Details

sample1.1s

Algorithm

intervals

Results

514.0ms	278×	body	10240	exit
180.0ms	107×	body	2560	valid
57.0ms	74×	body	1280	valid
49.0ms	91×	body	1280	nan
21.0ms	71×	body	640	nan
18.0ms	44×	body	640	valid
13.0ms	270×	body	80	nan
8.0ms	45×	body	320	nan
6.0ms	18×	body	320	valid
2.0ms	18×	body	160	nan
2.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	43	6
3	91	6
4	257	6
5	1277	6
6	5002	6

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 61.2b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.7b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.9b	(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:

2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series20.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
17.0ms	(fmod (cosh a) (* a a))

simplify89.0ms

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

Filtered

25 candidates to 20 candidates (80.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	19	6	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	6	26

Merged error: 59.9b

Counts

26 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.7b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(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` `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:

1.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(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

prune177.0ms

Filtered

45 candidates to 34 candidates (75.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	42	9	51

Merged error: 59.9b

Counts

51 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.0b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
10.7b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(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:

1.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(fmod (cosh a) (* a a))

series39.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
32.0ms	(- (/ 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 (164.0ms)

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

prune366.0ms

Filtered

118 candidates to 70 candidates (59.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 59.9b

Counts

127 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

8.5b	(fma (* PI PI) 1/4 (* (- 1) (pow (cbrt (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))) 6)))
10.7b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (pow a 2))

rewrite5.0ms

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:

1.0ms	(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))))
1.0ms	(fmod (cosh a) (* a a))
1.0ms	(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))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (8.0ms)

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

prune343.0ms

Filtered

57 candidates to 45 candidates (78.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 59.5b

Counts

65 → 9

regimes182.0ms

Accuracy

0% (0.0b remaining)

Error of 59.5b against oracle of 59.4b and baseline of 59.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	38	21
2	46	21
3	46	21

end0.0ms

sample25.3s

Algorithm

intervals

Results

13.9s	7944×	body	10240	exit
5.1s	3204×	body	2560	valid
1.8s	2473×	body	1280	valid
1.5s	2938×	body	1280	nan
719.0ms	2529×	body	640	nan
511.0ms	1259×	body	640	valid
408.0ms	8582×	body	80	nan
229.0ms	1290×	body	320	nan
180.0ms	625×	body	320	valid
77.0ms	653×	body	160	nan
68.0ms	333×	body	160	valid
18.0ms	8×	body	5120	nan
13.0ms	14×	body	2560	nan
11.0ms	106×	body	80	valid