Details

Time bar (total: 4.7min)

sample112.0ms

Algorithm
intervals
Results
53.0ms150×body1280valid
31.0ms31×body2560valid
12.0ms51×body640valid
3.0ms14×body320valid
1.0msbody160valid
0.0msbody80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.9b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(cos x)
0.6b
(- (cos (+ x eps)) (cos x))
4.0b
(cos (+ x eps))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity add-log-exp
pow1 add-exp-log add-cube-cbrt add-cbrt-cube
cos-sum
associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
3 → 31
Calls
3 calls:
2.0ms
(cos x)
7.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

series19.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(cos x)
11.0ms
(- (cos (+ x eps)) (cos x))
6.0ms
(cos (+ x eps))

simplify44.4s

Counts
40 → 40
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
055
165
done65
055
165
done65
055
165
done65
055
165
done65
0611
1711
done711
055
165
done65
0614
1814
2106
3156
4216
5316
6546
71106
83196
912596
done50016
055
165
done65
055
165
done65
01117
12117
23317
34215
44713
55613
68113
79113
811213
913513
1015213
1116513
1217913
1322413
1443713
1591313
16224411
done500011
089
1118
2138
3168
4198
5258
6298
7458
8498
9548
10618
11808
121018
131138
141168
done1168
078
1108
2118
done118
078
1138
2168
3198
4258
5298
6458
7498
8548
9618
10798
111008
121138
131168
done1168
0817
11117
21217
done1217
078
1108
2118
done118
0823
11223
2279
3709
41799
55079
617179
749529
done50009
078
1108
2118
done118
078
1108
2118
done118
0911
12511
24711
38111
416511
549711
6223811
done500011
01023
11820
22620
32918
43018
done3018
033
done33
0815
11415
22115
33615
46115
510215
616615
733415
8164415
done500015
067
187
done87
089
1109
done109
089
1119
2129
done129
067
197
2107
done107
078
198
done98
033
done33
033
done33
033
done33
047
done47
033
done33
048
158
274
3124
4184
5284
6494
71084
83164
912364
done50004
033
done33
033
done33
01011
12311
24511
31029
42389
56249
625259
done50009
044
154
done54
044
154
done54
01417
13717
29115
319615
438813
584413
6246513
done500013
067
197
2107
done107
067
197
2107
done107
01213
12813
27313
318613
455413
5127513
6439013
done500013
022
done22
022
done22

prune76.0ms

Filtered
31 candidates to 40 candidates (-29.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New33740
Fresh000
Picked101
Done000
Total34741

Merged error: 0.4b

Counts
41 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (+ x (/ eps 2)))))
0.3b
(* (sin (/ eps 2)) (sin (+ x (/ eps 2))))
4.1b
(sin (+ x (/ eps 2)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-cbrt-cube
add-sqr-sqrt
sin-sum
add-cube-cbrt *-un-lft-identity associate-*l*
distribute-rgt-in distribute-lft-in
associate-*r* pow-prod-down prod-exp cbrt-unprod
add-log-exp
*-commutative sin-mult
associate-*r/ unswap-sqr
Counts
3 → 52
Calls
3 calls:
18.0ms
(* -2 (* (sin (/ eps 2)) (sin (+ x (/ eps 2)))))
11.0ms
(* (sin (/ eps 2)) (sin (+ x (/ eps 2))))
8.0ms
(sin (+ x (/ eps 2)))

series37.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(* -2 (* (sin (/ eps 2)) (sin (+ x (/ eps 2)))))
13.0ms
(* (sin (/ eps 2)) (sin (+ x (/ eps 2))))
8.0ms
(sin (+ x (/ eps 2)))

simplify1.2min

Counts
61 → 61
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
077
187
done87
077
187
done87
077
187
done87
077
187
done87
0815
1915
done915
077
187
done87
0820
11020
2128
3168
4228
5328
6538
71148
83278
912618
done50008
077
187
done87
077
187
done87
01021
11821
23121
34513
45512
518911
68339
715917
837737
done50017
0811
11011
done1011
01013
11213
done1213
0912
11412
21512
done1512
0912
11312
21812
32612
44912
510712
624912
771112
8271012
done500012
01235
12035
24515
38315
413713
525613
665913
7243613
done500113
01025
11225
done1225
0912
11112
done1112
01035
12235
25113
39513
411313
515913
631013
776813
8278113
done500113
0912
11112
done1112
0912
11112
done1112
01013
11213
done1213
01013
11213
done1213
0912
11312
21912
done1912
0812
11012
21312
done1312
0912
11312
21912
done1912
0812
11212
21312
done1312
01020
11420
21620
done1620
0912
11112
done1112
066
194
2124
done124
0912
11112
done1112
0912
11112
done1112
0811
11011
done1011
01013
11513
22113
done2113
01013
11513
22113
done2113
01316
11816
22416
done2416
01215
11815
22315
32715
done2715
01114
11914
23214
34614
done4614
01114
11814
23114
35914
411914
526114
666914
7235814
done500014
01641
13237
28817
327017
483215
5226215
done500015
01441
13437
29215
330015
475615
5148215
6246115
done500015
01229
11729
22329
32529
done2529
01114
11614
22214
32414
done2414
01241
12839
29715
340615
4113115
5156015
6237715
done500015
01114
11614
22214
32414
done2414
01114
11614
22214
32414
done2414
01114
11814
23814
36014
46114
done6114
01014
11514
22814
34414
44814
done4814
01114
11814
23714
36214
46414
done6414
01014
11714
23014
34214
44314
done4314
01114
11814
23714
36314
46514
done6514
01014
11514
22714
34314
44514
done4514
01114
11814
23814
36314
46414
done6414
01014
11714
23214
34214
done4214
066
176
done76
01114
11614
22214
done2214
01114
11614
22214
done2214
01013
11513
22113
done2113
01223
12123
24023
35915
47314
520713
685011
715669
837529
done50019
01011
12511
25711
312511
427011
562911
6201711
done500011
066
186
done86
066
186
done86
01517
13417
28717
314517
425615
539915
664215
7122315
8280415
done500115
0811
11111
done1111
0811
11111
done1111
01315
12915
27115
312415
419413
530513
651513
7103413
8276113
done500113
01013
11613
22213
32413
done2413
01013
11613
22213
32413
done2413

prune182.0ms

Filtered
50 candidates to 61 candidates (-22.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New53861
Fresh246
Picked101
Done000
Total561268

Merged error: 0.1b

Counts
68 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (sin (/ eps 2)))
0.2b
(* (sin x) (cos (/ eps 2)))
0.2b
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))
0.3b
(* (sin (/ eps 2)) (* (sin x) (cos (/ eps 2))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×associate-*l*
10×add-cube-cbrt *-un-lft-identity
associate-*r* pow-prod-down prod-exp cbrt-unprod
*-commutative add-log-exp
sin-cos-mult unswap-sqr
associate-*r/
Counts
4 → 74
Calls
4 calls:
6.0ms
(* (cos x) (sin (/ eps 2)))
5.0ms
(* (sin x) (cos (/ eps 2)))
14.0ms
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))
9.0ms
(* (sin (/ eps 2)) (* (sin x) (cos (/ eps 2))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (cos x) (sin (/ eps 2)))
11.0ms
(* (sin x) (cos (/ eps 2)))
13.0ms
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))
19.0ms
(* (sin (/ eps 2)) (* (sin x) (cos (/ eps 2))))

simplify1.4min

Counts
86 → 86
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0912
11312
21912
done1912
0912
11312
21912
done1912
01215
11615
22215
32415
done2415
01114
11614
22114
32514
done2514
01013
11713
23013
34213
44413
done4413
01013
11613
22913
35413
411113
525013
661313
7180513
done500113
01538
12838
29418
333018
4107816
5296016
done500116
01338
13038
29816
337516
4106214
5203614
6490814
done500014
01127
11527
22127
done2127
01013
11413
22013
done2013
01138
12538
29614
341314
4121614
5170014
6315114
done500014
01013
11413
22013
done2013
01013
11413
22013
done2013
077
187
done87
01013
11413
22013
32213
done2213
01013
11413
22013
32213
done2213
0912
11312
21912
done1912
01118
12218
22618
done2618
0812
11012
21312
done1312
0812
11012
21312
done1312
01015
11215
21515
31611
41711
done1711
01014
11414
21714
31911
42011
done2011
0913
11413
22113
32713
42811
52911
done2911
0913
11313
22113
33913
48313
518913
647313
7145613
done500113
01238
12238
26918
319911
441211
5106011
6377411
done500011
01238
12838
29216
324416
442714
5100111
6308311
done500011
01027
11227
21527
done1527
0913
11113
21413
done1413
01038
12238
27014
318214
435014
554411
6134811
7444011
done500011
0913
11113
21413
done1413
0913
11113
21413
done1413
077
187
done87
0913
11313
21913
done1913
0913
11313
21913
done1913
0812
11012
21312
done1312
0913
11313
21613
done1613
077
187
done87
099
1109
done109
088
1128
2138
done138
088
1118
2168
3248
4478
51038
62408
77028
827088
done50008
01123
11823
24311
37911
41359
52609
66599
724589
done50019
0917
11017
done1017
088
198
done98
0923
12023
2499
3919
41079
51539
62959
77479
827509
done50019
088
198
done98
088
198
done98
099
1109
done109
099
1109
done109
0914
11214
21414
done1414
088
198
done98
044
172
2102
done102
088
198
done98
088
198
done98
077
187
done87
077
187
done87
099
1109
done109
088
1128
2138
done138
088
1118
2168
3248
4478
51038
62408
77028
827088
done50008
01123
11823
24311
37911
41359
52609
66599
724589
done50019
0917
11017
done1017
088
198
done98
0923
12023
2499
3919
41079
51539
62959
77479
827509
done50019
088
198
done98
088
198
done98
099
1109
done109
099
1109
done109
0914
11214
21414
done1414
088
198
done98
044
172
2102
done102
088
198
done98
088
198
done98
077
187
done87
055
195
2155
done155
0912
11412
22012
done2012
0912
11412
22012
done2012
01621
13821
213217
326017
455617
5102517
6156917
7291617
done500017
099
1169
2319
3509
41019
52519
67869
732559
done50019
099
1169
2319
3509
41019
52519
67869
732559
done50019
01315
13515
28815
318615
442615
590215
6290015
done500115
077
197
done97
077
197
done97
01517
13817
29215
319715
444515
594015
6302315
done500115
077
197
done97
077
197
done97

prune289.0ms

Filtered
65 candidates to 86 candidates (-32.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New79786
Fresh3811
Picked101
Done000
Total831598

Merged error: 0.0b

Counts
98 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (sin (/ eps 2)))
0.2b
(* (* (sin (/ eps 2)) (sin x)) (cos (/ eps 2)))
0.2b
(* (sin (/ eps 2)) (sin x))
0.2b
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
pow-prod-down prod-exp cbrt-unprod
*-commutative add-log-exp
sin-mult unswap-sqr
associate-*l/
Counts
4 → 74
Calls
4 calls:
6.0ms
(* (cos x) (sin (/ eps 2)))
8.0ms
(* (* (sin (/ eps 2)) (sin x)) (cos (/ eps 2)))
7.0ms
(* (sin (/ eps 2)) (sin x))
10.0ms
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (cos x) (sin (/ eps 2)))
18.0ms
(* (* (sin (/ eps 2)) (sin x)) (cos (/ eps 2)))
11.0ms
(* (sin (/ eps 2)) (sin x))
13.0ms
(* (sin (/ eps 2)) (* (cos x) (sin (/ eps 2))))

simplify1.3min

Counts
86 → 86
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0812
11012
21312
done1312
0812
11012
21312
done1312
01015
11215
21515
31611
41711
done1711
01014
11414
21714
31911
42011
done2011
0913
11413
22113
32713
42811
52911
done2911
0913
11313
22113
33913
48313
518913
647313
7145613
done500113
01238
12238
26918
319911
441211
5106011
6377411
done500011
01238
12838
29216
324416
442714
5100111
6308311
done500011
01027
11227
21527
done1527
0913
11113
21413
done1413
01038
12238
27014
318214
435014
554411
6134811
7444011
done500011
0913
11113
21413
done1413
0913
11113
21413
done1413
077
187
done87
0913
11313
21913
done1913
0913
11313
21913
done1913
0812
11012
21312
done1312
0913
11413
21613
done1613
077
187
done87
099
1109
done109
088
1128
2138
done138
088
1118
2168
3248
4478
51038
62408
77018
827148
done50008
01123
11823
24311
38011
41389
52659
66529
724409
done50019
0917
11017
done1017
088
198
done98
0923
12023
2499
3929
41089
51549
62929
77569
827509
done50019
088
198
done98
088
198
done98
099
1109
done109
099
1109
done109
0912
11212
21412
done1412
088
198
done98
066
194
2124
done124
088
198
done98
088
198
done98
077
187
done87
0912
11312
21912
done1912
0912
11312
21912
done1912
01215
11615
22215
32415
done2415
01114
11614
22114
32514
done2514
01013
11713
23013
34213
44413
done4413
01013
11613
23213
35413
411013
525113
659613
7157513
done500013
01538
12838
29318
333918
4109716
5300016
done500116
01338
13038
29716
337216
4112114
5217114
done500014
01127
11527
22127
done2127
01013
11413
22013
done2013
01138
12538
29514
343114
4122414
5170414
6328914
done500014
01013
11413
22013
done2013
01013
11413
22013
done2013
01119
11719
23019
34019
done4019
01013
11413
22013
32213
done2213
099
1157
2277
3357
done357
077
187
done87
01118
11718
22518
33018
43418
done3418
077
187
done87
099
1109
done109
088
1128
2138
done138
088
1118
2168
3248
4478
51038
62408
77028
827088
done50008
01123
11823
24311
37911
41359
52609
66599
724589
done50019
0917
11017
done1017
088
198
done98
0923
12023
2499
3919
41079
51539
62959
77479
827509
done50019
088
198
done98
088
198
done98
099
1109
done109
099
1109
done109
0914
11214
21414
done1414
088
198
done98
044
172
2102
done102
088
198
done98
088
198
done98
077
187
done87
01621
13821
213217
326017
455617
5102517
6156917
7291617
done500017
099
1169
2319
3509
41019
52519
67869
732559
done50019
099
1169
2319
3509
41019
52519
67869
732559
done50019
055
195
2155
done155
077
197
done97
077
197
done97
055
195
2155
done155
0912
11412
22012
done2012
0912
11412
22012
done2012
01517
13817
29215
319715
444515
594015
6302315
done500115
077
197
done97
077
197
done97

prune203.0ms

Filtered
66 candidates to 86 candidates (-30.3%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New86086
Fresh01414
Picked011
Done000
Total8615101

Merged error: 0.0b

Counts
101 → 15

regimes324.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01527
12127
done2127

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s4477×body1280valid
533.0ms641×body2560valid
472.0ms1865×body640valid
117.0ms646×body320valid
34.0ms291×body160valid
5.0ms80×body80valid

Profiling

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