Details

sample978.0ms

Algorithm

intervals

Results

437.0ms	250×	body	10240	exit
165.0ms	104×	body	2560	valid
64.0ms	89×	body	1280	valid
36.0ms	572×	body	80	nan
14.0ms	37×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	1×	body	5120	nan
1.0ms	7×	body	160	valid
1.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh a)
1.4b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.6b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 23

Calls

3 calls:

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

series66.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(cosh a)
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
9.0ms	(fmod (cosh a) (* a a))

simplify156.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	96	184
1	202	161
2	643	153
3	4010	151
4	5001	151

prune119.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh a)
1.4b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.6b	(log (exp (fmod (cosh a) (* a a))))
59.6b	(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` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`acos-asin` `cosh-def` `rem-log-exp`

Counts

4 → 38

Calls

4 calls:

0.0ms	(cosh 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))

series53.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cosh 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))

simplify162.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	122	305
1	234	263
2	716	255
3	4418	253
4	5001	253

prune182.0ms

Filtered

50 candidates to 37 candidates (74.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.9b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.4b	(log (sqrt (exp (fmod (cosh a) (* a a)))))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `exp-prod` `sqrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow1/2` `rem-log-exp`

Counts

4 → 54

Calls

4 calls:

2.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series220.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
106.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify90.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	66	488
1	98	434
2	180	434
3	439	430
4	2003	430
5	5002	430

prune283.0ms

Filtered

66 candidates to 48 candidates (72.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 59.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.9b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
10.6b	(log (exp (fmod (cosh a) (* a a))))
59.6b	(fmod (cosh a) (* a a))

rewrite14.0ms

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:

0.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.0ms	(- (/ 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))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
33.0ms	(- (/ 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))

simplify135.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (129.0ms)

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

prune188.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 59.9b

regimes194.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16

end0.0ms

sample22.5s

Algorithm

intervals

Results

13.7s	7934×	body	10240	exit
5.0s	3155×	body	2560	valid
1.8s	2504×	body	1280	valid
682.0ms	16004×	body	80	nan
472.0ms	1216×	body	640	valid
194.0ms	701×	body	320	valid
59.0ms	311×	body	160	valid
19.0ms	9×	body	5120	nan
12.0ms	13×	body	2560	nan
11.0ms	113×	body	80	valid
3.0ms	13×	body	320	nan
3.0ms	5×	body	1280	nan
2.0ms	6×	body	640	nan
1.0ms	6×	body	160	nan