Details

sample1.3s

Algorithm

intervals

Results

582.0ms	234×	body	5120	exit
180.0ms	94×	body	2560	valid
78.0ms	87×	body	1280	valid
70.0ms	101×	body	1280	nan
53.0ms	85×	body	640	nan
25.0ms	292×	body	80	nan
21.0ms	42×	body	640	valid
10.0ms	38×	body	320	nan
5.0ms	15×	body	320	valid
3.0ms	17×	body	160	nan
3.0ms	11×	body	160	valid
1.0ms	7×	body	80	valid

simplify49.0ms

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: 60.5b

Counts

2 → 1

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
2.3b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.7b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log`
3×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

3 → 32

Calls

3 calls:

3.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series123.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
8.0ms	(fmod (cosh a) (* a a))

simplify141.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	291
1	249	265
2	805	265
3	3873	265
4	5001	265

prune124.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	35	6	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	6	42

Merged error: 59.1b

Counts

42 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.3b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.2b	(log (exp (fmod (cosh a) (* a a))))
58.7b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`log-pow`
7×	`pow1` `unpow-prod-down`
6×	`exp-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

3.0ms	(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))

series116.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(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))

simplify191.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	135	479
1	312	424
2	956	424
3	4680	420
4	5001	420

prune186.0ms

Filtered

63 candidates to 43 candidates (68.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 59.1b

Counts

69 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.3b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
12.2b	(log (exp (fmod (cosh a) (* a a))))
58.7b	(fmod (cosh a) (* a a))

rewrite12.0ms

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))

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))

simplify137.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (131.0ms)

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

prune197.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	57	10	67

Merged error: 59.1b

Counts

67 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

12.2b	(log (exp (fmod (cosh a) (* a a))))
58.7b	(fmod (cosh a) (* a a))
58.7b	(fmod (cosh a) (* a a))
58.7b	(fmod (cosh a) (* a a))

rewrite5.0ms

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×	`rem-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))

series8.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	52	246
1	75	212
2	157	212
3	405	212
4	1946	212
5	5003	212

prune208.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	49	9	58

Merged error: 59.1b

Counts

58 → 9

regimes113.0ms

Accuracy

0% (0.4b remaining)

Error of 60.2b against oracle of 59.7b and baseline of 60.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	17	35

end0.0ms

sample32.0s

Algorithm

intervals

Results

18.5s	7725×	body	5120	exit
5.6s	3111×	body	2560	valid
2.2s	2568×	body	1280	valid
2.0s	2956×	body	1280	nan
984.0ms	2452×	body	640	nan
678.0ms	8699×	body	80	nan
599.0ms	1228×	body	640	valid
329.0ms	1274×	body	320	nan
221.0ms	643×	body	320	valid
102.0ms	604×	body	160	nan
77.0ms	335×	body	160	valid
22.0ms	9×	body	5120	nan
15.0ms	115×	body	80	valid
9.0ms	6×	body	2560	nan

Details

sample1.3s

simplify49.0ms

prune5.0ms

localize19.0ms

rewrite8.0ms

series123.0ms

simplify141.0ms

prune124.0ms

localize12.0ms

rewrite8.0ms

series116.0ms

simplify191.0ms

prune186.0ms

localize16.0ms

rewrite12.0ms

series41.0ms

simplify137.0ms

prune197.0ms

localize23.0ms

rewrite5.0ms

series8.0ms

simplify83.0ms

prune208.0ms

regimes113.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample32.0s

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