Details

sample1.1s

Algorithm

intervals

Results

547.0ms	310×	body	10240	exit
145.0ms	90×	body	2560	valid
74.0ms	100×	body	1280	valid
33.0ms	550×	body	80	nan
14.0ms	36×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	1×	body	5120	nan
1.0ms	1×	body	2560	nan
1.0ms	4×	body	160	valid
0.0ms	3×	body	80	valid

simplify52.0ms

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	5002	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.1b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.5b	(fmod (cosh a) (* a a))

rewrite3.0ms

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×	`acos-asin`

Counts

2 → 19

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))

simplify88.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	48	166
1	76	146
2	160	146
3	411	146
4	2000	146
5	5001	146

prune98.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize13.0ms

Local error

Found 3 expressions with local error:

2.1b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
8.0b	(log (exp (fmod (cosh a) (* a a))))
59.5b	(fmod (cosh a) (* a a))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `log-pow`
3×	`add-exp-log` `expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `rem-log-exp`

Counts

3 → 36

Calls

3 calls:

0.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series7.0ms

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))

simplify110.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	79	299
1	113	260
2	227	260
3	599	260
4	2974	260
5	5001	260

prune163.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 60.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.3b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
8.0b	(log (exp (fmod (cosh a) (* a a))))
59.5b	(fmod (cosh a) (* a a))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`log-prod` `exp-prod`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 106

Calls

4 calls:

0.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
14.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
1.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
35.0ms	(- (/ 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))

simplify182.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	309	2819
1	761	1452
2	4112	1425
3	5001	1396

prune354.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 60.3b

localize34.0ms

Local error

Found 4 expressions with local error:

6.7b	(fma (* PI PI) 1/4 (* (- 1) (pow (cbrt (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))) 6)))
8.0b	(log (exp (fmod (cosh a) (* a a))))
59.5b	(fmod (cosh a) (* a a))
59.5b	(fmod (cosh a) (pow a 2))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

0.0ms	(fma (* PI PI) 1/4 (* (- 1) (pow (cbrt (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))) 6)))
1.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (pow a 2))

series97.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (* PI PI) 1/4 (* (- 1) (pow (cbrt (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))) 6)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (pow a 2))

simplify32.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	119	433
1	218	377
2	761	369
3	5001	369

prune352.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 59.8b

regimes40.0ms

Accuracy

0% (0.0b remaining)

Error of 59.5b against oracle of 59.5b and baseline of 59.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	31
1	38	31
2	46	31
3	46	31

end0.0ms

sample23.0s

Algorithm

intervals

Results

14.0s	7991×	body	10240	exit
5.1s	3179×	body	2560	valid
1.9s	2551×	body	1280	valid
711.0ms	16205×	body	80	nan
502.0ms	1261×	body	640	valid
164.0ms	574×	body	320	valid
64.0ms	322×	body	160	valid
18.0ms	8×	body	5120	nan
11.0ms	113×	body	80	valid
11.0ms	11×	body	2560	nan
4.0ms	7×	body	1280	nan
2.0ms	5×	body	640	nan
2.0ms	10×	body	160	nan
1.0ms	6×	body	320	nan