Details

Time bar (total: 5.9min)

sample117.0ms

Algorithm
intervals
Results
56.0ms113×body1280valid
26.0ms31×body2560valid
13.0ms47×body640valid
4.0ms21×body320valid
3.0ms36×body80valid
1.0msbody160valid

simplify3.0ms

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: 38.4b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sin x)
0.9b
(- (sin (+ x eps)) (sin x))
4.3b
(sin (+ x eps))

rewrite14.0ms

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

series19.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(sin x)
10.0ms
(- (sin (+ x eps)) (sin x))
6.0ms
(sin (+ x eps))

simplify44.2s

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
1591213
16223511
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
1108
2118
done118
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
089
1229
2549
31169
42529
56089
619709
done50009
044
154
done54
044
154
done54
01217
13515
29415
318313
439311
572211
6127011
7160811
8213311
9407611
done500111
067
197
2107
done107
067
197
2107
done107
01113
13013
27213
315813
434513
585213
6283413
done500113
022
done22
022
done22

prune58.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New37340
Fresh000
Picked101
Done000
Total38341

Merged error: 0.4b

Counts
41 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (sin (/ eps 2)) (cos (+ x (/ eps 2))))
4.1b
(cos (+ x (/ eps 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
associate-*r* associate-*l*
add-log-exp
cos-sum pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod unswap-sqr
Counts
2 → 27
Calls
2 calls:
6.0ms
(* (sin (/ eps 2)) (cos (+ x (/ eps 2))))
7.0ms
(cos (+ x (/ eps 2)))

series17.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(* (sin (/ eps 2)) (cos (+ x (/ eps 2))))
6.0ms
(cos (+ x (/ eps 2)))

simplify33.0s

Counts
33 → 33
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
11721
22921
34313
45512
519012
68379
716037
837657
done50007
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
01020
11420
21620
done1620
0912
11112
done1112
066
194
2124
done124
0912
11112
done1112
0912
11112
done1112
0811
11011
done1011
01113
12911
2649
31499
43389
58519
636299
done50009
066
186
done86
066
186
done86
01517
13717
29517
319515
445915
597413
6306413
done500013
0811
11111
done1111
0811
11111
done1111

prune91.0ms

Filtered
27 candidates to 33 candidates (-22.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New29433
Fresh022
Picked101
Done000
Total30636

Merged error: 0.1b

Counts
36 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
associate-*r* associate-*l*
add-log-exp
cos-mult sin-mult
associate-*r/
sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
distribute-rgt-in flip3-- distribute-lft-in frac-sub flip-- sub-div
diff-log
Counts
4 → 78
Calls
4 calls:
8.0ms
(* (cos x) (cos (/ eps 2)))
5.0ms
(- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2))))
11.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2)))))
6.0ms
(* (sin x) (sin (/ eps 2)))

series69.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (cos x) (cos (/ eps 2)))
20.0ms
(- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2))))
27.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2)))))
11.0ms
(* (sin x) (sin (/ eps 2)))

simplify1.3min

Counts
90 → 90
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0913
11413
21813
done1813
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
01220
11720
23020
35220
45820
done5820
01422
11922
22622
done2622
01321
12121
23521
35721
46121
done6121
01321
12021
23821
38021
416221
533221
6107021
7453621
done500021
01662
12762
27724
332124
4163922
done500022
01443
11943
23243
35443
46243
done6243
01321
11821
23121
35321
45921
done5921
01462
12962
28922
336022
4152922
done500022
01321
11821
23121
35321
45921
done5921
01321
11821
23121
35321
45921
done5921
01422
11922
22622
done2622
01422
11922
22622
done2622
0912
11312
21912
done1912
0913
11713
22713
33213
done3213
0912
11312
21912
done1912
0913
11713
22713
33213
done3213
0912
11312
21912
done1912
0913
11713
22613
33213
done3213
0912
11312
21912
done1912
0913
11713
22613
33213
done3213
01438
12138
23038
done3038
01321
11821
22521
done2521
066
194
2124
done124
01321
11821
23121
36021
47421
58221
done8221
01321
11821
23121
36021
47421
58221
done8221
01220
11720
23020
35220
45820
done5820
01332
12632
26532
313820
421213
573513
6387313
done500013
01536
12636
25834
314034
436734
561215
692913
7387013
done500013
01524
13824
212824
345424
4146024
5421924
done500024
01436
13636
28736
321236
444136
573733
6117133
7199033
done500133
01317
12116
23316
36416
416316
560716
6392416
done500016
01216
11616
22316
done2316
01216
11916
23616
35716
412316
545516
6244016
done500016
01333
11733
22433
done2433
01216
11616
22316
done2316
01347
11847
23917
312917
451017
5191417
done500117
01216
11616
22316
done2316
01216
11616
22316
done2316
01127
12327
24627
38415
41148
54678
626428
done50008
01331
12331
24929
39329
420429
530510
64158
721698
done50008
023
131
done31
01419
13619
212019
338219
492419
5238219
done500119
01547
14239
29939
314139
415139
515339
done15339
088
1138
2158
done158
01331
13431
27531
313331
419831
533131
650531
786931
8267731
done500031
01115
11415
done1415
088
1138
2158
done158
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
055
195
2155
done155
077
197
done97
077
197
done97
01517
13717
29517
319515
445915
597413
6306413
done500013
01220
11820
23120
35320
45920
done5920
01220
11820
23120
35320
45920
done5920
01113
12911
2649
31499
43389
58519
636299
done50009
01115
11615
22315
done2315
01115
11615
22315
done2315
01213
12813
26113
314613
437513
5104213
6421013
done500013
077
197
done97
077
197
done97

prune273.0ms

Filtered
70 candidates to 90 candidates (-28.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New82890
Fresh235
Picked101
Done000
Total851196

Merged error: 0.0b

Counts
96 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (/ eps 2)) (- (* (cos x) (cos (/ eps 2))) (cbrt (pow (* (sin x) (sin (/ eps 2))) 3))))
0.2b
(* (sin x) (sin (/ eps 2)))
0.3b
(pow (* (sin x) (sin (/ eps 2))) 3)
25.5b
(cbrt (pow (* (sin x) (sin (/ eps 2))) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1 add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
cbrt-prod
associate-*r* associate-*l*
sin-mult add-log-exp
cube-div pow-unpow associate-*r/ pow-prod-down prod-exp cbrt-unprod
distribute-rgt-in cube-mult sub-neg unpow-prod-down cbrt-div pow-pow distribute-lft-in unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt unswap-sqr sqr-pow
pow-to-exp flip3-- pow1/3 cos-mult frac-sub flip-- rem-cbrt-cube
Counts
4 → 85
Calls
4 calls:
13.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (/ eps 2))) (cbrt (pow (* (sin x) (sin (/ eps 2))) 3))))
7.0ms
(* (sin x) (sin (/ eps 2)))
7.0ms
(pow (* (sin x) (sin (/ eps 2))) 3)
6.0ms
(cbrt (pow (* (sin x) (sin (/ eps 2))) 3))

series74.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (/ eps 2))) (cbrt (pow (* (sin x) (sin (/ eps 2))) 3))))
11.0ms
(* (sin x) (sin (/ eps 2)))
22.0ms
(pow (* (sin x) (sin (/ eps 2))) 3)
12.0ms
(cbrt (pow (* (sin x) (sin (/ eps 2))) 3))

simplify3.3min

Counts
97 → 97
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01111
1228
2618
31408
42638
56458
623728
done50018
01111
1228
2618
31468
42798
56848
625088
done50018
055
1132
2192
3292
4502
51062
63212
712362
done50002
077
1144
2204
3304
4534
51184
63354
712694
done50014
0916
11716
22816
32916
done2916
088
198
done98
01222
12216
25716
313116
424816
564316
6242916
done500016
01111
1228
2578
31368
42478
56278
623888
done50008
055
1132
2192
3292
4502
51062
63212
712362
done50002
077
1144
2204
3304
4534
51184
63354
712694
done50014
088
198
done98
0916
11716
22816
32916
done2916
01111
12211
25811
313711
426511
564111
6240911
done500011
01111
12211
25811
313711
426511
564111
6240911
done500011
022
141
done41
01010
1217
2567
31347
42547
56427
624117
done50007
01112
11710
22310
33310
45610
511710
634010
7126510
done500110
01112
11710
22310
33310
45610
511710
634010
7126510
done500110
01216
12413
24613
39413
421813
559213
6199613
done500013
044
1131
2171
3231
4331
5561
61151
73331
812671
done50011
01223
12317
25817
313917
426017
563417
6238217
done500017
01111
1228
2578
31368
42478
56278
623888
done50008
01232
1219
2569
31349
42529
56449
623999
done50019
01111
1228
2578
31368
42478
56278
623888
done50008
01111
1228
2578
31368
42478
56278
623888
done50008
01111
11311
22111
done2111
01010
11510
22210
32310
done2310
01010
11510
22210
32310
done2310
033
161
done61
033
161
done61
01113
11513
22213
34613
410213
526313
688413
7330113
done500013
01010
11410
21910
33710
47810
518910
656810
7220010
done500110
099
1167
2237
3347
4567
51207
63317
712697
done50017
044
1124
2184
3284
4494
51114
63254
712434
done50004
066
1136
2196
3296
4526
51126
63236
712506
done50006
0815
11615
22715
done2715
01010
12310
27110
320010
444910
5106210
6387610
done500010
01010
12110
26410
318310
445310
5130410
6491910
done500010
01121
12115
25615
313415
425215
564515
6239915
done500015
01010
1217
2567
31347
42547
56427
624117
done50007
01129
12619
210511
371411
done500011
044
1124
2184
3284
4494
51114
63254
712434
done50004
066
1136
2196
3296
4526
51126
63236
712506
done50006
01115
12315
24515
39315
421715
558915
6201415
done500015
033
1121
2161
3221
4321
5531
61131
73241
812571
done50001
0815
11615
22715
done2715
01010
12110
25710
313510
425910
563310
6237610
done500010
01010
12110
25710
313510
425910
563310
6237610
done500010
01011
1169
2229
3329
4559
51229
63409
712699
done50009
01011
1169
2229
3329
4559
51229
63409
712699
done50009
0913
11413
21813
done1813
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
01523
13020
27820
317320
427320
564520
6242620
done500020
01725
13222
27422
315222
425322
563522
6239222
done500022
01624
13421
28321
317921
428321
565821
6241021
done500121
01624
13321
28621
319821
437121
591621
6339321
done500121
01971
14062
212024
344724
4199622
done500022
01749
13243
28043
317443
427543
566343
6244443
done500043
01624
13121
27921
317121
427421
564421
6239821
done500021
01771
14262
213522
347422
4171122
done500022
01624
13121
27921
317121
427421
564421
6239821
done500021
01624
13121
27921
317121
427421
564421
6239821
done500021
01725
13222
27422
315222
425322
563522
6239222
done500022
01725
13222
27422
315222
425322
563522
6239222
done500022
0912
11312
21912
done1912
01216
12613
26813
315213
426613
565713
6250413
done500113
0912
11312
21912
done1912
01216
12613
26813
315213
426613
565713
6250413
done500113
0912
11312
21912
done1912
01216
12613
26813
315513
426713
564013
6240013
done500013
0912
11312
21912
done1912
01216
12613
26813
315513
426713
564013
6240013
done500013
01744
13438
27838
314938
424938
562538
6244138
done500038
01624
13121
27321
314721
424721
561721
6242421
done500021
066
194
2124
done124
01624
13121
27921
318221
429421
569121
6249421
done500121
01624
13121
27921
318221
429421
569121
6249421
done500121
01523
13020
27820
317320
427320
564520
6242620
done500020
02042
14536
29536
321834
456034
5120715
6297213
done500113
01727
14224
213224
345524
4146824
5422224
done500024
01742
14136
210436
327234
462733
5136233
6379633
done500033
055
195
2155
done155
077
197
done97
077
197
done97
01929
15529
219629
375825
4330225
done500025
01011
12511
26211
318911
455211
521069
done50009
01011
12511
26211
318911
455211
521069
done50009
055
195
2155
done155
077
197
done97
077
197
done97
01517
13717
29517
319515
445915
597413
6306413
done500013
01220
11820
23120
35320
45920
done5920
01220
11820
23120
35320
45920
done5920

prune246.0ms

Filtered
77 candidates to 97 candidates (-26.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh01010
Picked011
Done000
Total9711108

Merged error: 0.0b

Counts
108 → 11

regimes180.0ms

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
01625
12025
done2025

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s3298×body1280valid
576.0ms641×body2560valid
572.0ms1890×body640valid
160.0ms754×body320valid
70.0ms1086×body80valid
45.0ms331×body160valid

Profiling

Loading profile data...