Details

sample1.1s

Algorithm

intervals

Results

512.0ms	290×	body	10240	exit
153.0ms	93×	body	2560	valid
63.0ms	88×	body	1280	valid
34.0ms	38×	body	640	valid
25.0ms	603×	body	80	nan
5.0ms	18×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	1×	body	5120	nan
0.0ms	4×	body	80	valid
0.0ms	1×	body	160	nan

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize12.0ms

Local error

Found 2 expressions with local error:

2.2b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.8b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin`

Counts

2 → 15

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
10.0ms	(fmod (cosh a) (* a a))

simplify84.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	44	144
1	72	124
2	156	124
3	405	124
4	1968	124
5	5002	124

prune83.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.5b

localize12.0ms

Local error

Found 3 expressions with local error:

2.2b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.0b	(log (exp (fmod (cosh a) (* a a))))
58.8b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

1.0ms	(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))

series8.0ms

Counts

3 → 9

Calls

3 calls:

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))

simplify106.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	73	265
1	107	226
2	221	226
3	590	226
4	2934	226
5	5002	226

prune148.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.5b

localize17.0ms

Local error

Found 4 expressions with local error:

10.0b	(log (exp (fmod (cosh a) (* a a))))
58.8b	(fmod (cosh a) (* a a))
58.8b	(fmod (cosh a) (* a a))
58.8b	(fmod (cosh a) (* a a))

rewrite4.0ms

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))

simplify79.0ms

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

prune241.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.2b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
10.0b	(log (exp (fmod (cosh a) (* a a))))
58.8b	(fmod (cosh a) (* a a))

rewrite26.0ms

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)))
21.0ms	(- (/ PI 2) (asin (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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
30.0ms	(- (/ 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))

simplify136.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (130.0ms)

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

prune184.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 59.4b

regimes264.0ms

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	27
1	20	27

end0.0ms

sample23.1s

Algorithm

intervals

Results

14.1s	8117×	body	10240	exit
4.9s	3111×	body	2560	valid
1.9s	2573×	body	1280	valid
704.0ms	16213×	body	80	nan
498.0ms	1270×	body	640	valid
170.0ms	624×	body	320	valid
65.0ms	313×	body	160	valid
29.0ms	14×	body	5120	nan
11.0ms	109×	body	80	valid
9.0ms	9×	body	2560	nan
4.0ms	8×	body	1280	nan
2.0ms	7×	body	640	nan
1.0ms	6×	body	320	nan
1.0ms	7×	body	160	nan