Details

sample492.0ms

Algorithm

intervals

Results

286.0ms	104×	body	5120	exit
127.0ms	80×	body	1280	valid
41.0ms	54×	body	640	valid
14.0ms	88×	body	80	valid
9.0ms	23×	body	320	valid
3.0ms	11×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series70.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
64.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify120.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212

prune163.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	26	14	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	14	41

Merged error: 32.9b

Counts

41 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.7b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
3.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series44.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
38.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify127.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	112	597
1	390	538
2	2787	532
3	5001	532

prune207.0ms

Filtered

70 candidates to 34 candidates (48.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	66	18	84

Merged error: 32.6b

Counts

84 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
0.7b	(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

93×	`cbrt-prod`
39×	`unpow-prod-down` `cube-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`cube-mult` `unpow3` `sqr-pow`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`pow1/3`
1×	`pow-to-exp` `pow-pow` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 110

Calls

4 calls:

5.0ms	(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
6.0ms	(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series76.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
5.0ms	(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
34.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify40.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	197	1401
1	617	1231
2	5002	1207

prune252.0ms

Filtered

122 candidates to 42 candidates (34.4%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	121	19	140

Merged error: 32.6b

Counts

140 → 19

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
39.1b	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
39.1b	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
1.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
1.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series42.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
2.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
3.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify129.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	93	594
1	352	494
2	2840	490
3	5001	490

prune235.0ms

Filtered

56 candidates to 36 candidates (64.3%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	16	16
Picked	1	0	1
Done	0	2	2
Total	52	23	75

Merged error: 32.4b

Counts

75 → 23

regimes299.0ms

Accuracy

0% (1.6b remaining)

Error of 33.4b against oracle of 31.8b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	22	38

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.1s	2559×	body	5120	exit
3.8s	2228×	body	1280	valid
1.2s	1682×	body	640	valid
325.0ms	2812×	body	80	valid
305.0ms	837×	body	320	valid
103.0ms	431×	body	160	valid
29.0ms	6×	body	5120	valid
8.0ms	4×	body	2560	valid