effective_operation
stringclasses
4 values
encoded_tokens
int64
17
162
internal_answer
stringlengths
4
7
natural_answer
stringlengths
1
8
operand_a
int64
-999
999
operand_b
int64
-999
999
operand_digits
stringclasses
9 values
operation
stringclasses
4 values
prompt
stringlengths
4
10
representation
stringclasses
1 value
result_sign
stringclasses
2 values
rounding
stringclasses
1 value
scenario
stringclasses
25 values
sign_pattern
stringclasses
4 values
split
stringclasses
3 values
state
stringlengths
6
6
steps
listlengths
0
21
text
stringlengths
37
276
mul
118
449157
751944
969
776
3x3
*
969*776=
scratchpad-v3
positive
null
high_column_sum
++
train
969677
[ { "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", ...
969*776=<mul><pos><state>969677<step>9654054<col>405<step>9763068<step>6636104<col>410<step>9763073<step>6742115<step>9654169<col>916<step>6742058<step>9763121<col>112<step>9763075<col>507<ans>449157
add
42
1070
701
229
472
3x3
+
229+472=
scratchpad-v3
positive
null
cascading_carry
++
train
922274
[ { "a_digit": 9, "b_digit": 2, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "92011" }, { "a_digit": 2, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "27101" }, { "a_digit":...
229+472=<add><pos><state>922274<step>92011<step>27101<step>24170<ans>1070
sub
41
7350
-537
2
-539
1x3
+
2+-539=
scratchpad-v3
negative
null
magnitude_subtraction
+-
train
935200
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 7, "serialized": "92070", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 3, "output_digit": 3, "serialized": "30030", "subtrahend...
2+-539=<sub><neg><state>935200<step>92070<step>30030<step>50050<ans>7350
mul
119
037016
-610730
-785
778
3x3
*
-785*778=
scratchpad-v3
negative
null
high_column_sum
-+
train
587877
[ { "a_digit": 5, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 40, "running_total": 40, "serialized": "5840040", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 40, "kind": "column", ...
-785*778=<mul><neg><state>587877<step>5840040<col>004<step>5735039<step>8864103<col>310<step>5735045<step>8756101<step>7856157<col>715<step>8756071<step>7749120<col>012<step>7749061<col>106<ans>037016
mul
117
428100
-1824
57
-32
2x2
*
57*-32=
scratchpad-v3
negative
null
low_column_sum
+-
train
750230
[ { "a_digit": 7, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 14, "running_total": 14, "serialized": "7214014", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 14, "kind": "column", ...
57*-32=<mul><neg><state>750230<step>7214014<col>401<step>7321022<step>5210032<col>203<step>7000003<step>5315018<step>0200018<col>801<step>5000001<step>0300001<col>100<step>0000000<col>000<ans>428100
div
159
000.013
-0.013
-5
377
1x3
/
-5/377=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
005377
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 377, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-5/377=<div><neg><state>005377<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>10377<rem>123<step>12301230<qmul>31131<rem>099<step>09900990<qmul>20754<rem>236<ans>000.013
mul
118
329208
802923
957
839
3x3
*
957*839=
scratchpad-v3
positive
null
high_column_sum
++
train
759938
[ { "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", ...
957*839=<mul><pos><state>759938<step>7963063<col>306<step>7321027<step>5945072<col>207<step>7856063<step>5315078<step>9981159<col>915<step>5840055<step>9327082<col>208<step>9872080<col>008<ans>329208
div
161
000.331
-0.331
293
-884
3x3
/
293/-884=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
293884
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 884, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
293/-884=<div><neg><state>293884<step>00020002<qmul>00000<rem>002<step>00290029<qmul>00000<rem>029<step>02930293<qmul>00000<rem>293<step>29302930<qmul>32652<rem>278<step>27802780<qmul>32652<rem>128<step>12801280<qmul>10884<rem>396<step>39603960<qmul>43536<rem>424<ans>000.331
sub
42
4000
-4
-25
-21
2x2
-
-25--21=
scratchpad-v3
negative
null
negative_result
--
train
520120
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 4, "serialized": "51040", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 2, "output_digit": 0, "serialized": "22000", "subtrahend...
-25--21=<sub><neg><state>520120<step>51040<step>22000<step>00000<ans>4000
div
161
001.725
-1.725
997
-578
3x3
/
997/-578=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
997578
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 578, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
997/-578=<div><neg><state>997578<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09970997<qmul>10578<rem>419<step>41904190<qmul>74046<rem>144<step>14401440<qmul>21156<rem>284<step>28402840<qmul>42312<rem>528<step>52805280<qmul>95202<rem>078<ans>001.725
div
160
001.412
1.412
802
568
3x3
/
802/568=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
train
802568
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 568, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
802/568=<div><pos><state>802568<step>00080008<qmul>00000<rem>008<step>00800080<qmul>00000<rem>080<step>08020802<qmul>10568<rem>234<step>23402340<qmul>42272<rem>068<step>06800680<qmul>10568<rem>112<step>11201120<qmul>10568<rem>552<step>55205520<qmul>95112<rem>408<ans>001.412
sub
41
1500
-51
65
116
2x3
-
65-116=
scratchpad-v3
negative
null
negative_result
++
train
611560
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 6, "output_digit": 1, "serialized": "65010", "subtrahend_digit": 5 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 1, "output_digit": 5, "serialized": "16051", "subtrahend...
65-116=<sub><neg><state>611560<step>65010<step>16051<step>10100<ans>1500
add
41
5430
345
290
55
3x2
+
290+55=
scratchpad-v3
positive
null
single_carry
++
train
092550
[ { "a_digit": 0, "b_digit": 5, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "05050" }, { "a_digit": 9, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 4, "serialized": "95041" }, { "a_digit":...
290+55=<add><pos><state>092550<step>05050<step>95041<step>20130<ans>5430
add
42
7750
-577
-9
-568
1x3
+
-9+-568=
scratchpad-v3
negative
null
single_carry
--
train
900865
[ { "a_digit": 9, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 7, "serialized": "98071" }, { "a_digit": 0, "b_digit": 6, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "06170" }, { "a_digit":...
-9+-568=<add><neg><state>900865<step>98071<step>06170<step>05050<ans>7750
sub
40
8100
18
87
69
2x2
-
87-69=
scratchpad-v3
positive
null
single_borrow
++
train
780960
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 7, "output_digit": 8, "serialized": "79081", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 8, "output_digit": 1, "serialized": "86110", "subtrahend...
87-69=<sub><pos><state>780960<step>79081<step>86110<step>00000<ans>8100
sub
42
7310
-137
336
473
3x3
-
336-473=
scratchpad-v3
negative
null
negative_result
++
train
374633
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 7, "serialized": "36071", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 3, "serialized": "73130", "subtrahend...
336-473=<sub><neg><state>374633<step>36071<step>73130<step>43010<ans>7310
div
160
000.125
-0.125
53
-424
2x3
/
53/-424=
scratchpad-v3
negative
round-half-up
exact
+-
train
053424
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 424, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
53/-424=<div><neg><state>053424<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00530053<qmul>00000<rem>053<step>05300530<qmul>10424<rem>106<step>10601060<qmul>20848<rem>212<step>21202120<qmul>52120<rem>000<step>00000000<qmul>00000<rem>000<ans>000.125
add
41
6280
826
90
736
2x3
+
90+736=
scratchpad-v3
positive
null
single_carry
++
train
090637
[ { "a_digit": 0, "b_digit": 6, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "06060" }, { "a_digit": 9, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "93021" }, { "a_digit":...
90+736=<add><pos><state>090637<step>06060<step>93021<step>07180<ans>6280
sub
43
0540
-450
-983
533
3x3
+
-983+533=
scratchpad-v3
negative
null
magnitude_subtraction
-+
train
389335
[ { "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": 8, "output_digit": 5, "serialized": "83050", "subtrahend...
-983+533=<sub><neg><state>389335<step>33000<step>83050<step>95040<ans>0540
div
161
000.669
-0.669
210
-314
3x3
/
210/-314=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
+-
train
210314
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 314, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
210/-314=<div><neg><state>210314<step>00020002<qmul>00000<rem>002<step>00210021<qmul>00000<rem>021<step>02100210<qmul>00000<rem>210<step>21002100<qmul>61884<rem>216<step>21602160<qmul>61884<rem>276<step>27602760<qmul>82512<rem>248<step>24802480<qmul>72198<rem>282<ans>000.669
div
161
016.583
16.583
-398
-24
3x2
/
-398/-24=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
398024
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 24, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-398/-24=<div><pos><state>398024<step>00030003<qmul>00000<rem>003<step>00390039<qmul>10024<rem>015<step>01580158<qmul>60144<rem>014<step>01400140<qmul>50120<rem>020<step>02000200<qmul>80192<rem>008<step>00800080<qmul>30072<rem>008<step>00800080<qmul>30072<rem>008<ans>016.583
mul
118
543431
134345
485
277
3x3
*
485*277=
scratchpad-v3
positive
null
medium_column_sum
++
train
584772
[ { "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", ...
485*277=<mul><pos><state>584772<step>5735035<col>503<step>5735038<step>8756094<col>409<step>5210019<step>8756075<step>4728103<col>310<step>8216026<step>4728054<col>405<step>4208013<col>301<ans>543431
div
161
001.082
-1.082
-822
760
3x3
/
-822/760=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
822760
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 760, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-822/760=<div><neg><state>822760<step>00080008<qmul>00000<rem>008<step>00820082<qmul>00000<rem>082<step>08220822<qmul>10760<rem>062<step>06200620<qmul>00000<rem>620<step>62006200<qmul>86080<rem>120<step>12001200<qmul>10760<rem>440<step>44004400<qmul>53800<rem>600<ans>001.082
div
158
000.000
0
0
-71
1x2
/
0/-71=
scratchpad-v3
negative
round-half-up
zero_numerator
+-
train
000071
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 71, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
0/-71=<div><neg><state>000071<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
sub
43
1160
-611
-999
388
3x3
+
-999+388=
scratchpad-v3
negative
null
magnitude_subtraction
-+
train
999883
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 1, "serialized": "98010", "subtrahend_digit": 8 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 1, "serialized": "98010", "subtrahend...
-999+388=<sub><neg><state>999883<step>98010<step>98010<step>93060<ans>1160
div
159
004.250
4.25
221
52
3x2
/
221/52=
scratchpad-v3
positive
round-half-up
exact
++
train
221052
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 52, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
221/52=<div><pos><state>221052<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02210221<qmul>40208<rem>013<step>01300130<qmul>20104<rem>026<step>02600260<qmul>50260<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>004.250
sub
44
0000
0
-709
-709
3x3
-
-709--709=
scratchpad-v3
positive
null
identity
--
train
907907
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 0, "serialized": "99000", "subtrahend_digit": 9 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 0, "output_digit": 0, "serialized": "00000", "subtrahend...
-709--709=<sub><pos><state>907907<step>99000<step>00000<step>77000<ans>0000
mul
118
069000
960
-48
-20
2x2
*
-48*-20=
scratchpad-v3
positive
null
contains_zero_digit
--
train
840020
[ { "a_digit": 8, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "8000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
-48*-20=<mul><pos><state>840020<step>8000000<col>000<step>8216016<step>4000016<col>601<step>8000001<step>4208009<step>0000009<col>900<step>4000000<step>0200000<col>000<step>0000000<col>000<ans>069000
div
159
000.506
-0.506
39
-77
2x2
/
39/-77=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
039077
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 77, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
39/-77=<div><neg><state>039077<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00390039<qmul>00000<rem>039<step>03900390<qmul>50385<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>60462<rem>038<step>03800380<qmul>40308<rem>072<ans>000.506
div
160
076.286
76.286
-534
-7
3x1
/
-534/-7=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
534007
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 7, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-534/-7=<div><pos><state>534007<step>00050005<qmul>00000<rem>005<step>00530053<qmul>70049<rem>004<step>00440044<qmul>60042<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<step>00400040<qmul>50035<rem>005<step>00500050<qmul>70049<rem>001<ans>076.286
sub
42
5520
255
885
630
3x3
-
885-630=
scratchpad-v3
positive
null
no_borrow
++
train
588036
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 5, "serialized": "50050", "subtrahend_digit": 0 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 8, "output_digit": 5, "serialized": "83050", "subtrahend...
885-630=<sub><pos><state>588036<step>50050<step>83050<step>86020<ans>5520
add
42
3311
1133
615
518
3x3
+
615+518=
scratchpad-v3
positive
null
overflow
++
train
516815
[ { "a_digit": 5, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 3, "serialized": "58031" }, { "a_digit": 1, "b_digit": 1, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "11130" }, { "a_digit":...
615+518=<add><pos><state>516815<step>58031<step>11130<step>65011<ans>3311
mul
118
869730
-37968
-791
48
3x2
*
-791*48=
scratchpad-v3
negative
null
medium_column_sum
-+
train
197840
[ { "a_digit": 1, "a_index": 0, "b_digit": 8, "b_index": 0, "column": 0, "kind": "term", "product": 8, "running_total": 8, "serialized": "1808008", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 8, "kind": "column", "o...
-791*48=<mul><neg><state>197840<step>1808008<col>800<step>1404004<step>9872076<col>607<step>1000007<step>9436043<step>7856099<col>909<step>9000009<step>7428037<col>703<step>7000003<col>300<ans>869730
mul
119
235917
-719532
828
-869
3x3
*
828*-869=
scratchpad-v3
negative
null
high_column_sum
+-
train
828968
[ { "a_digit": 8, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 72, "running_total": 72, "serialized": "8972072", "term_index": 0 }, { "carry_in": 0, "carry_out": 7, "column": 0, "column_sum": 72, "kind": "column", ...
828*-869=<mul><neg><state>828968<step>8972072<col>207<step>8648055<step>2918073<col>307<step>8864071<step>2612083<step>8972155<col>515<step>2816031<step>8648079<col>907<step>8864071<col>107<ans>235917
add
44
0250
-520
-137
-383
3x3
+
-137+-383=
scratchpad-v3
negative
null
multi_carry
--
train
731383
[ { "a_digit": 7, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "73001" }, { "a_digit": 3, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "38121" }, { "a_digit":...
-137+-383=<add><neg><state>731383<step>73001<step>38121<step>13150<ans>0250
sub
42
6440
-446
544
990
3x3
-
544-990=
scratchpad-v3
negative
null
negative_result
++
train
099445
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 0, "output_digit": 6, "serialized": "04061", "subtrahend_digit": 4 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 4, "serialized": "94140", "subtrahend...
544-990=<sub><neg><state>099445<step>04061<step>94140<step>95040<ans>6440
div
160
008.000
-8
248
-31
3x2
/
248/-31=
scratchpad-v3
negative
round-half-up
exact
+-
train
248031
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 31, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
248/-31=<div><neg><state>248031<step>00020002<qmul>00000<rem>002<step>00240024<qmul>00000<rem>024<step>02480248<qmul>80248<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>008.000
mul
119
414172
-271414
286
-949
3x3
*
286*-949=
scratchpad-v3
negative
null
medium_column_sum
+-
train
682949
[ { "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", ...
286*-949=<mul><neg><state>682949<step>6954054<col>405<step>6424029<step>8972101<col>110<step>6954064<step>8432096<step>2918114<col>411<step>8972083<step>2408091<col>109<step>2918027<col>702<ans>414172
div
161
001.217
-1.217
-902
741
3x3
/
-902/741=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
902741
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 741, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-902/741=<div><neg><state>902741<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09020902<qmul>10741<rem>161<step>16101610<qmul>21482<rem>128<step>12801280<qmul>10741<rem>539<step>53905390<qmul>75187<rem>203<step>20302030<qmul>21482<rem>548<ans>001.217
mul
117
455100
1554
111
14
3x2
*
111*14=
scratchpad-v3
positive
null
repeated_digit
++
train
111410
[ { "a_digit": 1, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 4, "running_total": 4, "serialized": "1404004", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 4, "kind": "column", "o...
111*14=<mul><pos><state>111410<step>1404004<col>400<step>1101001<step>1404005<col>500<step>1000000<step>1101001<step>1404005<col>500<step>1000000<step>1101001<col>100<step>1000000<col>000<ans>455100
sub
42
3610
163
599
436
3x3
-
599-436=
scratchpad-v3
positive
null
no_borrow
++
train
995634
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 3, "serialized": "96030", "subtrahend_digit": 6 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 6, "serialized": "93060", "subtrahend...
599-436=<sub><pos><state>995634<step>96030<step>93060<step>54010<ans>3610
div
160
000.952
0.952
-59
-62
2x2
/
-59/-62=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
059062
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 62, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-59/-62=<div><pos><state>059062<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00590059<qmul>00000<rem>059<step>05900590<qmul>90558<rem>032<step>03200320<qmul>50310<rem>010<step>01000100<qmul>10062<rem>038<step>03800380<qmul>60372<rem>008<ans>000.952
sub
41
8180
818
906
88
3x2
-
906-88=
scratchpad-v3
positive
null
borrow_through_zero
++
train
609880
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 8, "serialized": "68081", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
906-88=<sub><pos><state>609880<step>68081<step>08111<step>90180<ans>8180
add
41
6810
186
184
-2
3x1
-
184--2=
scratchpad-v3
positive
null
magnitude_addition
+-
train
481200
[ { "a_digit": 4, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "42060" }, { "a_digit": 8, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "80080" }, { "a_digit":...
184--2=<add><pos><state>481200<step>42060<step>80080<step>10010<ans>6810
add
42
5101
1015
482
533
3x3
+
482+533=
scratchpad-v3
positive
null
cascading_carry
++
train
284335
[ { "a_digit": 2, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "23050" }, { "a_digit": 8, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "83011" }, { "a_digit":...
482+533=<add><pos><state>284335<step>23050<step>83011<step>45101<ans>5101
mul
120
670647
746076
-948
-787
3x3
*
-948*-787=
scratchpad-v3
positive
null
high_column_sum
--
train
849787
[ { "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", ...
-948*-787=<mul><pos><state>849787<step>8756056<col>605<step>8864069<step>4728097<col>709<step>8756065<step>4832097<step>9763160<col>016<step>4728044<step>9872116<col>611<step>9763074<col>407<ans>670647
sub
41
8050
508
600
92
3x2
-
600-92=
scratchpad-v3
positive
null
borrow_through_zero
++
train
006290
[ { "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": 0, "output_digit": 0, "serialized": "09101", "subtrahend...
600-92=<sub><pos><state>006290<step>02081<step>09101<step>60150<ans>8050
div
159
000.769
-0.769
-20
26
2x2
/
-20/26=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
020026
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 26, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-20/26=<div><neg><state>020026<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>70182<rem>018<step>01800180<qmul>60156<rem>024<step>02400240<qmul>90234<rem>006<step>00600060<qmul>20052<rem>008<ans>000.769
mul
119
606792
-297606
386
-771
3x3
*
386*-771=
scratchpad-v3
negative
null
medium_column_sum
+-
test
683177
[ { "a_digit": 6, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 6, "running_total": 6, "serialized": "6106006", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 6, "kind": "column", "o...
386*-771=<mul><neg><state>683177<step>6106006<col>600<step>6742042<step>8108050<col>005<step>6742047<step>8756103<step>3103106<col>610<step>8756066<step>3721087<col>708<step>3721029<col>902<ans>606792
div
160
062.333
62.333
-561
-9
3x1
/
-561/-9=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
561009
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 9, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-561/-9=<div><pos><state>561009<step>00050005<qmul>00000<rem>005<step>00560056<qmul>60054<rem>002<step>00210021<qmul>20018<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<step>00300030<qmul>30027<rem>003<ans>062.333
add
41
8380
-838
0
-838
1x3
+
0+-838=
scratchpad-v3
negative
null
identity
+-
train
000838
[ { "a_digit": 0, "b_digit": 8, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 8, "serialized": "08080" }, { "a_digit": 0, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "03030" }, { "a_digit":...
0+-838=<add><neg><state>000838<step>08080<step>03030<step>08080<ans>8380
div
162
001.414
1.414
-990
-700
3x3
/
-990/-700=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
990700
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 700, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-990/-700=<div><pos><state>990700<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09900990<qmul>10700<rem>290<step>29002900<qmul>42800<rem>100<step>10001000<qmul>10700<rem>300<step>30003000<qmul>42800<rem>200<step>20002000<qmul>21400<rem>600<ans>001.414
sub
40
1100
-11
55
66
2x2
-
55-66=
scratchpad-v3
negative
null
negative_result
++
train
660550
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 6, "output_digit": 1, "serialized": "65010", "subtrahend_digit": 5 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 6, "output_digit": 1, "serialized": "65010", "subtrahend...
55-66=<sub><neg><state>660550<step>65010<step>65010<step>00000<ans>1100
sub
43
7450
547
-55
-602
2x3
-
-55--602=
scratchpad-v3
positive
null
borrow_through_zero
--
train
206550
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 7, "serialized": "25071", "subtrahend_digit": 5 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 4, "serialized": "05141", "subtrahend...
-55--602=<sub><pos><state>206550<step>25071<step>05141<step>60150<ans>7450
div
162
000.415
0.415
-227
-547
3x3
/
-227/-547=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
227547
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 547, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-227/-547=<div><pos><state>227547<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02270227<qmul>00000<rem>227<step>22702270<qmul>42188<rem>082<step>08200820<qmul>10547<rem>273<step>27302730<qmul>42188<rem>542<step>54205420<qmul>94923<rem>497<ans>000.415
add
44
1640
-461
-182
-279
3x3
+
-182+-279=
scratchpad-v3
negative
null
multi_carry
--
train
281972
[ { "a_digit": 2, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "29011" }, { "a_digit": 8, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 6, "serialized": "87161" }, { "a_digit":...
-182+-279=<add><neg><state>281972<step>29011<step>87161<step>12140<ans>1640
div
162
000.979
0.979
-565
-577
3x3
/
-565/-577=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
565577
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 577, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-565/-577=<div><pos><state>565577<step>00050005<qmul>00000<rem>005<step>00560056<qmul>00000<rem>056<step>05650565<qmul>00000<rem>565<step>56505650<qmul>95193<rem>457<step>45704570<qmul>74039<rem>531<step>53105310<qmul>95193<rem>117<step>11701170<qmul>21154<rem>016<ans>000.979
div
160
001.442
1.442
789
547
3x3
/
789/547=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
789547
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 547, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
789/547=<div><pos><state>789547<step>00070007<qmul>00000<rem>007<step>00780078<qmul>00000<rem>078<step>07890789<qmul>10547<rem>242<step>24202420<qmul>42188<rem>232<step>23202320<qmul>42188<rem>132<step>13201320<qmul>21094<rem>226<step>22602260<qmul>42188<rem>072<ans>001.442
sub
42
0030
-300
239
539
3x3
-
239-539=
scratchpad-v3
negative
null
negative_result
++
train
935932
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 0, "serialized": "99000", "subtrahend_digit": 9 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 3, "output_digit": 0, "serialized": "33000", "subtrahend...
239-539=<sub><neg><state>935932<step>99000<step>33000<step>52030<ans>0030
sub
43
9430
349
-59
-408
2x3
-
-59--408=
scratchpad-v3
positive
null
borrow_through_zero
--
train
804950
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 8, "output_digit": 9, "serialized": "89091", "subtrahend_digit": 9 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 4, "serialized": "05141", "subtrahend...
-59--408=<sub><pos><state>804950<step>89091<step>05141<step>40130<ans>9430
div
159
000.803
-0.803
-57
71
2x2
/
-57/71=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
-+
train
057071
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 71, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-57/71=<div><neg><state>057071<step>00000000<qmul>00000<rem>000<step>00050005<qmul>00000<rem>005<step>00570057<qmul>00000<rem>057<step>05700570<qmul>80568<rem>002<step>00200020<qmul>00000<rem>020<step>02000200<qmul>20142<rem>058<step>05800580<qmul>80568<rem>012<ans>000.803
add
42
4061
1604
703
901
3x3
+
703+901=
scratchpad-v3
positive
null
overflow
++
train
307109
[ { "a_digit": 3, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 4, "serialized": "31040" }, { "a_digit": 0, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 0, "serialized": "00000" }, { "a_digit":...
703+901=<add><pos><state>307109<step>31040<step>00000<step>79061<ans>4061
sub
40
8200
-28
18
46
2x2
-
18-46=
scratchpad-v3
negative
null
negative_result
++
train
640810
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 8, "serialized": "68081", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 4, "output_digit": 2, "serialized": "41120", "subtrahend...
18-46=<sub><neg><state>640810<step>68081<step>41120<step>00000<ans>8200
div
159
078.000
-78
-702
9
3x1
/
-702/9=
scratchpad-v3
negative
round-half-up
exact
-+
train
702009
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 9, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-702/9=<div><neg><state>702009<step>00070007<qmul>00000<rem>007<step>00700070<qmul>70063<rem>007<step>00720072<qmul>80072<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>078.000
mul
118
443166
661344
664
996
3x3
*
664*996=
scratchpad-v3
positive
null
medium_column_sum
++
train
466699
[ { "a_digit": 4, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 24, "running_total": 24, "serialized": "4624024", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 24, "kind": "column", ...
664*996=<mul><pos><state>466699<step>4624024<col>402<step>4936038<step>6636074<col>407<step>4936043<step>6954097<step>6636133<col>313<step>6954067<step>6954121<col>112<step>6954066<col>606<ans>443166
div
157
026.000
26
78
3
2x1
/
78/3=
scratchpad-v3
positive
round-half-up
exact
++
train
078003
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 3, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
78/3=<div><pos><state>078003<step>00000000<qmul>00000<rem>000<step>00070007<qmul>20006<rem>001<step>00180018<qmul>60018<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>026.000
mul
118
083200
2380
-70
-34
2x2
*
-70*-34=
scratchpad-v3
positive
null
contains_zero_digit
--
train
070430
[ { "a_digit": 0, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0400000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
-70*-34=<mul><pos><state>070430<step>0400000<col>000<step>0300000<step>7428028<col>802<step>0000002<step>7321023<step>0400023<col>302<step>7000002<step>0300002<col>200<step>0000000<col>000<ans>083200
add
41
6550
556
514
42
3x2
+
514+42=
scratchpad-v3
positive
null
no_carry
++
train
415240
[ { "a_digit": 4, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "42060" }, { "a_digit": 1, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 5, "serialized": "14050" }, { "a_digit":...
514+42=<add><pos><state>415240<step>42060<step>14050<step>50050<ans>6550
div
160
133.167
133.167
-799
-6
3x1
/
-799/-6=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
799006
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 1, "quotient_product": 6, "serialized": "10006" }, { "kind": ...
-799/-6=<div><pos><state>799006<step>00070007<qmul>10006<rem>001<step>00190019<qmul>30018<rem>001<step>00190019<qmul>30018<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>133.167
mul
118
100980
-89001
957
-93
3x2
*
957*-93=
scratchpad-v3
negative
null
medium_column_sum
+-
train
759390
[ { "a_digit": 7, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 21, "running_total": 21, "serialized": "7321021", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 21, "kind": "column", ...
957*-93=<mul><neg><state>759390<step>7321021<col>102<step>7963065<step>5315080<col>008<step>7000008<step>5945053<step>9327080<col>008<step>5000008<step>9981089<col>908<step>9000008<col>800<ans>100980
mul
120
300938
839003
-979
-857
3x3
*
-979*-857=
scratchpad-v3
positive
null
high_column_sum
--
train
979758
[ { "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", ...
-979*-857=<mul><pos><state>979758<step>9763063<col>306<step>9545051<step>7749100<col>010<step>9872082<step>7535117<step>9763180<col>018<step>7856074<step>9545119<col>911<step>9872083<col>308<ans>300938
sub
42
3820
-283
212
495
3x3
-
212-495=
scratchpad-v3
negative
null
negative_result
++
train
594212
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 5, "output_digit": 3, "serialized": "52030", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 9, "output_digit": 8, "serialized": "91080", "subtrahend...
212-495=<sub><neg><state>594212<step>52030<step>91080<step>42020<ans>3820
sub
41
1700
71
148
77
3x2
-
148-77=
scratchpad-v3
positive
null
single_borrow
++
train
841770
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 8, "output_digit": 1, "serialized": "87010", "subtrahend_digit": 7 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 4, "output_digit": 7, "serialized": "47071", "subtrahend...
148-77=<sub><pos><state>841770<step>87010<step>47071<step>10100<ans>1700
add
44
0080
-800
-469
-331
3x3
+
-469+-331=
scratchpad-v3
negative
null
cascading_carry
--
test
964133
[ { "a_digit": 9, "b_digit": 1, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "91001" }, { "a_digit": 6, "b_digit": 3, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "63101" }, { "a_digit":...
-469+-331=<add><neg><state>964133<step>91001<step>63101<step>43180<ans>0080
mul
119
580247
-742085
-769
965
3x3
*
-769*965=
scratchpad-v3
negative
null
high_column_sum
-+
train
967569
[ { "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", ...
-769*965=<mul><neg><state>967569<step>9545045<col>504<step>9654058<step>6530088<col>808<step>9981089<step>6636125<step>7535160<col>016<step>6954070<step>7642112<col>211<step>7963074<col>407<ans>580247
mul
119
488577
-775884
-779
996
3x3
*
-779*996=
scratchpad-v3
negative
null
high_column_sum
-+
train
977699
[ { "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", ...
-779*996=<mul><neg><state>977699<step>9654054<col>405<step>9981086<step>7642128<col>812<step>9981093<step>7963156<step>7642198<col>819<step>7963082<step>7963145<col>514<step>7963077<col>707<ans>488577
div
159
084.333
-84.333
506
-6
3x1
/
506/-6=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
506006
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
506/-6=<div><neg><state>506006<step>00050005<qmul>00000<rem>005<step>00500050<qmul>80048<rem>002<step>00260026<qmul>40024<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<step>00200020<qmul>30018<rem>002<ans>084.333
mul
117
974100
-1479
-29
51
2x2
*
-29*51=
scratchpad-v3
negative
null
low_column_sum
-+
train
920150
[ { "a_digit": 9, "a_index": 0, "b_digit": 1, "b_index": 0, "column": 0, "kind": "term", "product": 9, "running_total": 9, "serialized": "9109009", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 9, "kind": "column", "o...
-29*51=<mul><neg><state>920150<step>9109009<col>900<step>9545045<step>2102047<col>704<step>9000004<step>2510014<step>0100014<col>401<step>2000001<step>0500001<col>100<step>0000000<col>000<ans>974100
mul
120
388611
116883
-999
-117
3x3
*
-999*-117=
scratchpad-v3
positive
null
repeated_digit
--
train
999711
[ { "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", ...
-999*-117=<mul><pos><state>999711<step>9763063<col>306<step>9109015<step>9763078<col>807<step>9109016<step>9109025<step>9763088<col>808<step>9109017<step>9109026<col>602<step>9109011<col>101<ans>388611
add
41
0860
-680
0
-680
1x3
+
0+-680=
scratchpad-v3
negative
null
identity
+-
train
000086
[ { "a_digit": 0, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 0, "serialized": "00000" }, { "a_digit": 0, "b_digit": 8, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "08080" }, { "a_digit":...
0+-680=<add><neg><state>000086<step>00000<step>08080<step>06060<ans>0860
add
42
6370
736
158
578
3x3
+
158+578=
scratchpad-v3
positive
null
multi_carry
++
val
851875
[ { "a_digit": 8, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 6, "serialized": "88061" }, { "a_digit": 5, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "57131" }, { "a_digit":...
158+578=<add><pos><state>851875<step>88061<step>57131<step>15170<ans>6370
div
160
000.487
0.487
384
789
3x3
/
384/789=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
384789
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 789, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
384/789=<div><pos><state>384789<step>00030003<qmul>00000<rem>003<step>00380038<qmul>00000<rem>038<step>03840384<qmul>00000<rem>384<step>38403840<qmul>43156<rem>684<step>68406840<qmul>86312<rem>528<step>52805280<qmul>64734<rem>546<step>54605460<qmul>64734<rem>726<ans>000.487
mul
116
000000
0
0
230
1x3
*
0*230=
scratchpad-v3
positive
null
identity
++
train
000032
[ { "a_digit": 0, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
0*230=<mul><pos><state>000032<step>0000000<col>000<step>0300000<step>0000000<col>000<step>0200000<step>0300000<step>0000000<col>000<step>0200000<step>0300000<col>000<step>0200000<col>000<ans>000000
sub
42
5740
475
954
479
3x3
-
954-479=
scratchpad-v3
positive
null
multi_borrow
++
train
459974
[ { "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": 5, "output_digit": 7, "serialized": "57171", "subtrahend...
954-479=<sub><pos><state>459974<step>49051<step>57171<step>94140<ans>5740
add
44
1490
-941
-269
-672
3x3
+
-269+-672=
scratchpad-v3
negative
null
multi_carry
--
train
962276
[ { "a_digit": 9, "b_digit": 2, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "92011" }, { "a_digit": 6, "b_digit": 7, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 4, "serialized": "67141" }, { "a_digit":...
-269+-672=<add><neg><state>962276<step>92011<step>67141<step>26190<ans>1490
add
42
6231
1326
823
503
3x3
+
823+503=
scratchpad-v3
positive
null
overflow
++
train
328305
[ { "a_digit": 3, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "33060" }, { "a_digit": 2, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 2, "serialized": "20020" }, { "a_digit":...
823+503=<add><pos><state>328305<step>33060<step>20020<step>85031<ans>6231
div
160
006.685
-6.685
361
-54
3x2
/
361/-54=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
361054
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 54, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
361/-54=<div><neg><state>361054<step>00030003<qmul>00000<rem>003<step>00360036<qmul>00000<rem>036<step>03610361<qmul>60324<rem>037<step>03700370<qmul>60324<rem>046<step>04600460<qmul>80432<rem>028<step>02800280<qmul>50270<rem>010<step>01000100<qmul>10054<rem>046<ans>006.685
mul
118
099460
-64990
-670
97
3x2
*
-670*97=
scratchpad-v3
negative
null
contains_zero_digit
-+
train
076790
[ { "a_digit": 0, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "0700000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
-670*97=<mul><neg><state>076790<step>0700000<col>000<step>0900000<step>7749049<col>904<step>0000004<step>7963067<step>6742109<col>910<step>7000010<step>6954064<col>406<step>6000006<col>600<ans>099460
div
159
097.667
-97.667
293
-3
3x1
/
293/-3=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
293003
[ { "incoming_digit": 2, "kind": "partial", "partial": 2, "position": 0, "remainder_in": 0, "serialized": "00020002" }, { "divisor": 3, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
293/-3=<div><neg><state>293003<step>00020002<qmul>00000<rem>002<step>00290029<qmul>90027<rem>002<step>00230023<qmul>70021<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<step>00200020<qmul>60018<rem>002<ans>097.667
sub
41
9810
-189
17
206
2x3
-
17-206=
scratchpad-v3
negative
null
negative_result
++
train
602710
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 6, "output_digit": 9, "serialized": "67091", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 8, "serialized": "01181", "subtrahend...
17-206=<sub><neg><state>602710<step>67091<step>01181<step>20110<ans>9810
sub
44
2300
32
-693
-725
3x3
-
-693--725=
scratchpad-v3
positive
null
single_borrow
--
train
527396
[ { "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": 2, "output_digit": 3, "serialized": "29031", "subtrahend...
-693--725=<sub><pos><state>527396<step>53020<step>29031<step>76100<ans>2300
sub
44
7440
447
-476
-923
3x3
-
-476--923=
scratchpad-v3
positive
null
multi_borrow
--
train
329674
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 7, "serialized": "36071", "subtrahend_digit": 6 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 2, "output_digit": 4, "serialized": "27141", "subtrahend...
-476--923=<sub><pos><state>329674<step>36071<step>27141<step>94140<ans>7440
mul
118
095400
-4590
-17
270
2x3
*
-17*270=
scratchpad-v3
negative
null
contains_zero_digit
-+
train
710072
[ { "a_digit": 7, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "7000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
-17*270=<mul><neg><state>710072<step>7000000<col>000<step>7749049<step>1000049<col>904<step>7214018<step>1707025<step>0000025<col>502<step>1202004<step>0700004<col>400<step>0200000<col>000<ans>095400
add
42
2780
872
321
551
3x3
+
321+551=
scratchpad-v3
positive
null
no_carry
++
train
123155
[ { "a_digit": 1, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "11020" }, { "a_digit": 2, "b_digit": 5, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "25070" }, { "a_digit":...
321+551=<add><pos><state>123155<step>11020<step>25070<step>35080<ans>2780
div
158
000.873
0.873
62
71
2x2
/
62/71=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
062071
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 71, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
62/71=<div><pos><state>062071<step>00000000<qmul>00000<rem>000<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06200620<qmul>80568<rem>052<step>05200520<qmul>70497<rem>023<step>02300230<qmul>30213<rem>017<step>01700170<qmul>20142<rem>028<ans>000.873
sub
44
0000
0
-479
-479
3x3
-
-479--479=
scratchpad-v3
positive
null
identity
--
train
974974
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 0, "serialized": "99000", "subtrahend_digit": 9 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 0, "serialized": "77000", "subtrahend...
-479--479=<sub><pos><state>974974<step>99000<step>77000<step>44000<ans>0000
mul
118
383570
-75383
847
-89
3x2
*
847*-89=
scratchpad-v3
negative
null
medium_column_sum
+-
train
748980
[ { "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", ...
847*-89=<mul><neg><state>748980<step>7963063<col>306<step>7856062<step>4936098<col>809<step>7000009<step>4832041<step>8972113<col>311<step>4000011<step>8864075<col>507<step>8000007<col>700<ans>383570
add
42
0081
1800
988
812
3x3
+
988+812=
scratchpad-v3
positive
null
cascading_carry
++
train
889218
[ { "a_digit": 8, "b_digit": 2, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 0, "serialized": "82001" }, { "a_digit": 8, "b_digit": 1, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "81101" }, { "a_digit":...
988+812=<add><pos><state>889218<step>82001<step>81101<step>98181<ans>0081
mul
120
346872
278643
-951
-293
3x3
*
-951*-293=
scratchpad-v3
positive
null
medium_column_sum
--
train
159392
[ { "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...
-951*-293=<mul><pos><state>159392<step>1303003<col>300<step>1909009<step>5315024<col>402<step>1202004<step>5945049<step>9327076<col>607<step>5210017<step>9981098<col>809<step>9218027<col>702<ans>346872
div
161
001.010
-1.01
-490
485
3x3
/
-490/485=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
490485
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 485, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-490/485=<div><neg><state>490485<step>00040004<qmul>00000<rem>004<step>00490049<qmul>00000<rem>049<step>04900490<qmul>10485<rem>005<step>00500050<qmul>00000<rem>050<step>05000500<qmul>10485<rem>015<step>01500150<qmul>00000<rem>150<step>15001500<qmul>31455<rem>045<ans>001.010