Details

sample995.0ms

Algorithm

intervals

Results

444.0ms	256×	body	10240	exit
164.0ms	103×	body	2560	valid
62.0ms	78×	body	1280	valid
22.0ms	519×	body	80	nan
17.0ms	43×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	2×	body	1280	nan
0.0ms	1×	body	640	nan
0.0ms	1×	body	80	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	43	6
3	91	6
4	257	6
5	1277	6
6	5001	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
2.9b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.8b	(fmod (cosh a) (* a a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log`
3×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

3 → 32

Calls

3 calls:

4.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series125.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
8.0ms	(fmod (cosh a) (* a a))

simplify138.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	291
1	249	265
2	805	265
3	3873	265
4	5001	265

prune148.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 60.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.9b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.1b	(log (exp (fmod (cosh a) (* a a))))
59.8b	(fmod (cosh a) (* a a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`log-pow`
7×	`pow1` `unpow-prod-down`
6×	`exp-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

6.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series115.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
3.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify189.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	135	479
1	312	424
2	956	424
3	4680	420
4	5001	420

prune225.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 60.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.9b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
11.1b	(log (exp (fmod (cosh a) (* a a))))
59.8b	(fmod (cosh a) (* a a))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod` `exp-prod`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 46

Calls

4 calls:

1.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
20.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
6.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series36.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
29.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify134.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (128.0ms)

Iter	Nodes	Cost
0	148	533
1	295	476
2	702	474
3	2899	474
4	5001	472

prune237.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 60.3b

localize18.0ms

Local error

Found 4 expressions with local error:

11.1b	(log (exp (fmod (cosh a) (* a a))))
59.8b	(fmod (cosh a) (* a a))
59.8b	(fmod (cosh a) (* a a))
59.8b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`rem-log-exp`

Counts

4 → 36

Calls

4 calls:

3.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series8.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify80.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	52	246
1	75	212
2	157	212
3	405	212
4	1946	212
5	5003	212

prune218.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 60.3b

regimes202.0ms

Accuracy

0% (0.4b remaining)

Error of 60.3b against oracle of 59.9b and baseline of 60.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	22	26
2	22	26

end0.0ms

sample22.6s

Algorithm

intervals

Results

13.6s	7797×	body	10240	exit
5.0s	3175×	body	2560	valid
1.9s	2551×	body	1280	valid
679.0ms	15763×	body	80	nan
480.0ms	1223×	body	640	valid
167.0ms	616×	body	320	valid
62.0ms	318×	body	160	valid
13.0ms	6×	body	5120	nan
12.0ms	117×	body	80	valid
7.0ms	13×	body	1280	nan
3.0ms	8×	body	640	nan
3.0ms	3×	body	2560	nan
2.0ms	10×	body	160	nan
1.0ms	6×	body	320	nan