Details

sample419.0ms

Algorithm

intervals

Results

239.0ms	87×	body	5120	exit
108.0ms	59×	body	1280	valid
38.0ms	50×	body	640	valid
12.0ms	110×	body	80	valid
7.0ms	20×	body	320	valid
4.0ms	17×	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: 29.5b

Counts

2 → 1

localize17.0ms

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)))
33.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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

series153.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
56.0ms	(sin (expm1 a))
88.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify124.0ms

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	2934	264
4	5001	264

prune191.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	40	11	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	12	52

Merged error: 28.1b

Counts

52 → 12

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)
33.7b	(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` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `expm1-log1p` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

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

series125.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
36.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify137.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	150	655
1	516	595
2	3329	589
3	5001	589

prune261.0ms

Filtered

80 candidates to 44 candidates (55.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	70	10	80
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	73	19	92

Merged error: 27.9b

Counts

92 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
33.7b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
33.7b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
33.7b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 52

Calls

4 calls:

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify127.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	92	608
1	341	520
2	2697	516
3	5002	516

prune346.0ms

Filtered

64 candidates to 44 candidates (68.8%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	59	24	83

Merged error: 27.8b

Counts

83 → 24

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.7b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
33.7b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
33.7b	(fmod (cbrt (log (exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)))) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`exp-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`unpow-prod-down` `cube-prod`
1×	`cube-mult` `unpow3` `rem-exp-log` `sqr-pow`

Counts

4 → 49

Calls

4 calls:

4.0ms	(exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (log (exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)))) a)

series69.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (log (exp (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)))) a)

simplify100.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	97	583
1	205	506
2	617	506
3	3056	506
4	5001	506

prune299.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	21	22
Picked	1	0	1
Done	0	1	1
Total	58	27	85

Merged error: 27.7b

Counts

85 → 27

regimes521.0ms

Accuracy

0% (1.8b remaining)

Error of 33.5b against oracle of 31.7b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	45
1	24	45

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.1s	2608×	body	5120	exit
3.9s	2277×	body	1280	valid
1.2s	1631×	body	640	valid
310.0ms	2795×	body	80	valid
304.0ms	841×	body	320	valid
101.0ms	446×	body	160	valid
19.0ms	4×	body	5120	valid
13.0ms	6×	body	2560	valid

Details

sample419.0ms

simplify2.0ms

prune3.0ms

localize17.0ms

rewrite5.0ms

series153.0ms

simplify124.0ms

prune191.0ms

localize16.0ms

rewrite7.0ms

series125.0ms

simplify137.0ms

prune261.0ms

localize21.0ms

rewrite5.0ms

series39.0ms

simplify127.0ms

prune346.0ms

localize30.0ms

rewrite9.0ms

series69.0ms

simplify100.0ms

prune299.0ms

regimes521.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.0s

Profiling