Details

sample1.4s

Algorithm

intervals

Results

639.0ms	249×	body	5120	exit
195.0ms	98×	body	2560	valid
83.0ms	83×	body	1280	valid
64.0ms	86×	body	1280	nan
35.0ms	76×	body	640	nan
27.0ms	319×	body	80	nan
19.0ms	37×	body	640	valid
12.0ms	41×	body	320	nan
10.0ms	23×	body	320	valid
5.0ms	2×	body	5120	nan
4.0ms	20×	body	160	nan
3.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify50.0ms

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

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)))
58.6b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 15

Calls

2 calls:

1.0ms	(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

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	44	144
1	72	124
2	156	124
3	405	124
4	1938	124
5	5002	124

prune74.0ms

Filtered

21 candidates to 16 candidates (76.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	17	4	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	5	22

Merged error: 59.8b

Counts

22 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
9.7b	(log (exp (fmod (cosh a) (* a a))))
58.6b	(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` `log-prod` `exp-prod` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin` `rem-log-exp`

Counts

3 → 30

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))

series8.0ms

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))

simplify115.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	73	265
1	107	226
2	221	226
3	590	226
4	2934	226
5	5001	226

prune117.0ms

Filtered

39 candidates to 28 candidates (71.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	38	6	44

Merged error: 59.8b

Counts

44 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(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))))
9.7b	(log (exp (fmod (cosh a) (* a a))))
58.6b	(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:

1.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
7.0ms	(- (/ 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)))
31.0ms	(- (/ 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))

simplify132.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (125.0ms)

Iter	Nodes	Cost
0	148	533
1	291	476
2	677	476
3	2774	474
4	5002	472

prune191.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	6	58
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	54	10	64

Merged error: 59.8b

Counts

64 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (/ PI 2) (- (* 1/2 PI) (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
9.7b	(log (exp (fmod (cosh a) (* a a))))
58.6b	(fmod (cosh a) (* a a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod` `exp-prod` `diff-log` `associate--r+`
2×	`acos-asin` `sub-neg` `flip3--` `frac-sub` `flip--` `associate--r-` `difference-of-squares`
1×	`times-frac` `rem-log-exp` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

10.0ms	(- (/ PI 2) (- (* 1/2 PI) (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
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))

series12.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (/ PI 2) (- (* 1/2 PI) (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))

simplify80.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	248	721
1	661	643
2	2660	620
3	5001	596

prune201.0ms

Filtered

64 candidates to 48 candidates (75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	65	9	74

Merged error: 59.8b

Counts

74 → 9

regimes173.0ms

Accuracy

0% (0.4b remaining)

Error of 60.3b against oracle of 59.9b and baseline of 60.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	54
1	53	54
2	53	54

end0.0ms

sample33.7s

Algorithm

intervals

Results

19.8s	8123×	body	5120	exit
5.7s	3141×	body	2560	valid
2.2s	2502×	body	1280	valid
2.1s	2945×	body	1280	nan
1.0s	2483×	body	640	nan
726.0ms	8829×	body	80	nan
653.0ms	1297×	body	640	valid
359.0ms	1325×	body	320	nan
229.0ms	645×	body	320	valid
111.0ms	628×	body	160	nan
78.0ms	319×	body	160	valid
25.0ms	10×	body	5120	nan
11.0ms	96×	body	80	valid
7.0ms	6×	body	2560	nan

Details

sample1.4s

simplify50.0ms

prune5.0ms

localize12.0ms

rewrite4.0ms

series12.0ms

simplify87.0ms

prune74.0ms

localize12.0ms

rewrite5.0ms

series8.0ms

simplify115.0ms

prune117.0ms

localize15.0ms

rewrite14.0ms

series39.0ms

simplify132.0ms

prune191.0ms

localize17.0ms

rewrite15.0ms

series12.0ms

simplify80.0ms

prune201.0ms

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample33.7s

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