Details

sample441.0ms

Algorithm

intervals

Results

210.0ms	77×	body	10240	exit
139.0ms	70×	body	1280	valid
46.0ms	55×	body	640	valid
15.0ms	83×	body	80	valid
10.0ms	23×	body	320	valid
7.0ms	24×	body	160	valid
2.0ms	1×	body	2560	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: 34.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.7b	(sin (expm1 a))
38.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

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

series149.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
83.0ms	(expm1 (sin (expm1 a)))
61.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify120.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune205.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(sin (expm1 a))
38.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `rem-exp-log` `expm1-udef`

Counts

4 → 49

Calls

4 calls:

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
55.0ms	(sin (expm1 a))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify78.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	467
1	208	407
2	487	407
3	1838	407
4	5001	407

prune260.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(sin (expm1 a))
38.8b	(fmod (log (expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff` `rem-exp-log`

Counts

4 → 43

Calls

4 calls:

0.0ms	(expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(sin (expm1 a))
0.0ms	(fmod (log (expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series225.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
28.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
58.0ms	(sin (expm1 a))
3.0ms	(fmod (log (expm1 (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify72.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	101	443
1	189	392
2	440	392
3	1635	392
4	5001	392

prune280.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(sin (expm1 a))
0.7b	(sin (expm1 a))
0.7b	(sin (expm1 a))
38.8b	(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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sin-diff` `expm1-udef`

Counts

4 → 39

Calls

4 calls:

1.0ms	(sin (expm1 a))
1.0ms	(sin (expm1 a))
1.0ms	(sin (expm1 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)

series184.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (expm1 a))
61.0ms	(sin (expm1 a))
60.0ms	(sin (expm1 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)

simplify65.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	72	444
1	144	383
2	368	383
3	1409	368
4	5001	368

prune232.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 32.9b

regimes332.0ms

Accuracy

0% (1.8b remaining)

Error of 33.8b against oracle of 31.9b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	12	22

end0.0ms

sample13.4s

Algorithm

intervals

Results

6.8s	2516×	body	10240	exit
4.1s	2277×	body	1280	valid
1.3s	1652×	body	640	valid
501.0ms	2768×	body	80	valid
371.0ms	868×	body	320	valid
133.0ms	432×	body	160	valid
10.0ms	2×	body	5120	valid
2.0ms	1×	body	2560	valid