138<col>813<step>9872085<col>508<ans>616858
mul
118
805575
575508
796
723
3x3
*
796*723=
scratchpad-v3
positive
null
medium_column_sum
++
train
697327
[ { "a_digit": 6, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "6318018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
796*723=<mul><pos><state>697327<step>6318018<col>801<step>6212013<step>9327040<col>004<step>6742046<step>9218064<step>7321085<col>508<step>9763071<step>7214085<col>508<step>7749057<col>705<ans>805575
mul
118
614857
758416
856
886
3x3
*
856*886=
scratchpad-v3
positive
null
medium_column_sum
++
train
658688
[ { "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", ...
856*886=<mul><pos><state>658688<step>6636036<col>603<step>6848051<step>5630081<col>108<step>6848056<step>5840096<step>8648144<col>414<step>5840054<step>8864118<col>811<step>8864075<col>507<ans>614857
add
44
0290
-920
-561
-359
3x3
+
-561+-359=
scratchpad-v3
negative
null
multi_carry
--
train
165953
[ { "a_digit": 1, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "19001" }, { "a_digit": 6, "b_digit": 5, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "65121" }, { "a_digit":...
-561+-359=<add><neg><state>165953<step>19001<step>65121<step>53190<ans>0290
div
158
000.509
0.509
27
53
2x2
/
27/53=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
027053
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 53, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
27/53=<div><pos><state>027053<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00270027<qmul>00000<rem>027<step>02700270<qmul>50265<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>90477<rem>023<step>02300230<qmul>40212<rem>018<ans>000.509
div
159
004.704
4.704
461
98
3x2
/
461/98=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
461098
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 98, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
461/98=<div><pos><state>461098<step>00040004<qmul>00000<rem>004<step>00460046<qmul>00000<rem>046<step>04610461<qmul>40392<rem>069<step>06900690<qmul>70686<rem>004<step>00400040<qmul>00000<rem>040<step>04000400<qmul>40392<rem>008<step>00800080<qmul>00000<rem>080<ans>004.704
mul
116
405000
504
504
1
3x1
*
504*1=
scratchpad-v3
positive
null
identity
++
train
405100
[ { "a_digit": 4, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 4, "running_total": 4, "serialized": "4104004", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 4, "kind": "column", "o...
504*1=<mul><pos><state>405100<step>4104004<col>400<step>4000000<step>0100000<col>000<step>4000000<step>0000000<step>5105005<col>500<step>0000000<step>5000000<col>000<step>5000000<col>000<ans>405000
div
158
000.137
-0.137
-7
51
1x2
/
-7/51=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
007051
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 51, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-7/51=<div><neg><state>007051<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00700070<qmul>10051<rem>019<step>01900190<qmul>30153<rem>037<step>03700370<qmul>70357<rem>013<step>01300130<qmul>20102<rem>028<ans>000.137
div
158
000.034
-0.034
-1
29
1x2
/
-1/29=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
001029
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 29, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-1/29=<div><neg><state>001029<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>30087<rem>013<step>01300130<qmul>40116<rem>014<step>01400140<qmul>40116<rem>024<ans>000.034
add
42
7620
267
123
144
3x3
+
123+144=
scratchpad-v3
positive
null
no_carry
++
train
321441
[ { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "34070" }, { "a_digit": 2, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "24060" }, { "a_digit":...
123+144=<add><pos><state>321441<step>34070<step>24060<step>11020<ans>7620
sub
43
8460
648
-159
807
3x3
+
-159+807=
scratchpad-v3
positive
null
magnitude_subtraction
-+
train
708951
[ { "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": 4, "serialized": "05141", "subtrahend...
-159+807=<sub><pos><state>708951<step>79081<step>05141<step>81160<ans>8460
mul
117
431400
-4134
-53
78
2x2
*
-53*78=
scratchpad-v3
negative
null
low_column_sum
-+
train
350870
[ { "a_digit": 3, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 24, "running_total": 24, "serialized": "3824024", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 24, "kind": "column", ...
-53*78=<mul><neg><state>350870<step>3824024<col>402<step>3721023<step>5840063<col>306<step>3000006<step>5735041<step>0800041<col>104<step>5000004<step>0700004<col>400<step>0000000<col>000<ans>431400
div
160
000.444
0.444
220
496
3x3
/
220/496=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
220496
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 496, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
220/496=<div><pos><state>220496<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02200220<qmul>00000<rem>220<step>22002200<qmul>41984<rem>216<step>21602160<qmul>41984<rem>176<step>17601760<qmul>31488<rem>272<step>27202720<qmul>52480<rem>240<ans>000.444
div
162
001.926
1.926
-917
-476
3x3
/
-917/-476=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
val
917476
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 476, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-917/-476=<div><pos><state>917476<step>00090009<qmul>00000<rem>009<step>00910091<qmul>00000<rem>091<step>09170917<qmul>10476<rem>441<step>44104410<qmul>94284<rem>126<step>12601260<qmul>20952<rem>308<step>30803080<qmul>62856<rem>224<step>22402240<qmul>41904<rem>336<ans>001.926
sub
41
0720
-270
3
-273
1x3
+
3+-273=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
372300
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 3, "output_digit": 0, "serialized": "33000", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 7, "serialized": "70070", "subtrahend...
3+-273=<sub><neg><state>372300<step>33000<step>70070<step>20020<ans>0720
sub
42
6600
66
544
478
3x3
-
544-478=
scratchpad-v3
positive
null
multi_borrow
++
train
445874
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 6, "serialized": "48061", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 6, "serialized": "47161", "subtrahend...
544-478=<sub><pos><state>445874<step>48061<step>47161<step>54100<ans>6600
div
159
011.231
11.231
730
65
3x2
/
730/65=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
train
730065
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 65, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
730/65=<div><pos><state>730065<step>00070007<qmul>00000<rem>007<step>00730073<qmul>10065<rem>008<step>00800080<qmul>10065<rem>015<step>01500150<qmul>20130<rem>020<step>02000200<qmul>30195<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>70455<rem>045<ans>011.231
add
44
2021
-1202
-478
-724
3x3
+
-478+-724=
scratchpad-v3
negative
null
cascading_carry
--
train
874427
[ { "a_digit": 8, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "84021" }, { "a_digit": 7, "b_digit": 2, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "72101" }, { "a_digit":...
-478+-724=<add><neg><state>874427<step>84021<step>72101<step>47121<ans>2021
mul
119
533817
-718335
-939
765
3x3
*
-939*765=
scratchpad-v3
negative
null
medium_column_sum
-+
train
939567
[ { "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", ...
-939*765=<mul><neg><state>939567<step>9545045<col>504<step>9654058<step>3515073<col>307<step>9763070<step>3618088<step>9545133<col>313<step>3721034<step>9654088<col>808<step>9763071<col>107<ans>533817
sub
42
2520
252
405
153
3x3
-
405-153=
scratchpad-v3
positive
null
single_borrow
++
train
504351
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 2, "serialized": "53020", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 5, "serialized": "05051", "subtrahend...
405-153=<sub><pos><state>504351<step>53020<step>05051<step>41120<ans>2520
add
44
2001
-1002
-587
-415
3x3
+
-587+-415=
scratchpad-v3
negative
null
cascading_carry
--
train
785514
[ { "a_digit": 7, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "75021" }, { "a_digit": 8, "b_digit": 1, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "81101" }, { "a_digit":...
-587+-415=<add><neg><state>785514<step>75021<step>81101<step>54101<ans>2001
sub
43
7510
-157
672
-829
3x3
+
672+-829=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
928276
[ { "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": 5, "serialized": "27051", "subtrahend...
672+-829=<sub><neg><state>928276<step>92070<step>27051<step>86110<ans>7510
sub
44
9340
439
-387
-826
3x3
-
-387--826=
scratchpad-v3
positive
null
multi_borrow
--
train
628783
[ { "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": 2, "output_digit": 3, "serialized": "28131", "subtrahend...
-387--826=<sub><pos><state>628783<step>67091<step>28131<step>83140<ans>9340
sub
40
5100
15
36
21
2x2
-
36-21=
scratchpad-v3
positive
null
no_borrow
++
train
630120
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 6, "output_digit": 5, "serialized": "61050", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 3, "output_digit": 1, "serialized": "32010", "subtrahend...
36-21=<sub><pos><state>630120<step>61050<step>32010<step>00000<ans>5100
add
44
5301
-1035
-435
-600
3x3
+
-435+-600=
scratchpad-v3
negative
null
overflow
--
train
534006
[ { "a_digit": 5, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "50050" }, { "a_digit": 3, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "30030" }, { "a_digit":...
-435+-600=<add><neg><state>534006<step>50050<step>30030<step>46001<ans>5301
mul
119
275220
22572
-594
-38
3x2
*
-594*-38=
scratchpad-v3
positive
null
medium_column_sum
--
test
495830
[ { "a_digit": 4, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 32, "running_total": 32, "serialized": "4832032", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 32, "kind": "column", ...
-594*-38=<mul><pos><state>495830<step>4832032<col>203<step>4312015<step>9872087<col>708<step>4000008<step>9327035<step>5840075<col>507<step>9000007<step>5315022<col>202<step>5000002<col>200<ans>275220
add
41
7640
467
408
59
3x2
+
408+59=
scratchpad-v3
positive
null
single_carry
++
train
804950
[ { "a_digit": 8, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 7, "serialized": "89071" }, { "a_digit": 0, "b_digit": 5, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "05160" }, { "a_digit":...
408+59=<add><pos><state>804950<step>89071<step>05160<step>40040<ans>7640
div
161
012.023
12.023
-529
-44
3x2
/
-529/-44=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
529044
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 44, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-529/-44=<div><pos><state>529044<step>00050005<qmul>00000<rem>005<step>00520052<qmul>10044<rem>008<step>00890089<qmul>20088<rem>001<step>00100010<qmul>00000<rem>010<step>01000100<qmul>20088<rem>012<step>01200120<qmul>20088<rem>032<step>03200320<qmul>70308<rem>012<ans>012.023
mul
119
330676
-676033
787
-859
3x3
*
787*-859=
scratchpad-v3
negative
null
high_column_sum
+-
train
787958
[ { "a_digit": 7, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 63, "running_total": 63, "serialized": "7963063", "term_index": 0 }, { "carry_in": 0, "carry_out": 6, "column": 0, "column_sum": 63, "kind": "column", ...
787*-859=<mul><neg><state>787958<step>7963063<col>306<step>7535041<step>8972113<col>311<step>7856067<step>8540107<step>7963170<col>017<step>8864081<step>7535116<col>611<step>7856067<col>706<ans>330676
mul
118
689380
-83986
-857
98
3x2
*
-857*98=
scratchpad-v3
negative
null
medium_column_sum
-+
val
758890
[ { "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", ...
-857*98=<mul><neg><state>758890<step>7856056<col>605<step>7963068<step>5840108<col>810<step>7000010<step>5945055<step>8864119<col>911<step>5000011<step>8972083<col>308<step>8000008<col>800<ans>689380
sub
42
8910
-198
28
-226
2x3
+
28+-226=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
622820
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 8, "serialized": "68081", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 9, "serialized": "22191", "subtrahend...
28+-226=<sub><neg><state>622820<step>68081<step>22191<step>20110<ans>8910
add
44
7090
-907
-798
-109
3x3
+
-798+-109=
scratchpad-v3
negative
null
cascading_carry
--
train
897901
[ { "a_digit": 8, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 7, "serialized": "89071" }, { "a_digit": 9, "b_digit": 0, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "90101" }, { "a_digit":...
-798+-109=<add><neg><state>897901<step>89071<step>90101<step>71190<ans>7090
div
159
078.750
-78.75
630
-8
3x1
/
630/-8=
scratchpad-v3
negative
round-half-up
exact
+-
train
630008
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 8, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
630/-8=<div><neg><state>630008<step>00060006<qmul>00000<rem>006<step>00630063<qmul>70056<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<step>00000000<qmul>00000<rem>000<ans>078.750
div
160
000.737
0.737
-28
-38
2x2
/
-28/-38=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
028038
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 38, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-28/-38=<div><pos><state>028038<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00280028<qmul>00000<rem>028<step>02800280<qmul>70266<rem>014<step>01400140<qmul>30114<rem>026<step>02600260<qmul>60228<rem>032<step>03200320<qmul>80304<rem>016<ans>000.737
add
42
1290
-921
-918
-3
3x1
+
-918+-3=
scratchpad-v3
negative
null
single_carry
--
train
819300
[ { "a_digit": 8, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "83011" }, { "a_digit": 1, "b_digit": 0, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "10120" }, { "a_digit":...
-918+-3=<add><neg><state>819300<step>83011<step>10120<step>90090<ans>1290
sub
42
7520
257
615
358
3x3
-
615-358=
scratchpad-v3
positive
null
multi_borrow
++
train
516853
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 5, "output_digit": 7, "serialized": "58071", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 5, "serialized": "15151", "subtrahend...
615-358=<sub><pos><state>516853<step>58071<step>15151<step>63120<ans>7520
add
42
3201
1023
588
435
3x3
+
588+435=
scratchpad-v3
positive
null
cascading_carry
++
train
885534
[ { "a_digit": 8, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "85031" }, { "a_digit": 8, "b_digit": 3, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "83121" }, { "a_digit":...
588+435=<add><pos><state>885534<step>85031<step>83121<step>54101<ans>3201
sub
40
1000
1
17
16
2x2
-
17-16=
scratchpad-v3
positive
null
no_borrow
++
train
710610
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 7, "output_digit": 1, "serialized": "76010", "subtrahend_digit": 6 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 0, "serialized": "11000", "subtrahend...
17-16=<sub><pos><state>710610<step>76010<step>11000<step>00000<ans>1000
div
160
011.000
-11
836
-76
3x2
/
836/-76=
scratchpad-v3
negative
round-half-up
exact
+-
train
836076
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 76, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
836/-76=<div><neg><state>836076<step>00080008<qmul>00000<rem>008<step>00830083<qmul>10076<rem>007<step>00760076<qmul>10076<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>011.000
div
161
024.816
24.816
-943
-38
3x2
/
-943/-38=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
943038
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 38, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-943/-38=<div><pos><state>943038<step>00090009<qmul>00000<rem>009<step>00940094<qmul>20076<rem>018<step>01830183<qmul>40152<rem>031<step>03100310<qmul>80304<rem>006<step>00600060<qmul>10038<rem>022<step>02200220<qmul>50190<rem>030<step>03000300<qmul>70266<rem>034<ans>024.816
mul
119
226440
44622
-666
-67
3x2
*
-666*-67=
scratchpad-v3
positive
null
repeated_digit
--
train
666760
[ { "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*-67=<mul><pos><state>666760<step>6742042<col>204<step>6636040<step>6742082<col>208<step>6000008<step>6636044<step>6742086<col>608<step>6000008<step>6636044<col>404<step>6000004<col>400<ans>226440
div
160
000.388
0.388
-26
-67
2x2
/
-26/-67=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
026067
[ { "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":...
-26/-67=<div><pos><state>026067<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00260026<qmul>00000<rem>026<step>02600260<qmul>30201<rem>059<step>05900590<qmul>80536<rem>054<step>05400540<qmul>80536<rem>004<step>00400040<qmul>00000<rem>040<ans>000.388
div
162
001.443
1.443
-518
-359
3x3
/
-518/-359=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
val
518359
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 359, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-518/-359=<div><pos><state>518359<step>00050005<qmul>00000<rem>005<step>00510051<qmul>00000<rem>051<step>05180518<qmul>10359<rem>159<step>15901590<qmul>41436<rem>154<step>15401540<qmul>41436<rem>104<step>10401040<qmul>20718<rem>322<step>32203220<qmul>82872<rem>348<ans>001.443
mul
118
071200
2170
-31
-70
2x2
*
-31*-70=
scratchpad-v3
positive
null
contains_zero_digit
--
train
130070
[ { "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...
-31*-70=<mul><pos><state>130070<step>1000000<col>000<step>1707007<step>3000007<col>700<step>1000000<step>3721021<step>0000021<col>102<step>3000002<step>0700002<col>200<step>0000000<col>000<ans>071200
mul
119
810711
-117018
297
-394
3x3
*
297*-394=
scratchpad-v3
negative
null
medium_column_sum
+-
train
792493
[ { "a_digit": 7, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 28, "running_total": 28, "serialized": "7428028", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 28, "kind": "column", ...
297*-394=<mul><neg><state>792493<step>7428028<col>802<step>7963065<step>9436101<col>110<step>7321031<step>9981112<step>2408120<col>012<step>9327039<step>2918057<col>705<step>2306011<col>101<ans>810711
mul
118
470834
438074
754
581
3x3
*
754*581=
scratchpad-v3
positive
null
medium_column_sum
++
train
457185
[ { "a_digit": 4, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 4, "running_total": 4, "serialized": "4104004", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 4, "kind": "column", "o...
754*581=<mul><pos><state>457185<step>4104004<col>400<step>4832032<step>5105037<col>703<step>4520023<step>5840063<step>7107070<col>007<step>5525032<step>7856088<col>808<step>7535043<col>304<ans>470834
add
42
5460
645
456
189
3x3
+
456+189=
scratchpad-v3
positive
null
multi_carry
++
train
654981
[ { "a_digit": 6, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "69051" }, { "a_digit": 5, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 4, "serialized": "58141" }, { "a_digit":...
456+189=<add><pos><state>654981<step>69051<step>58141<step>41160<ans>5460
sub
42
8260
-628
243
871
3x3
-
243-871=
scratchpad-v3
negative
null
negative_result
++
train
178342
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 8, "serialized": "13081", "subtrahend_digit": 3 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 2, "serialized": "74120", "subtrahend...
243-871=<sub><neg><state>178342<step>13081<step>74120<step>82060<ans>8260
div
158
000.149
-0.149
-7
47
1x2
/
-7/47=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
-+
train
007047
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 47, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-7/47=<div><neg><state>007047<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00700070<qmul>10047<rem>023<step>02300230<qmul>40188<rem>042<step>04200420<qmul>80376<rem>044<step>04400440<qmul>90423<rem>017<ans>000.149
mul
117
037000
-730
-1
730
1x3
*
-1*730=
scratchpad-v3
negative
null
identity
-+
train
100037
[ { "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*730=<mul><neg><state>100037<step>1000000<col>000<step>1303003<step>0000003<col>300<step>1707007<step>0300007<step>0000007<col>700<step>0700000<step>0300000<col>000<step>0700000<col>000<ans>037000
mul
119
350940
49053
-591
-83
3x2
*
-591*-83=
scratchpad-v3
positive
null
medium_column_sum
--
train
195380
[ { "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...
-591*-83=<mul><pos><state>195380<step>1303003<col>300<step>1808008<step>9327035<col>503<step>1000003<step>9872075<step>5315090<col>009<step>9000009<step>5840049<col>904<step>5000004<col>400<ans>350940
div
160
015.292
-15.292
-994
65
3x2
/
-994/65=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
test
994065
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 65, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-994/65=<div><neg><state>994065<step>00090009<qmul>00000<rem>009<step>00990099<qmul>10065<rem>034<step>03440344<qmul>50325<rem>019<step>01900190<qmul>20130<rem>060<step>06000600<qmul>90585<rem>015<step>01500150<qmul>20130<rem>020<step>02000200<qmul>30195<rem>005<ans>015.292
mul
118
044330
33440
152
220
3x3
*
152*220=
scratchpad-v3
positive
null
contains_zero_digit
++
train
251022
[ { "a_digit": 2, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "2000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
152*220=<mul><pos><state>251022<step>2000000<col>000<step>2204004<step>5000004<col>400<step>2204004<step>5210014<step>1000014<col>401<step>5210011<step>1202013<col>301<step>1202003<col>300<ans>044330
mul
117
441200
-2144
32
-67
2x2
*
32*-67=
scratchpad-v3
negative
null
low_column_sum
+-
train
230760
[ { "a_digit": 2, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 14, "running_total": 14, "serialized": "2714014", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 14, "kind": "column", ...
32*-67=<mul><neg><state>230760<step>2714014<col>401<step>2612013<step>3721034<col>403<step>2000003<step>3618021<step>0700021<col>102<step>3000002<step>0600002<col>200<step>0000000<col>000<ans>441200
div
161
005.444
5.444
-343
-63
3x2
/
-343/-63=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
343063
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 63, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-343/-63=<div><pos><state>343063<step>00030003<qmul>00000<rem>003<step>00340034<qmul>00000<rem>034<step>03430343<qmul>50315<rem>028<step>02800280<qmul>40252<rem>028<step>02800280<qmul>40252<rem>028<step>02800280<qmul>40252<rem>028<step>02800280<qmul>40252<rem>028<ans>005.444
mul
118
827172
271728
272
999
3x3
*
272*999=
scratchpad-v3
positive
null
repeated_digit
++
val
272999
[ { "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", ...
272*999=<mul><pos><state>272999<step>2918018<col>801<step>2918019<step>7963082<col>208<step>2918026<step>7963089<step>2918107<col>710<step>7963073<step>2918091<col>109<step>2918027<col>702<ans>827172
mul
118
320100
1023
-93
-11
2x2
*
-93*-11=
scratchpad-v3
positive
null
repeated_digit
--
train
390110
[ { "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...
-93*-11=<mul><pos><state>390110<step>3103003<col>300<step>3103003<step>9109012<col>201<step>3000001<step>9109010<step>0100010<col>001<step>9000001<step>0100001<col>100<step>0000000<col>000<ans>320100
sub
42
5600
65
520
455
3x3
-
520-455=
scratchpad-v3
positive
null
multi_borrow
++
test
025554
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 5, "serialized": "05051", "subtrahend_digit": 5 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 6, "serialized": "25161", "subtrahend...
520-455=<sub><pos><state>025554<step>05051<step>25161<step>54100<ans>5600
mul
118
659300
3956
-43
-92
2x2
*
-43*-92=
scratchpad-v3
positive
null
low_column_sum
--
train
340290
[ { "a_digit": 3, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 6, "running_total": 6, "serialized": "3206006", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 6, "kind": "column", "o...
-43*-92=<mul><pos><state>340290<step>3206006<col>600<step>3927027<step>4208035<col>503<step>3000003<step>4936039<step>0200039<col>903<step>4000003<step>0900003<col>300<step>0000000<col>000<ans>659300
add
43
2350
-532
-80
-452
2x3
+
-80+-452=
scratchpad-v3
negative
null
single_carry
--
train
080254
[ { "a_digit": 0, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "02020" }, { "a_digit": 8, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "85031" }, { "a_digit":...
-80+-452=<add><neg><state>080254<step>02020<step>85031<step>04150<ans>2350
sub
42
9730
379
534
155
3x3
-
534-155=
scratchpad-v3
positive
null
multi_borrow
++
train
435551
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 4, "output_digit": 9, "serialized": "45091", "subtrahend_digit": 5 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 3, "output_digit": 7, "serialized": "35171", "subtrahend...
534-155=<sub><pos><state>435551<step>45091<step>35171<step>51130<ans>9730
div
159
000.058
0.058
52
900
2x3
/
52/900=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
052900
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 900, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
52/900=<div><pos><state>052900<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00520052<qmul>00000<rem>052<step>05200520<qmul>00000<rem>520<step>52005200<qmul>54500<rem>700<step>70007000<qmul>76300<rem>700<step>70007000<qmul>76300<rem>700<ans>000.058
mul
118
063171
171360
288
595
3x3
*
288*595=
scratchpad-v3
positive
null
medium_column_sum
++
train
882595
[ { "a_digit": 8, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 40, "running_total": 40, "serialized": "8540040", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 40, "kind": "column", ...
288*595=<mul><pos><state>882595<step>8540040<col>004<step>8972076<step>8540116<col>611<step>8540051<step>8972123<step>2510133<col>313<step>8540053<step>2918071<col>107<step>2510017<col>701<ans>063171
add
42
2180
812
599
213
3x3
+
599+213=
scratchpad-v3
positive
null
multi_carry
++
train
995312
[ { "a_digit": 9, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "93021" }, { "a_digit": 9, "b_digit": 1, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "91111" }, { "a_digit":...
599+213=<add><pos><state>995312<step>93021<step>91111<step>52180<ans>2180
div
161
008.835
8.835
-857
-97
3x2
/
-857/-97=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
857097
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 97, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-857/-97=<div><pos><state>857097<step>00080008<qmul>00000<rem>008<step>00850085<qmul>00000<rem>085<step>08570857<qmul>80776<rem>081<step>08100810<qmul>80776<rem>034<step>03400340<qmul>30291<rem>049<step>04900490<qmul>50485<rem>005<step>00500050<qmul>00000<rem>050<ans>008.835
mul
118
620992
299026
434
689
3x3
*
434*689=
scratchpad-v3
positive
null
medium_column_sum
++
train
434986
[ { "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", ...
434*689=<mul><pos><state>434986<step>4936036<col>603<step>4832035<step>3927062<col>206<step>4624030<step>3824054<step>4936090<col>009<step>3618027<step>4832059<col>905<step>4624029<col>902<ans>620992
sub
44
6630
-366
-912
-546
3x3
-
-912--546=
scratchpad-v3
negative
null
negative_result
--
train
219645
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 6, "serialized": "26061", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 6, "serialized": "14161", "subtrahend...
-912--546=<sub><neg><state>219645<step>26061<step>14161<step>95130<ans>6630
div
159
000.285
0.285
53
186
2x3
/
53/186=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
053186
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 186, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
53/186=<div><pos><state>053186<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00530053<qmul>00000<rem>053<step>05300530<qmul>20372<rem>158<step>15801580<qmul>81488<rem>092<step>09200920<qmul>40744<rem>176<step>17601760<qmul>91674<rem>086<ans>000.285
sub
42
9770
779
-4
-783
1x3
-
-4--783=
scratchpad-v3
positive
null
single_borrow
--
train
387400
[ { "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": 8, "output_digit": 7, "serialized": "80170", "subtrahend...
-4--783=<sub><pos><state>387400<step>34091<step>80170<step>70070<ans>9770
add
41
3250
-523
0
-523
1x3
+
0+-523=
scratchpad-v3
negative
null
identity
+-
train
000325
[ { "a_digit": 0, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 3, "serialized": "03030" }, { "a_digit": 0, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "02020" }, { "a_digit":...
0+-523=<add><neg><state>000325<step>03030<step>02020<step>05050<ans>3250
mul
118
063000
360
-20
-18
2x2
*
-20*-18=
scratchpad-v3
positive
null
contains_zero_digit
--
train
020810
[ { "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...
-20*-18=<mul><pos><state>020810<step>0800000<col>000<step>0100000<step>2816016<col>601<step>0000001<step>2102003<step>0800003<col>300<step>2000000<step>0100000<col>000<step>0000000<col>000<ans>063000
mul
116
045000
540
15
36
2x2
*
15*36=
scratchpad-v3
positive
null
low_column_sum
++
train
510630
[ { "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", ...
15*36=<mul><pos><state>510630<step>5630030<col>003<step>5315018<step>1606024<col>402<step>5000002<step>1303005<step>0600005<col>500<step>1000000<step>0300000<col>000<step>0000000<col>000<ans>045000
sub
44
7850
587
-379
-966
3x3
-
-379--966=
scratchpad-v3
positive
null
multi_borrow
--
train
669973
[ { "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": 6, "output_digit": 8, "serialized": "67181", "subtrahend...
-379--966=<sub><pos><state>669973<step>69071<step>67181<step>93150<ans>7850
sub
40
0000
0
12
12
2x2
-
12-12=
scratchpad-v3
positive
null
identity
++
train
210210
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 2, "output_digit": 0, "serialized": "22000", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 0, "serialized": "11000", "subtrahend...
12-12=<sub><pos><state>210210<step>22000<step>11000<step>00000<ans>0000
mul
119
291844
-448192
-752
596
3x3
*
-752*596=
scratchpad-v3
negative
null
medium_column_sum
-+
train
257695
[ { "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", ...
-752*596=<mul><neg><state>257695<step>2612012<col>201<step>2918019<step>5630049<col>904<step>2510014<step>5945059<step>7642101<col>110<step>5525035<step>7963098<col>809<step>7535044<col>404<ans>291844
sub
42
9000
-9
-53
-44
2x2
-
-53--44=
scratchpad-v3
negative
null
negative_result
--
train
350440
[ { "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": 5, "output_digit": 0, "serialized": "54100", "subtrahend...
-53--44=<sub><neg><state>350440<step>34091<step>54100<step>00000<ans>9000
sub
41
6650
566
621
55
3x2
-
621-55=
scratchpad-v3
positive
null
multi_borrow
++
train
126550
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 1, "output_digit": 6, "serialized": "15061", "subtrahend_digit": 5 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 6, "serialized": "25161", "subtrahend...
621-55=<sub><pos><state>126550<step>15061<step>25161<step>60150<ans>6650
div
160
002.218
2.218
945
426
3x3
/
945/426=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
test
945426
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 426, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
945/426=<div><pos><state>945426<step>00090009<qmul>00000<rem>009<step>00940094<qmul>00000<rem>094<step>09450945<qmul>20852<rem>093<step>09300930<qmul>20852<rem>078<step>07800780<qmul>10426<rem>354<step>35403540<qmul>83408<rem>132<step>13201320<qmul>31278<rem>042<ans>002.218
sub
43
2210
-122
538
-660
3x3
+
538+-660=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
066835
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 2, "serialized": "08021", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 6, "output_digit": 2, "serialized": "63120", "subtrahend...
538+-660=<sub><neg><state>066835<step>08021<step>63120<step>65010<ans>2210
sub
42
9800
89
217
128
3x3
-
217-128=
scratchpad-v3
positive
null
multi_borrow
++
train
712821
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 7, "output_digit": 9, "serialized": "78091", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 8, "serialized": "12181", "subtrahend...
217-128=<sub><pos><state>712821<step>78091<step>12181<step>21100<ans>9800
div
159
009.667
9.667
-58
-6
2x1
/
-58/-6=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
058006
[ { "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": ...
-58/-6=<div><pos><state>058006<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00580058<qmul>90054<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<step>00400040<qmul>60036<rem>004<ans>009.667