Details

sample418.0ms

Algorithm

intervals

Results

208.0ms	80×	body	10240	exit
146.0ms	77×	body	1280	valid
33.0ms	48×	body	640	valid
10.0ms	99×	body	80	valid
8.0ms	24×	body	320	valid
2.0ms	8×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
36.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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

series156.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
65.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify123.0ms

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

prune217.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite5.0ms

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

series95.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(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

prune276.0ms

Filtered

61 candidates to 43 candidates (70.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 30.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(fmod (log (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`
1×	`rem-exp-log`

Counts

4 → 40

Calls

4 calls:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	498
1	64	429
2	83	429
3	124	429
4	224	429
5	546	429
6	2617	429
7	5001	429

prune347.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.9b	(fmod (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`
1×	`rem-exp-log`

Counts

4 → 40

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify77.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	53	426
1	69	375
2	88	375
3	129	375
4	229	375
5	551	375
6	2622	375
7	5001	375

prune280.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 30.2b

regimes330.0ms

Accuracy

0% (1.8b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.6s	2624×	body	10240	exit
3.9s	2299×	body	1280	valid
1.1s	1616×	body	640	valid
294.0ms	2813×	body	80	valid
281.0ms	848×	body	320	valid
95.0ms	416×	body	160	valid
14.0ms	3×	body	5120	valid
10.0ms	5×	body	2560	valid