Details

sample1.3s

Algorithm

intervals

Results

619.0ms	249×	body	5120	exit
180.0ms	98×	body	2560	valid
73.0ms	103×	body	1280	nan
72.0ms	76×	body	1280	valid
42.0ms	77×	body	640	nan
23.0ms	283×	body	80	nan
20.0ms	38×	body	640	valid
13.0ms	47×	body	320	nan
9.0ms	24×	body	320	valid
4.0ms	14×	body	160	valid
3.0ms	16×	body	160	nan
1.0ms	6×	body	80	valid

simplify51.0ms

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: 60.2b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

2.8b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.9b	(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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify87.0ms

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

prune95.0ms

Filtered

25 candidates to 20 candidates (80.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	4	26

Merged error: 58.8b

Counts

26 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

2.8b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.2b	(log (exp (fmod (cosh a) (* a a))))
58.9b	(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

prune148.0ms

Filtered

45 candidates to 35 candidates (77.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	42	7	49

Merged error: 58.8b

Counts

49 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.8b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
11.2b	(log (exp (fmod (cosh a) (* a a))))
58.9b	(fmod (cosh a) (* a a))

rewrite17.0ms

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)))
9.0ms	(- (/ 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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
36.0ms	(- (/ 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))

simplify183.0ms

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

prune317.0ms

Filtered

118 candidates to 71 candidates (60.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	115	10	125

Merged error: 58.8b

Counts

125 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

8.3b	(fma (* PI PI) 1/4 (* (- 1) (pow (cbrt (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))) 6)))
11.2b	(log (exp (fmod (cosh a) (* a a))))
58.9b	(fmod (cosh a) (* a a))
58.9b	(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))

series99.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(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 (8.0ms)

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

prune313.0ms

Filtered

57 candidates to 45 candidates (78.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	55	12	67

Merged error: 58.3b

Counts

67 → 12

regimes279.0ms

Accuracy

0% (0.0b remaining)

Error of 59.3b against oracle of 59.3b and baseline of 59.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	34	20
2	42	20
3	42	20

end0.0ms

sample32.5s

Algorithm

intervals

Results

19.0s	7873×	body	5120	exit
5.5s	3072×	body	2560	valid
2.2s	2566×	body	1280	valid
2.0s	2911×	body	1280	nan
1.0s	2522×	body	640	nan
691.0ms	8738×	body	80	nan
625.0ms	1257×	body	640	valid
340.0ms	1280×	body	320	nan
223.0ms	648×	body	320	valid
113.0ms	650×	body	160	nan
78.0ms	339×	body	160	valid
14.0ms	118×	body	80	valid
8.0ms	3×	body	5120	nan
5.0ms	4×	body	2560	nan

Details

sample1.3s

simplify51.0ms

prune5.0ms

localize12.0ms

rewrite4.0ms

series12.0ms

simplify87.0ms

prune95.0ms

localize13.0ms

rewrite5.0ms

series7.0ms

simplify110.0ms

prune148.0ms

localize15.0ms

rewrite17.0ms

series43.0ms

simplify183.0ms

prune317.0ms

localize34.0ms

rewrite5.0ms

series99.0ms

simplify32.0ms

prune313.0ms

regimes279.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample32.5s

Profiling