Details

sample441.0ms

Algorithm

intervals

Results

244.0ms	91×	body	10240	exit
126.0ms	74×	body	1280	valid
40.0ms	57×	body	640	valid
8.0ms	84×	body	80	valid
8.0ms	26×	body	320	valid
3.0ms	15×	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

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: 34.5b

Counts

2 → 1

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)))
0.4b	(sin (expm1 a))
39.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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:

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

series158.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
90.0ms	(expm1 (sin (expm1 a)))
64.0ms	(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

prune209.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	37	14	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	14	52

Merged error: 33.3b

Counts

52 → 14

localize19.0ms

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)))
0.4b	(sin (expm1 a))
39.4b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

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:

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

series97.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
34.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
59.0ms	(sin (expm1 a))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify79.0ms

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

prune265.0ms

Filtered

61 candidates to 43 candidates (70.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	58	17	75

Merged error: 33.0b

Counts

75 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(sin (expm1 a))
0.4b	(sin (expm1 a))
39.4b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite7.0ms

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×	`sin-diff` `expm1-udef`
1×	`rem-exp-log`

Counts

4 → 42

Calls

4 calls:

2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(sin (expm1 a))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series159.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
64.0ms	(sin (expm1 a))
62.0ms	(sin (expm1 a))
3.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify80.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	94	486
1	191	417
2	475	417
3	1899	417
4	5002	417

prune360.0ms

Filtered

54 candidates to 43 candidates (79.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	49	22	71

Merged error: 32.8b

Counts

71 → 22

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(sin (expm1 a))
39.4b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.4b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.4b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

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`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	70	432
1	146	369
2	368	369
3	1398	369
4	5001	369

prune249.0ms

Filtered

49 candidates to 41 candidates (83.7%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	44	27	71

Merged error: 32.6b

Counts

71 → 27

regimes374.0ms

Accuracy

0% (1.9b remaining)

Error of 33.4b against oracle of 31.5b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	17	28

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.1s	2619×	body	10240	exit
3.9s	2300×	body	1280	valid
1.1s	1643×	body	640	valid
292.0ms	2817×	body	80	valid
273.0ms	824×	body	320	valid
93.0ms	412×	body	160	valid
14.0ms	3×	body	5120	valid
2.0ms	1×	body	2560	valid