Details

sample343.0ms

Algorithm

intervals

Results

260.0ms	255×	body	5120	exit
36.0ms	76×	body	1280	valid
11.0ms	44×	body	640	valid
6.0ms	157×	body	80	nan
5.0ms	101×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	2×	body	2560	valid
1.0ms	12×	body	160	valid

simplify228.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	14	3
2	16	3
3	18	3
4	19	3
5	24	3
6	44	3
7	69	3
8	169	3
9	1127	3
10	5002	3

prune2.0ms

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: 32.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(cosh c)
36.2b	(fmod (cosh c) (log1p a))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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×	`cosh-def`

Counts

2 → 19

Calls

2 calls:

1.0ms	(cosh c)
1.0ms	(fmod (cosh c) (log1p a))

series46.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(cosh c)
2.0ms	(fmod (cosh c) (log1p a))

simplify148.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	82	99
1	173	89
2	590	81
3	3626	79
4	5001	79

prune76.0ms

Filtered

25 candidates to 20 candidates (80.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	18	7	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	7	26

Merged error: 31.9b

Counts

26 → 7

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
36.2b	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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×	`fma-udef`

Counts

2 → 19

Calls

2 calls:

1.0ms	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
1.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

series44.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
4.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

simplify30.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	54	176
1	151	154
2	683	154
3	5002	154

prune98.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 31.9b

Counts

32 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
0.6b	(exp (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))))
1.0b	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
36.2b	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

1.0ms	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
2.0ms	(exp (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))))
1.0ms	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
1.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

series77.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1))
5.0ms	(exp (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))))
25.0ms	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
4.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

simplify35.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	91	517
1	213	459
2	789	444
3	5001	438

prune251.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	54	15	69

Merged error: 31.9b

Counts

69 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)
0.6b	(exp (cbrt (pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)))
1.0b	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
36.2b	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

17×	`exp-prod`
14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 77

Calls

4 calls:

2.0ms	(pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)
5.0ms	(exp (cbrt (pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)))
1.0ms	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
3.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

series84.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)
5.0ms	(exp (cbrt (pow (log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))) 3)))
26.0ms	(log (fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a)))
4.0ms	(fmod (fma 1/24 (pow c 4) (fma 1/2 (pow c 2) 1)) (log1p a))

simplify153.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	153	826
1	526	743
2	3299	738
3	5001	738

prune272.0ms

Filtered

89 candidates to 52 candidates (58.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	77	12	89
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	83	21	104

Merged error: 31.9b

Counts

104 → 21

regimes586.0ms

Accuracy

0% (0.2b remaining)

Error of 34.7b against oracle of 34.4b and baseline of 34.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample10.7s

Algorithm

intervals

Results

8.1s	7723×	body	5120	exit
1.1s	2364×	body	1280	valid
381.0ms	1582×	body	640	valid
182.0ms	165×	body	2560	valid
173.0ms	5229×	body	80	nan
135.0ms	2723×	body	80	valid
116.0ms	754×	body	320	valid
49.0ms	397×	body	160	valid
24.0ms	15×	body	5120	valid