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
117
146200
2641
139
19
3x2
*
139*19=
scratchpad-v3
positive
null
medium_column_sum
++
train
931910
[ { "a_digit": 9, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 81, "running_total": 81, "serialized": "9981081", "term_index": 0 }, { "carry_in": 0, "carry_out": 8, "column": 0, "column_sum": 81, "kind": "column", ...
139*19=<mul><pos><state>931910<step>9981081<col>108<step>9109017<step>3927044<col>404<step>9000004<step>3103007<step>1909016<col>601<step>3000001<step>1101002<col>200<step>1000000<col>000<ans>146200
div
161
001.309
-1.309
-305
233
3x3
/
-305/233=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
305233
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 233, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-305/233=<div><neg><state>305233<step>00030003<qmul>00000<rem>003<step>00300030<qmul>00000<rem>030<step>03050305<qmul>10233<rem>072<step>07200720<qmul>30699<rem>021<step>02100210<qmul>00000<rem>210<step>21002100<qmul>92097<rem>003<step>00300030<qmul>00000<rem>030<ans>001.309
div
157
000.000
0
0
37
1x2
/
0/37=
scratchpad-v3
positive
round-half-up
zero_numerator
++
train
000037
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 37, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
0/37=<div><pos><state>000037<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
mul
117
509700
-7905
93
-85
2x2
*
93*-85=
scratchpad-v3
negative
null
low_column_sum
+-
train
390580
[ { "a_digit": 3, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 15, "running_total": 15, "serialized": "3515015", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 15, "kind": "column", ...
93*-85=<mul><neg><state>390580<step>3515015<col>501<step>3824025<step>9545070<col>007<step>3000007<step>9872079<step>0500079<col>907<step>9000007<step>0800007<col>700<step>0000000<col>000<ans>509700
mul
119
815161
-161518
973
-166
3x3
*
973*-166=
scratchpad-v3
negative
null
medium_column_sum
+-
train
379661
[ { "a_digit": 3, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 18, "running_total": 18, "serialized": "3618018", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 18, "kind": "column", ...
973*-166=<mul><neg><state>379661<step>3618018<col>801<step>3618019<step>7642061<col>106<step>3103009<step>7642051<step>9654105<col>510<step>7107017<step>9654071<col>107<step>9109016<col>601<ans>815161
mul
118
191418
814191
959
849
3x3
*
959*849=
scratchpad-v3
positive
null
high_column_sum
++
train
959948
[ { "a_digit": 9, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 81, "running_total": 81, "serialized": "9981081", "term_index": 0 }, { "carry_in": 0, "carry_out": 8, "column": 0, "column_sum": 81, "kind": "column", ...
959*849=<mul><pos><state>959948<step>9981081<col>108<step>9436044<step>5945089<col>908<step>9872080<step>5420100<step>9981181<col>118<step>5840058<step>9436094<col>409<step>9872081<col>108<ans>191418
add
44
7780
-877
-633
-244
3x3
+
-633+-244=
scratchpad-v3
negative
null
no_carry
--
train
336442
[ { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "34070" }, { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "34070" }, { "a_digit":...
-633+-244=<add><neg><state>336442<step>34070<step>34070<step>62080<ans>7780
mul
118
211310
-13112
44
-298
2x3
*
44*-298=
scratchpad-v3
negative
null
repeated_digit
+-
train
440892
[ { "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", ...
44*-298=<mul><neg><state>440892<step>4832032<col>203<step>4936039<step>4832071<col>107<step>4208015<step>4936051<step>0800051<col>105<step>4208013<step>0900013<col>301<step>0200001<col>100<ans>211310
div
162
000.500
0.5
-403
-806
3x3
/
-403/-806=
scratchpad-v3
positive
round-half-up
exact
--
train
403806
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 806, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-403/-806=<div><pos><state>403806<step>00040004<qmul>00000<rem>004<step>00400040<qmul>00000<rem>040<step>04030403<qmul>00000<rem>403<step>40304030<qmul>54030<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<ans>000.500
add
43
8820
-288
-54
-234
2x3
+
-54+-234=
scratchpad-v3
negative
null
no_carry
--
train
450432
[ { "a_digit": 4, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 8, "serialized": "44080" }, { "a_digit": 5, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "53080" }, { "a_digit":...
-54+-234=<add><neg><state>450432<step>44080<step>53080<step>02020<ans>8820
mul
119
390397
-793093
827
-959
3x3
*
827*-959=
scratchpad-v3
negative
null
high_column_sum
+-
train
728959
[ { "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", ...
827*-959=<mul><neg><state>728959<step>7963063<col>306<step>7535041<step>2918059<col>905<step>7963068<step>2510078<step>8972150<col>015<step>2918033<step>8540073<col>307<step>8972079<col>907<ans>390397
mul
120
825552
255528
-338
-756
3x3
*
-338*-756=
scratchpad-v3
positive
null
medium_column_sum
--
train
833657
[ { "a_digit": 8, "a_index": 0, "b_digit": 6, "b_index": 0, "column": 0, "kind": "term", "product": 48, "running_total": 48, "serialized": "8648048", "term_index": 0 }, { "carry_in": 0, "carry_out": 4, "column": 0, "column_sum": 48, "kind": "column", ...
-338*-756=<mul><pos><state>833657<step>8648048<col>804<step>8540044<step>3618062<col>206<step>8756062<step>3515077<step>3618095<col>509<step>3721030<step>3515045<col>504<step>3721025<col>502<ans>825552
sub
44
3610
-163
-965
-802
3x3
-
-965--802=
scratchpad-v3
negative
null
negative_result
--
val
569208
[ { "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": 6, "output_digit": 6, "serialized": "60060", "subtrahend...
-965--802=<sub><neg><state>569208<step>52030<step>60060<step>98010<ans>3610
div
161
000.908
-0.908
-554
610
3x3
/
-554/610=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
-+
train
554610
[ { "incoming_digit": 5, "kind": "partial", "partial": 5, "position": 0, "remainder_in": 0, "serialized": "00050005" }, { "divisor": 610, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-554/610=<div><neg><state>554610<step>00050005<qmul>00000<rem>005<step>00550055<qmul>00000<rem>055<step>05540554<qmul>00000<rem>554<step>55405540<qmul>95490<rem>050<step>05000500<qmul>00000<rem>500<step>50005000<qmul>84880<rem>120<step>12001200<qmul>10610<rem>590<ans>000.908
sub
41
9070
709
804
95
3x2
-
804-95=
scratchpad-v3
positive
null
borrow_through_zero
++
train
408590
[ { "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": 0, "output_digit": 0, "serialized": "09101", "subtrahend...
804-95=<sub><pos><state>408590<step>45091<step>09101<step>80170<ans>9070
sub
41
5160
615
700
85
3x2
-
700-85=
scratchpad-v3
positive
null
borrow_through_zero
++
test
007580
[ { "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": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
700-85=<sub><pos><state>007580<step>05051<step>08111<step>70160<ans>5160
div
161
000.191
0.191
-43
-225
2x3
/
-43/-225=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
--
train
043225
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 225, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-43/-225=<div><pos><state>043225<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04300430<qmul>10225<rem>205<step>20502050<qmul>92025<rem>025<step>02500250<qmul>10225<rem>025<step>02500250<qmul>10225<rem>025<ans>000.191
add
40
5980
895
890
5
3x1
+
890+5=
scratchpad-v3
positive
null
no_carry
++
train
098500
[ { "a_digit": 0, "b_digit": 5, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 5, "serialized": "05050" }, { "a_digit": 9, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "90090" }, { "a_digit":...
890+5=<add><pos><state>098500<step>05050<step>90090<step>80080<ans>5980
div
160
000.470
0.47
435
925
3x3
/
435/925=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
435925
[ { "incoming_digit": 4, "kind": "partial", "partial": 4, "position": 0, "remainder_in": 0, "serialized": "00040004" }, { "divisor": 925, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
435/925=<div><pos><state>435925<step>00040004<qmul>00000<rem>004<step>00430043<qmul>00000<rem>043<step>04350435<qmul>00000<rem>435<step>43504350<qmul>43700<rem>650<step>65006500<qmul>76475<rem>025<step>02500250<qmul>00000<rem>250<step>25002500<qmul>21850<rem>650<ans>000.470
sub
42
8710
178
947
769
3x3
-
947-769=
scratchpad-v3
positive
null
multi_borrow
++
train
749967
[ { "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": 4, "output_digit": 7, "serialized": "46171", "subtrahend...
947-769=<sub><pos><state>749967<step>79081<step>46171<step>97110<ans>8710
sub
41
6610
166
204
38
3x2
-
204-38=
scratchpad-v3
positive
null
borrow_through_zero
++
train
402830
[ { "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": 0, "output_digit": 6, "serialized": "03161", "subtrahend...
204-38=<sub><pos><state>402830<step>48061<step>03161<step>20110<ans>6610
add
42
4101
1014
565
449
3x3
+
565+449=
scratchpad-v3
positive
null
cascading_carry
++
train
565944
[ { "a_digit": 5, "b_digit": 9, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 4, "serialized": "59041" }, { "a_digit": 6, "b_digit": 4, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "64111" }, { "a_digit":...
565+449=<add><pos><state>565944<step>59041<step>64111<step>54101<ans>4101
mul
116
234200
2432
76
32
2x2
*
76*32=
scratchpad-v3
positive
null
low_column_sum
++
train
670230
[ { "a_digit": 6, "a_index": 0, "b_digit": 2, "b_index": 0, "column": 0, "kind": "term", "product": 12, "running_total": 12, "serialized": "6212012", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 12, "kind": "column", ...
76*32=<mul><pos><state>670230<step>6212012<col>201<step>6318019<step>7214033<col>303<step>6000003<step>7321024<step>0200024<col>402<step>7000002<step>0300002<col>200<step>0000000<col>000<ans>234200
div
162
000.533
0.533
-319
-599
3x3
/
-319/-599=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
319599
[ { "incoming_digit": 3, "kind": "partial", "partial": 3, "position": 0, "remainder_in": 0, "serialized": "00030003" }, { "divisor": 599, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-319/-599=<div><pos><state>319599<step>00030003<qmul>00000<rem>003<step>00310031<qmul>00000<rem>031<step>03190319<qmul>00000<rem>319<step>31903190<qmul>52995<rem>195<step>19501950<qmul>31797<rem>153<step>15301530<qmul>21198<rem>332<step>33203320<qmul>52995<rem>325<ans>000.533
mul
119
331479
-974133
-981
993
3x3
*
-981*993=
scratchpad-v3
negative
null
high_column_sum
-+
train
189399
[ { "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...
-981*993=<mul><neg><state>189399<step>1303003<col>300<step>1909009<step>8324033<col>303<step>1909012<step>8972084<step>9327111<col>111<step>8972083<step>9981164<col>416<step>9981097<col>709<ans>331479
mul
119
844650
56448
-882
-64
3x2
*
-882*-64=
scratchpad-v3
positive
null
medium_column_sum
--
train
288460
[ { "a_digit": 2, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 8, "running_total": 8, "serialized": "2408008", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 8, "kind": "column", "o...
-882*-64=<mul><pos><state>288460<step>2408008<col>800<step>2612012<step>8432044<col>404<step>2000004<step>8648052<step>8432084<col>408<step>8000008<step>8648056<col>605<step>8000005<col>500<ans>844650
div
159
000.143
0.143
-4
-28
1x2
/
-4/-28=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
004028
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 28, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
-4/-28=<div><pos><state>004028<step>00000000<qmul>00000<rem>000<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00400040<qmul>10028<rem>012<step>01200120<qmul>40112<rem>008<step>00800080<qmul>20056<rem>024<step>02400240<qmul>80224<rem>016<ans>000.143
div
159
149.500
-149.5
-897
6
3x1
/
-897/6=
scratchpad-v3
negative
round-half-up
exact
-+
train
897006
[ { "incoming_digit": 8, "kind": "partial", "partial": 8, "position": 0, "remainder_in": 0, "serialized": "00080008" }, { "divisor": 6, "kind": "quotient_product", "position": 0, "quotient_digit": 1, "quotient_product": 6, "serialized": "10006" }, { "kind": ...
-897/6=<div><neg><state>897006<step>00080008<qmul>10006<rem>002<step>00290029<qmul>40024<rem>005<step>00570057<qmul>90054<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>149.500
mul
117
053200
-2350
-25
94
2x2
*
-25*94=
scratchpad-v3
negative
null
low_column_sum
-+
train
520490
[ { "a_digit": 5, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 20, "running_total": 20, "serialized": "5420020", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 20, "kind": "column", ...
-25*94=<mul><neg><state>520490<step>5420020<col>002<step>5945047<step>2408055<col>505<step>5000005<step>2918023<step>0400023<col>302<step>2000002<step>0900002<col>200<step>0000000<col>000<ans>053200
add
42
2040
402
318
-84
3x2
-
318--84=
scratchpad-v3
positive
null
magnitude_addition
+-
train
813480
[ { "a_digit": 8, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "84021" }, { "a_digit": 1, "b_digit": 8, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "18101" }, { "a_digit":...
318--84=<add><pos><state>813480<step>84021<step>18101<step>30140<ans>2040
div
159
000.947
-0.947
36
-38
2x2
/
36/-38=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
036038
[ { "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":...
36/-38=<div><neg><state>036038<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00360036<qmul>00000<rem>036<step>03600360<qmul>90342<rem>018<step>01800180<qmul>40152<rem>028<step>02800280<qmul>70266<rem>014<step>01400140<qmul>30114<rem>026<ans>000.947
div
159
014.429
-14.429
-101
7
3x1
/
-101/7=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
-+
train
101007
[ { "incoming_digit": 1, "kind": "partial", "partial": 1, "position": 0, "remainder_in": 0, "serialized": "00010001" }, { "divisor": 7, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-101/7=<div><neg><state>101007<step>00010001<qmul>00000<rem>001<step>00100010<qmul>10007<rem>003<step>00310031<qmul>40028<rem>003<step>00300030<qmul>40028<rem>002<step>00200020<qmul>20014<rem>006<step>00600060<qmul>80056<rem>004<step>00400040<qmul>50035<rem>005<ans>014.429
add
42
1021
1201
557
644
3x3
+
557+644=
scratchpad-v3
positive
null
cascading_carry
++
train
755446
[ { "a_digit": 7, "b_digit": 4, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 1, "serialized": "74011" }, { "a_digit": 5, "b_digit": 4, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "54101" }, { "a_digit":...
557+644=<add><pos><state>755446<step>74011<step>54101<step>56121<ans>1021
div
159
000.652
-0.652
45
-69
2x2
/
45/-69=
scratchpad-v3
negative
round-half-up
rounded_below_one_down
+-
train
045069
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 69, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
45/-69=<div><neg><state>045069<step>00000000<qmul>00000<rem>000<step>00040004<qmul>00000<rem>004<step>00450045<qmul>00000<rem>045<step>04500450<qmul>60414<rem>036<step>03600360<qmul>50345<rem>015<step>01500150<qmul>20138<rem>012<step>01200120<qmul>10069<rem>051<ans>000.652
div
161
001.800
-1.8
727
-404
3x3
/
727/-404=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
train
727404
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 404, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
727/-404=<div><neg><state>727404<step>00070007<qmul>00000<rem>007<step>00720072<qmul>00000<rem>072<step>07270727<qmul>10404<rem>323<step>32303230<qmul>72828<rem>402<step>40204020<qmul>93636<rem>384<step>38403840<qmul>93636<rem>204<step>20402040<qmul>52020<rem>020<ans>001.800
add
43
8051
-1508
-695
813
3x3
-
-695-813=
scratchpad-v3
negative
null
magnitude_addition
-+
train
596318
[ { "a_digit": 5, "b_digit": 3, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 8, "serialized": "53080" }, { "a_digit": 9, "b_digit": 1, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "91001" }, { "a_digit":...
-695-813=<add><neg><state>596318<step>53080<step>91001<step>68151<ans>8051
add
43
7680
867
543
-324
3x3
-
543--324=
scratchpad-v3
positive
null
magnitude_addition
+-
train
345423
[ { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "34070" }, { "a_digit": 4, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 6, "serialized": "42060" }, { "a_digit":...
543--324=<add><pos><state>345423<step>34070<step>42060<step>53080<ans>7680
add
42
5760
675
379
296
3x3
+
379+296=
scratchpad-v3
positive
null
multi_carry
++
train
973692
[ { "a_digit": 9, "b_digit": 6, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 5, "serialized": "96051" }, { "a_digit": 7, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 7, "serialized": "79171" }, { "a_digit":...
379+296=<add><pos><state>973692<step>96051<step>79171<step>32160<ans>5760
mul
118
407220
-22704
44
-516
2x3
*
44*-516=
scratchpad-v3
negative
null
repeated_digit
+-
train
440615
[ { "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", ...
44*-516=<mul><neg><state>440615<step>4624024<col>402<step>4104006<step>4624030<col>003<step>4520023<step>4104027<step>0600027<col>702<step>4520022<step>0100022<col>202<step>0500002<col>200<ans>407220
add
43
6070
-706
-436
270
3x3
-
-436-270=
scratchpad-v3
negative
null
magnitude_addition
-+
train
634072
[ { "a_digit": 6, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 6, "serialized": "60060" }, { "a_digit": 3, "b_digit": 7, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 0, "serialized": "37001" }, { "a_digit":...
-436-270=<add><neg><state>634072<step>60060<step>37001<step>42170<ans>6070
mul
119
030030
30030
-385
-78
3x2
*
-385*-78=
scratchpad-v3
positive
null
medium_column_sum
--
train
583870
[ { "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", ...
-385*-78=<mul><pos><state>583870<step>5840040<col>004<step>5735039<step>8864103<col>310<step>5000010<step>8756066<step>3824090<col>009<step>8000009<step>3721030<col>003<step>3000003<col>300<ans>030030
sub
43
5840
485
-18
-503
2x3
-
-18--503=
scratchpad-v3
positive
null
borrow_through_zero
--
train
305810
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 3, "output_digit": 5, "serialized": "38051", "subtrahend_digit": 8 }, { "borrow_in": 1, "borrow_out": 1, "column": 1, "minuend_digit": 0, "output_digit": 8, "serialized": "01181", "subtrahend...
-18--503=<sub><pos><state>305810<step>38051<step>01181<step>50140<ans>5840
div
161
000.068
0.068
-25
-370
2x3
/
-25/-370=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
--
train
025370
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 370, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-25/-370=<div><pos><state>025370<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00250025<qmul>00000<rem>025<step>02500250<qmul>00000<rem>250<step>25002500<qmul>62220<rem>280<step>28002800<qmul>72590<rem>210<step>21002100<qmul>51850<rem>250<ans>000.068
add
41
4310
-134
-9
125
1x3
-
-9-125=
scratchpad-v3
negative
null
magnitude_addition
-+
train
900521
[ { "a_digit": 9, "b_digit": 5, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 4, "serialized": "95041" }, { "a_digit": 0, "b_digit": 2, "carry_in": 1, "carry_out": 0, "column": 1, "output_digit": 3, "serialized": "02130" }, { "a_digit":...
-9-125=<add><neg><state>900521<step>95041<step>02130<step>01010<ans>4310
mul
118
526270
-72625
875
-83
3x2
*
875*-83=
scratchpad-v3
negative
null
medium_column_sum
+-
train
578380
[ { "a_digit": 5, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 15, "running_total": 15, "serialized": "5315015", "term_index": 0 }, { "carry_in": 0, "carry_out": 1, "column": 0, "column_sum": 15, "kind": "column", ...
875*-83=<mul><neg><state>578380<step>5315015<col>501<step>5840041<step>7321062<col>206<step>5000006<step>7856062<step>8324086<col>608<step>7000008<step>8864072<col>207<step>8000007<col>700<ans>526270
mul
119
695220
22596
-269
-84
3x2
*
-269*-84=
scratchpad-v3
positive
null
medium_column_sum
--
train
962480
[ { "a_digit": 9, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "9436036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
-269*-84=<mul><pos><state>962480<step>9436036<col>603<step>9872075<step>6424099<col>909<step>9000009<step>6848057<step>2408065<col>506<step>6000006<step>2816022<col>202<step>2000002<col>200<ans>695220
add
42
9730
379
322
-57
3x2
-
322--57=
scratchpad-v3
positive
null
magnitude_addition
+-
train
223750
[ { "a_digit": 2, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 9, "serialized": "27090" }, { "a_digit": 2, "b_digit": 5, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "25070" }, { "a_digit":...
322--57=<add><pos><state>223750<step>27090<step>25070<step>30030<ans>9730
sub
40
5100
15
62
47
2x2
-
62-47=
scratchpad-v3
positive
null
single_borrow
++
train
260740
[ { "borrow_in": 0, "borrow_out": 1, "column": 0, "minuend_digit": 2, "output_digit": 5, "serialized": "27051", "subtrahend_digit": 7 }, { "borrow_in": 1, "borrow_out": 0, "column": 1, "minuend_digit": 6, "output_digit": 1, "serialized": "64110", "subtrahend...
62-47=<sub><pos><state>260740<step>27051<step>64110<step>00000<ans>5100
sub
41
1120
-211
1
-212
1x3
+
1+-212=
scratchpad-v3
negative
null
magnitude_subtraction
+-
test
212100
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 2, "output_digit": 1, "serialized": "21010", "subtrahend_digit": 1 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 1, "output_digit": 1, "serialized": "10010", "subtrahend...
1+-212=<sub><neg><state>212100<step>21010<step>10010<step>20020<ans>1120
div
160
011.691
-11.691
795
-68
3x2
/
795/-68=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
795068
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 68, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
795/-68=<div><neg><state>795068<step>00070007<qmul>00000<rem>007<step>00790079<qmul>10068<rem>011<step>01150115<qmul>10068<rem>047<step>04700470<qmul>60408<rem>062<step>06200620<qmul>90612<rem>008<step>00800080<qmul>10068<rem>012<step>01200120<qmul>10068<rem>052<ans>011.691
sub
41
6170
716
802
86
3x2
-
802-86=
scratchpad-v3
positive
null
borrow_through_zero
++
train
208680
[ { "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": 0, "output_digit": 1, "serialized": "08111", "subtrahend...
802-86=<sub><pos><state>208680<step>26061<step>08111<step>80170<ans>6170
mul
117
713000
-317
1
-317
1x3
*
1*-317=
scratchpad-v3
negative
null
identity
+-
train
100713
[ { "a_digit": 1, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 7, "running_total": 7, "serialized": "1707007", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 7, "kind": "column", "o...
1*-317=<mul><neg><state>100713<step>1707007<col>700<step>1101001<step>0700001<col>100<step>1303003<step>0100003<step>0700003<col>300<step>0300000<step>0100000<col>000<step>0300000<col>000<ans>713000
mul
119
654687
-786456
993
-792
3x3
*
993*-792=
scratchpad-v3
negative
null
high_column_sum
+-
train
399297
[ { "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...
993*-792=<mul><neg><state>399297<step>3206006<col>600<step>3927027<step>9218045<col>504<step>3721025<step>9981106<step>9218124<col>412<step>9763075<step>9981156<col>615<step>9763078<col>807<ans>654687
div
161
001.135
-1.135
999
-880
3x3
/
999/-880=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
999880
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 880, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
999/-880=<div><neg><state>999880<step>00090009<qmul>00000<rem>009<step>00990099<qmul>00000<rem>099<step>09990999<qmul>10880<rem>119<step>11901190<qmul>10880<rem>310<step>31003100<qmul>32640<rem>460<step>46004600<qmul>54400<rem>200<step>20002000<qmul>21760<rem>240<ans>001.135
sub
42
2710
172
637
465
3x3
-
637-465=
scratchpad-v3
positive
null
single_borrow
++
train
736564
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 7, "output_digit": 2, "serialized": "75020", "subtrahend_digit": 5 }, { "borrow_in": 0, "borrow_out": 1, "column": 1, "minuend_digit": 3, "output_digit": 7, "serialized": "36071", "subtrahend...
637-465=<sub><pos><state>736564<step>75020<step>36071<step>64110<ans>2710
div
159
000.592
0.592
71
120
2x3
/
71/120=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
071120
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 120, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
71/120=<div><pos><state>071120<step>00000000<qmul>00000<rem>000<step>00070007<qmul>00000<rem>007<step>00710071<qmul>00000<rem>071<step>07100710<qmul>50600<rem>110<step>11001100<qmul>91080<rem>020<step>02000200<qmul>10120<rem>080<step>08000800<qmul>60720<rem>080<ans>000.592
mul
117
500500
-5005
-77
65
2x2
*
-77*65=
scratchpad-v3
negative
null
repeated_digit
-+
val
770560
[ { "a_digit": 7, "a_index": 0, "b_digit": 5, "b_index": 0, "column": 0, "kind": "term", "product": 35, "running_total": 35, "serialized": "7535035", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 35, "kind": "column", ...
-77*65=<mul><neg><state>770560<step>7535035<col>503<step>7642045<step>7535080<col>008<step>7000008<step>7642050<step>0500050<col>005<step>7000005<step>0600005<col>500<step>0000000<col>000<ans>500500
sub
42
5100
15
-31
-46
2x2
-
-31--46=
scratchpad-v3
positive
null
no_borrow
--
train
640130
[ { "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": 4, "output_digit": 1, "serialized": "43010", "subtrahend...
-31--46=<sub><pos><state>640130<step>61050<step>43010<step>00000<ans>5100
add
44
2270
-722
-224
-498
3x3
+
-224+-498=
scratchpad-v3
negative
null
multi_carry
--
train
422894
[ { "a_digit": 4, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "48021" }, { "a_digit": 2, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 2, "serialized": "29121" }, { "a_digit":...
-224+-498=<add><neg><state>422894<step>48021<step>29121<step>24170<ans>2270
mul
119
312629
-926213
997
-929
3x3
*
997*-929=
scratchpad-v3
negative
null
high_column_sum
+-
train
799929
[ { "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", ...
997*-929=<mul><neg><state>799929<step>7963063<col>306<step>7214020<step>9981101<col>110<step>7963073<step>9218091<step>9981172<col>217<step>9981098<step>9218116<col>611<step>9981092<col>209<ans>312629
sub
41
6700
-76
-79
-3
2x1
-
-79--3=
scratchpad-v3
negative
null
negative_result
--
train
970300
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 9, "output_digit": 6, "serialized": "93060", "subtrahend_digit": 3 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 7, "output_digit": 7, "serialized": "70070", "subtrahend...
-79--3=<sub><neg><state>970300<step>93060<step>70070<step>00000<ans>6700
div
159
000.455
-0.455
30
-66
2x2
/
30/-66=
scratchpad-v3
negative
round-half-up
rounded_below_one_up
+-
train
030066
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 66, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
30/-66=<div><neg><state>030066<step>00000000<qmul>00000<rem>000<step>00030003<qmul>00000<rem>003<step>00300030<qmul>00000<rem>030<step>03000300<qmul>40264<rem>036<step>03600360<qmul>50330<rem>030<step>03000300<qmul>40264<rem>036<step>03600360<qmul>50330<rem>030<ans>000.455
mul
118
911000
119
-1
-119
1x3
*
-1*-119=
scratchpad-v3
positive
null
identity
--
train
100911
[ { "a_digit": 1, "a_index": 0, "b_digit": 9, "b_index": 0, "column": 0, "kind": "term", "product": 9, "running_total": 9, "serialized": "1909009", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 9, "kind": "column", "o...
-1*-119=<mul><pos><state>100911<step>1909009<col>900<step>1101001<step>0900001<col>100<step>1101001<step>0100001<step>0900001<col>100<step>0100000<step>0100000<col>000<step>0100000<col>000<ans>911000
mul
117
221830
38122
778
49
3x2
*
778*49=
scratchpad-v3
positive
null
medium_column_sum
++
train
877940
[ { "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", ...
778*49=<mul><pos><state>877940<step>8972072<col>207<step>8432039<step>7963102<col>210<step>8000010<step>7428038<step>7963101<col>110<step>7000010<step>7428038<col>803<step>7000003<col>300<ans>221830
div
160
064.000
64
-576
-9
3x1
/
-576/-9=
scratchpad-v3
positive
round-half-up
exact
--
train
576009
[ { "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": ...
-576/-9=<div><pos><state>576009<step>00050005<qmul>00000<rem>005<step>00570057<qmul>60054<rem>003<step>00360036<qmul>40036<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>064.000
div
161
001.216
-1.216
755
-621
3x3
/
755/-621=
scratchpad-v3
negative
round-half-up
rounded_ge_one_up
+-
test
755621
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 621, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
755/-621=<div><neg><state>755621<step>00070007<qmul>00000<rem>007<step>00750075<qmul>00000<rem>075<step>07550755<qmul>10621<rem>134<step>13401340<qmul>21242<rem>098<step>09800980<qmul>10621<rem>359<step>35903590<qmul>53105<rem>485<step>48504850<qmul>74347<rem>503<ans>001.216
mul
118
235560
-65532
762
-86
3x2
*
762*-86=
scratchpad-v3
negative
null
medium_column_sum
+-
train
267680
[ { "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", ...
762*-86=<mul><neg><state>267680<step>2612012<col>201<step>2816017<step>6636053<col>305<step>2000005<step>6848053<step>7642095<col>509<step>6000009<step>7856065<col>506<step>7000006<col>600<ans>235560
div
160
000.663
0.663
629
949
3x3
/
629/949=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
629949
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 949, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
629/949=<div><pos><state>629949<step>00060006<qmul>00000<rem>006<step>00620062<qmul>00000<rem>062<step>06290629<qmul>00000<rem>629<step>62906290<qmul>65694<rem>596<step>59605960<qmul>65694<rem>266<step>26602660<qmul>21898<rem>762<step>76207620<qmul>87592<rem>028<ans>000.663
div
160
074.444
74.444
-670
-9
3x1
/
-670/-9=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
670009
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 9, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind": ...
-670/-9=<div><pos><state>670009<step>00060006<qmul>00000<rem>006<step>00670067<qmul>70063<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<step>00400040<qmul>40036<rem>004<ans>074.444
add
42
2590
952
132
820
3x3
+
132+820=
scratchpad-v3
positive
null
no_carry
++
train
231028
[ { "a_digit": 2, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "20020" }, { "a_digit": 3, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 5, "serialized": "32050" }, { "a_digit":...
132+820=<add><pos><state>231028<step>20020<step>32050<step>18090<ans>2590
div
162
006.257
6.257
-707
-113
3x3
/
-707/-113=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
707113
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 113, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-707/-113=<div><pos><state>707113<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07070707<qmul>60678<rem>029<step>02900290<qmul>20226<rem>064<step>06400640<qmul>50565<rem>075<step>07500750<qmul>60678<rem>072<step>07200720<qmul>60678<rem>042<ans>006.257
add
43
2860
682
121
-561
3x3
-
121--561=
scratchpad-v3
positive
null
magnitude_addition
+-
train
121165
[ { "a_digit": 1, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "11020" }, { "a_digit": 2, "b_digit": 6, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "26080" }, { "a_digit":...
121--561=<add><pos><state>121165<step>11020<step>26080<step>15060<ans>2860
div
161
001.568
-1.568
690
-440
3x3
/
690/-440=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
+-
train
690440
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 440, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
690/-440=<div><neg><state>690440<step>00060006<qmul>00000<rem>006<step>00690069<qmul>00000<rem>069<step>06900690<qmul>10440<rem>250<step>25002500<qmul>52200<rem>300<step>30003000<qmul>62640<rem>360<step>36003600<qmul>83520<rem>080<step>08000800<qmul>10440<rem>360<ans>001.568
mul
119
881850
58188
-746
-78
3x2
*
-746*-78=
scratchpad-v3
positive
null
medium_column_sum
--
train
647870
[ { "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", ...
-746*-78=<mul><pos><state>647870<step>6848048<col>804<step>6742046<step>4832078<col>807<step>6000007<step>4728035<step>7856091<col>109<step>4000009<step>7749058<col>805<step>7000005<col>500<ans>881850
mul
120
460824
428064
-624
-686
3x3
*
-624*-686=
scratchpad-v3
positive
null
medium_column_sum
--
train
426686
[ { "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", ...
-624*-686=<mul><pos><state>426686<step>4624024<col>402<step>4832034<step>2612046<col>604<step>4624028<step>2816044<step>6636080<col>008<step>2612020<step>6848068<col>806<step>6636042<col>204<ans>460824
mul
118
832000
238
-14
-17
2x2
*
-14*-17=
scratchpad-v3
positive
null
low_column_sum
--
train
410710
[ { "a_digit": 4, "a_index": 0, "b_digit": 7, "b_index": 0, "column": 0, "kind": "term", "product": 28, "running_total": 28, "serialized": "4728028", "term_index": 0 }, { "carry_in": 0, "carry_out": 2, "column": 0, "column_sum": 28, "kind": "column", ...
-14*-17=<mul><pos><state>410710<step>4728028<col>802<step>4104006<step>1707013<col>301<step>4000001<step>1101002<step>0700002<col>200<step>1000000<step>0100000<col>000<step>0000000<col>000<ans>832000
add
42
7170
717
649
-68
3x2
-
649--68=
scratchpad-v3
positive
null
magnitude_addition
+-
train
946860
[ { "a_digit": 9, "b_digit": 8, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 7, "serialized": "98071" }, { "a_digit": 4, "b_digit": 6, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "46111" }, { "a_digit":...
649--68=<add><pos><state>946860<step>98071<step>46111<step>60170<ans>7170
sub
42
7840
487
819
332
3x3
-
819-332=
scratchpad-v3
positive
null
single_borrow
++
train
918233
[ { "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": 1, "output_digit": 8, "serialized": "13081", "subtrahend...
819-332=<sub><pos><state>918233<step>92070<step>13081<step>83140<ans>7840
mul
116
672100
1276
29
44
2x2
*
29*44=
scratchpad-v3
positive
null
repeated_digit
++
train
920440
[ { "a_digit": 9, "a_index": 0, "b_digit": 4, "b_index": 0, "column": 0, "kind": "term", "product": 36, "running_total": 36, "serialized": "9436036", "term_index": 0 }, { "carry_in": 0, "carry_out": 3, "column": 0, "column_sum": 36, "kind": "column", ...
29*44=<mul><pos><state>920440<step>9436036<col>603<step>9436039<step>2408047<col>704<step>9000004<step>2408012<step>0400012<col>201<step>2000001<step>0400001<col>100<step>0000000<col>000<ans>672100
div
162
001.512
1.512
-700
-463
3x3
/
-700/-463=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
700463
[ { "incoming_digit": 7, "kind": "partial", "partial": 7, "position": 0, "remainder_in": 0, "serialized": "00070007" }, { "divisor": 463, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-700/-463=<div><pos><state>700463<step>00070007<qmul>00000<rem>007<step>00700070<qmul>00000<rem>070<step>07000700<qmul>10463<rem>237<step>23702370<qmul>52315<rem>055<step>05500550<qmul>10463<rem>087<step>08700870<qmul>10463<rem>407<step>40704070<qmul>83704<rem>366<ans>001.512
add
43
1831
-1381
-880
501
3x3
-
-880-501=
scratchpad-v3
negative
null
magnitude_addition
-+
train
088105
[ { "a_digit": 0, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 1, "serialized": "01010" }, { "a_digit": 8, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 8, "serialized": "80080" }, { "a_digit":...
-880-501=<add><neg><state>088105<step>01010<step>80080<step>85031<ans>1831
sub
44
2320
232
-193
-425
3x3
-
-193--425=
scratchpad-v3
positive
null
single_borrow
--
train
524391
[ { "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...
-193--425=<sub><pos><state>524391<step>53020<step>29031<step>41120<ans>2320
div
158
000.000
0
0
351
1x3
/
0/351=
scratchpad-v3
positive
round-half-up
zero_numerator
++
train
000351
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 351, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
0/351=<div><pos><state>000351<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
add
44
2360
-632
-339
-293
3x3
+
-339+-293=
scratchpad-v3
negative
null
multi_carry
--
train
933392
[ { "a_digit": 9, "b_digit": 3, "carry_in": 0, "carry_out": 1, "column": 0, "output_digit": 2, "serialized": "93021" }, { "a_digit": 3, "b_digit": 9, "carry_in": 1, "carry_out": 1, "column": 1, "output_digit": 3, "serialized": "39131" }, { "a_digit":...
-339+-293=<add><neg><state>933392<step>93021<step>39131<step>32160<ans>2360
div
162
001.013
1.013
-940
-928
3x3
/
-940/-928=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
--
train
940928
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 928, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-940/-928=<div><pos><state>940928<step>00090009<qmul>00000<rem>009<step>00940094<qmul>00000<rem>094<step>09400940<qmul>10928<rem>012<step>01200120<qmul>00000<rem>120<step>12001200<qmul>10928<rem>272<step>27202720<qmul>21856<rem>864<step>86408640<qmul>98352<rem>288<ans>001.013
sub
44
6730
376
-157
-533
3x3
-
-157--533=
scratchpad-v3
positive
null
multi_borrow
--
train
335751
[ { "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": 3, "output_digit": 7, "serialized": "35171", "subtrahend...
-157--533=<sub><pos><state>335751<step>37061<step>35171<step>51130<ans>6730
mul
118
687312
213786
222
963
3x3
*
222*963=
scratchpad-v3
positive
null
repeated_digit
++
train
222369
[ { "a_digit": 2, "a_index": 0, "b_digit": 3, "b_index": 0, "column": 0, "kind": "term", "product": 6, "running_total": 6, "serialized": "2306006", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 6, "kind": "column", "o...
222*963=<mul><pos><state>222369<step>2306006<col>600<step>2612012<step>2306018<col>801<step>2918019<step>2612031<step>2306037<col>703<step>2918021<step>2612033<col>303<step>2918021<col>102<ans>687312
div
157
010.333
10.333
31
3
2x1
/
31/3=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
++
train
031003
[ { "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": ...
31/3=<div><pos><state>031003<step>00000000<qmul>00000<rem>000<step>00030003<qmul>10003<rem>000<step>00010001<qmul>00000<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<step>00100010<qmul>30009<rem>001<ans>010.333
add
41
2770
-772
-772
0
3x1
-
-772-0=
scratchpad-v3
negative
null
identity
-+
train
277000
[ { "a_digit": 2, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 2, "serialized": "20020" }, { "a_digit": 7, "b_digit": 0, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "70070" }, { "a_digit":...
-772-0=<add><neg><state>277000<step>20020<step>70070<step>70070<ans>2770
mul
118
029730
-37920
79
-480
2x3
*
79*-480=
scratchpad-v3
negative
null
contains_zero_digit
+-
train
970084
[ { "a_digit": 9, "a_index": 0, "b_digit": 0, "b_index": 0, "column": 0, "kind": "term", "product": 0, "running_total": 0, "serialized": "9000000", "term_index": 0 }, { "carry_in": 0, "carry_out": 0, "column": 0, "column_sum": 0, "kind": "column", "o...
79*-480=<mul><neg><state>970084<step>9000000<col>000<step>9872072<step>7000072<col>207<step>9436043<step>7856099<step>0000099<col>909<step>7428037<step>0800037<col>703<step>0400003<col>300<ans>029730
add
43
4980
-894
-802
-92
3x2
+
-802+-92=
scratchpad-v3
negative
null
no_carry
--
train
208290
[ { "a_digit": 2, "b_digit": 2, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 4, "serialized": "22040" }, { "a_digit": 0, "b_digit": 9, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 9, "serialized": "09090" }, { "a_digit":...
-802+-92=<add><neg><state>208290<step>22040<step>09090<step>80080<ans>4980
mul
119
865470
74568
-956
-78
3x2
*
-956*-78=
scratchpad-v3
positive
null
medium_column_sum
--
train
659870
[ { "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", ...
-956*-78=<mul><pos><state>659870<step>6848048<col>804<step>6742046<step>5840086<col>608<step>6000008<step>5735043<step>9872115<col>511<step>5000011<step>9763074<col>407<step>9000007<col>700<ans>865470
div
159
008.729
8.729
611
70
3x2
/
611/70=
scratchpad-v3
positive
round-half-up
rounded_ge_one_up
++
val
611070
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 70, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
611/70=<div><pos><state>611070<step>00060006<qmul>00000<rem>006<step>00610061<qmul>00000<rem>061<step>06110611<qmul>80560<rem>051<step>05100510<qmul>70490<rem>020<step>02000200<qmul>20140<rem>060<step>06000600<qmul>80560<rem>040<step>04000400<qmul>50350<rem>050<ans>008.729
div
161
001.124
-1.124
-697
620
3x3
/
-697/620=
scratchpad-v3
negative
round-half-up
rounded_ge_one_down
-+
train
697620
[ { "incoming_digit": 6, "kind": "partial", "partial": 6, "position": 0, "remainder_in": 0, "serialized": "00060006" }, { "divisor": 620, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-697/620=<div><neg><state>697620<step>00060006<qmul>00000<rem>006<step>00690069<qmul>00000<rem>069<step>06970697<qmul>10620<rem>077<step>07700770<qmul>10620<rem>150<step>15001500<qmul>21240<rem>260<step>26002600<qmul>42480<rem>120<step>12001200<qmul>10620<rem>580<ans>001.124
div
158
000.815
0.815
22
27
2x2
/
22/27=
scratchpad-v3
positive
round-half-up
rounded_below_one_up
++
train
022027
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 27, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
22/27=<div><pos><state>022027<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00220022<qmul>00000<rem>022<step>02200220<qmul>80216<rem>004<step>00400040<qmul>10027<rem>013<step>01300130<qmul>40108<rem>022<step>02200220<qmul>80216<rem>004<ans>000.815
div
158
000.774
0.774
24
31
2x2
/
24/31=
scratchpad-v3
positive
round-half-up
rounded_below_one_down
++
train
024031
[ { "incoming_digit": 0, "kind": "partial", "partial": 0, "position": 0, "remainder_in": 0, "serialized": "00000000" }, { "divisor": 31, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind":...
24/31=<div><pos><state>024031<step>00000000<qmul>00000<rem>000<step>00020002<qmul>00000<rem>002<step>00240024<qmul>00000<rem>024<step>02400240<qmul>70217<rem>023<step>02300230<qmul>70217<rem>013<step>01300130<qmul>40124<rem>006<step>00600060<qmul>10031<rem>029<ans>000.774
div
162
002.464
2.464
-902
-366
3x3
/
-902/-366=
scratchpad-v3
positive
round-half-up
rounded_ge_one_down
--
train
902366
[ { "incoming_digit": 9, "kind": "partial", "partial": 9, "position": 0, "remainder_in": 0, "serialized": "00090009" }, { "divisor": 366, "kind": "quotient_product", "position": 0, "quotient_digit": 0, "quotient_product": 0, "serialized": "00000" }, { "kind"...
-902/-366=<div><pos><state>902366<step>00090009<qmul>00000<rem>009<step>00900090<qmul>00000<rem>090<step>09020902<qmul>20732<rem>170<step>17001700<qmul>41464<rem>236<step>23602360<qmul>62196<rem>164<step>16401640<qmul>41464<rem>176<step>17601760<qmul>41464<rem>296<ans>002.464
add
44
7121
-1217
-390
-827
3x3
+
-390+-827=
scratchpad-v3
negative
null
overflow
--
train
093728
[ { "a_digit": 0, "b_digit": 7, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "07070" }, { "a_digit": 9, "b_digit": 2, "carry_in": 0, "carry_out": 1, "column": 1, "output_digit": 1, "serialized": "92011" }, { "a_digit":...
-390+-827=<add><neg><state>093728<step>07070<step>92011<step>38121<ans>7121
sub
40
4300
34
36
-2
2x1
+
36+-2=
scratchpad-v3
positive
null
magnitude_subtraction
+-
train
630200
[ { "borrow_in": 0, "borrow_out": 0, "column": 0, "minuend_digit": 6, "output_digit": 4, "serialized": "62040", "subtrahend_digit": 2 }, { "borrow_in": 0, "borrow_out": 0, "column": 1, "minuend_digit": 3, "output_digit": 3, "serialized": "30030", "subtrahend...
36+-2=<sub><pos><state>630200<step>62040<step>30030<step>00000<ans>4300
add
43
7720
-277
-263
-14
3x2
+
-263+-14=
scratchpad-v3
negative
null
no_carry
--
train
362410
[ { "a_digit": 3, "b_digit": 4, "carry_in": 0, "carry_out": 0, "column": 0, "output_digit": 7, "serialized": "34070" }, { "a_digit": 6, "b_digit": 1, "carry_in": 0, "carry_out": 0, "column": 1, "output_digit": 7, "serialized": "61070" }, { "a_digit":...
-263+-14=<add><neg><state>362410<step>34070<step>61070<step>20020<ans>7720