Details

sample1.0s

Algorithm

intervals

Results

459.0ms	250×	body	10240	exit
170.0ms	104×	body	2560	valid
67.0ms	89×	body	1280	valid
28.0ms	572×	body	80	nan
15.0ms	37×	body	640	valid
4.0ms	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	5002	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` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `cosh-def`

Counts

3 → 29

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))

series67.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(cosh a)
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
9.0ms	(fmod (cosh a) (* a a))

simplify159.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	104	208
1	216	185
2	693	177
3	4157	175
4	5001	175

prune141.0ms

Filtered

38 candidates to 31 candidates (81.6%)

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` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`acos-asin` `cosh-def` `rem-log-exp`

Counts

4 → 46

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))

series54.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(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))

simplify164.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	132	341
1	250	299
2	768	291
3	4567	289
4	5001	289

prune221.0ms

Filtered

58 candidates to 45 candidates (77.6%)

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))

rewrite5.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `rem-log-exp`

Counts

4 → 62

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))

series226.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
111.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify89.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	70	532
1	102	478
2	184	478
3	446	474
4	2034	474
5	5002	474

prune321.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 59.9b

localize14.0ms

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))

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))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
34.0ms	(- (/ 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))

simplify166.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	309	2828
1	761	1452
2	4010	1427
3	5001	1398

prune317.0ms

Filtered

118 candidates to 70 candidates (59.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.8b

regimes142.0ms

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

sample23.3s

Algorithm

intervals

Results

14.1s	7934×	body	10240	exit
5.2s	3155×	body	2560	valid
1.9s	2504×	body	1280	valid
705.0ms	16004×	body	80	nan
502.0ms	1216×	body	640	valid
210.0ms	701×	body	320	valid
66.0ms	311×	body	160	valid
19.0ms	9×	body	5120	nan
13.0ms	13×	body	2560	nan
12.0ms	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