Details

sample1.2s

Algorithm

intervals

Results

568.0ms	292×	body	10240	exit
161.0ms	90×	body	2560	valid
74.0ms	86×	body	1280	valid
51.0ms	555×	body	80	nan
23.0ms	46×	body	640	valid
6.0ms	16×	body	320	valid
4.0ms	11×	body	160	valid
1.0ms	7×	body	80	valid
0.0ms	1×	body	320	nan

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	5002	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.5b

localize12.0ms

Local error

Found 2 expressions with local error:

2.2b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.5b	(fmod (cosh a) (* a a))

rewrite4.0ms

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))

simplify80.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	48	166
1	74	146
2	146	146
3	386	146
4	1825	146
5	5001	146

prune96.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.2b

localize13.0ms

Local error

Found 3 expressions with local error:

2.2b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.3b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(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))

simplify109.0ms

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

prune167.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 59.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
2.2b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.3b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

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×	`acos-asin` `expm1-log1p` `rem-log-exp` `expm1-udef`

Counts

4 → 47

Calls

4 calls:

0.0ms	(expm1 (log1p (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
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))

series134.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(expm1 (log1p (acos (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))

simplify107.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	91	435
1	120	377
2	234	377
3	606	377
4	2981	377
5	5001	377

prune223.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 59.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(log (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
2.2b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.3b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `log-pow`
6×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`acos-asin` `rem-log-exp`
1×	`log-div` `exp-diff`

Counts

4 → 54

Calls

4 calls:

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

series10.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (exp (acos (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))

simplify127.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	109	530
1	146	461
2	279	461
3	717	461
4	3551	461
5	5002	461

prune264.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 59.2b

regimes234.0ms

Accuracy

0% (0.5b remaining)

Error of 60.1b against oracle of 59.7b and baseline of 60.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	19	26

end0.0ms

sample25.6s

Algorithm

intervals

Results

15.2s	7901×	body	10240	exit
5.4s	3120×	body	2560	valid
2.1s	2444×	body	1280	valid
1.4s	16013×	body	80	nan
646.0ms	1317×	body	640	valid
233.0ms	634×	body	320	valid
104.0ms	352×	body	160	valid
25.0ms	133×	body	80	valid
18.0ms	8×	body	5120	nan
6.0ms	9×	body	1280	nan
4.0ms	4×	body	2560	nan
4.0ms	8×	body	640	nan
2.0ms	7×	body	320	nan
2.0ms	9×	body	160	nan