Details

sample328.0ms

Algorithm

intervals

Results

147.0ms	59×	body	10240	exit
118.0ms	75×	body	1280	valid
30.0ms	39×	body	640	valid
9.0ms	95×	body	80	valid
9.0ms	29×	body	320	valid
4.0ms	18×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

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)))
37.0b	(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:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series74.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
62.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify122.0ms

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

prune157.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.9b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series348.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
115.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
117.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	38	628
1	68	546
2	145	540
3	478	525
4	2428	525
5	5002	525

prune225.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.9b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series339.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
111.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
111.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify78.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (73.0ms)

Iter	Nodes	Cost
0	47	638
1	110	554
2	381	548
3	2048	532
4	5001	529

prune233.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 31.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.9b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.9b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.9b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series122.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1)) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify80.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (74.0ms)

Iter	Nodes	Cost
0	47	874
1	110	726
2	381	724
3	2048	676
4	5001	675

prune206.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 30.8b

regimes285.0ms

Accuracy

0% (1.6b remaining)

Error of 33.9b against oracle of 32.2b and baseline of 33.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	74
1	30	74
2	30	74

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2592×	body	10240	exit
3.8s	2321×	body	1280	valid
1.1s	1667×	body	640	valid
275.0ms	2762×	body	80	valid
272.0ms	804×	body	320	valid
93.0ms	441×	body	160	valid
10.0ms	1×	body	5120	valid
8.0ms	4×	body	2560	valid