Details

sample1.0s

Algorithm

intervals

Results

463.0ms	254×	body	10240	exit
186.0ms	111×	body	2560	valid
53.0ms	69×	body	1280	valid
24.0ms	487×	body	80	nan
19.0ms	45×	body	640	valid
5.0ms	18×	body	320	valid
3.0ms	12×	body	160	valid
0.0ms	1×	body	80	valid

simplify47.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize13.0ms

Local error

Found 2 expressions with local error:

1.9b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
60.0b	(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:

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

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify81.0ms

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

prune76.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize14.0ms

Local error

Found 3 expressions with local error:

1.9b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.0b	(log (exp (fmod (cosh a) (* a a))))
60.0b	(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))

series9.0ms

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))))
4.0ms	(fmod (cosh a) (* a a))

simplify109.0ms

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

prune140.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 60.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))))
60.0b	(fmod (cosh a) (* a a))

rewrite22.0ms

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)))
17.0ms	(- (/ 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))

series37.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
28.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
4.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify137.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (131.0ms)

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

prune221.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 60.3b

localize25.0ms

Local error

Found 4 expressions with local error:

10.0b	(log (exp (fmod (cosh a) (* a a))))
60.0b	(fmod (cosh a) (* a a))
60.0b	(fmod (cosh a) (* a a))
60.0b	(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))

series7.0ms

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

prune227.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 60.2b

regimes216.0ms

Accuracy

0% (0.4b remaining)

Error of 60.3b against oracle of 59.8b and baseline of 60.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	44
1	27	44

end0.0ms

sample23.7s

Algorithm

intervals

Results

14.3s	8012×	body	10240	exit
5.1s	3138×	body	2560	valid
1.9s	2490×	body	1280	valid
816.0ms	16179×	body	80	nan
544.0ms	1293×	body	640	valid
190.0ms	638×	body	320	valid
69.0ms	332×	body	160	valid
19.0ms	9×	body	5120	nan
12.0ms	109×	body	80	valid
8.0ms	8×	body	2560	nan
3.0ms	6×	body	1280	nan
2.0ms	6×	body	640	nan
2.0ms	7×	body	320	nan
1.0ms	7×	body	160	nan