Details

sample1.3s

Algorithm

intervals

Results

569.0ms	230×	body	5120	exit
172.0ms	88×	body	2560	valid
81.0ms	85×	body	1280	valid
68.0ms	95×	body	1280	nan
37.0ms	90×	body	640	nan
26.0ms	309×	body	80	nan
21.0ms	42×	body	640	valid
12.0ms	45×	body	320	nan
7.0ms	18×	body	320	valid
5.0ms	27×	body	160	nan
4.0ms	17×	body	160	valid
1.0ms	6×	body	80	valid

simplify49.0ms

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	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: 60.0b

Counts

2 → 1

localize12.0ms

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)))
57.8b	(fmod (cosh a) (* a a))

rewrite7.0ms

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))

series128.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
16.0ms	(fmod (cosh a) (* a a))

simplify136.0ms

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

prune121.0ms

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: 58.6b

Counts

42 → 6

localize13.0ms

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)))
12.6b	(log (exp (fmod (cosh a) (* a a))))
57.8b	(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))

series112.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(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))

simplify192.0ms

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

prune183.0ms

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: 58.6b

Counts

69 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
2.3b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.6b	(log (exp (fmod (cosh a) (* a a))))
57.8b	(fmod (cosh a) (* a a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `log-pow`
6×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`acos-asin` `rem-log-exp`
1×	`log-div` `exp-diff`

Counts

4 → 46

Calls

4 calls:

2.0ms	(log (exp (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))

series10.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (exp (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))

simplify126.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	101	478
1	138	409
2	271	409
3	706	409
4	3505	409
5	5002	409

prune198.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	57	10	67

Merged error: 58.6b

Counts

67 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (log1p a))
2.3b	(acos (pow (pow (log (exp (fmod (cosh a) (* a a)))) (sqrt (log1p a))) (sqrt (log1p a))))
12.6b	(log (exp (fmod (cosh a) (* a a))))
57.8b	(fmod (cosh a) (* a a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `exp-prod` `sqrt-prod`
1×	`acos-asin` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 43

Calls

4 calls:

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (log1p a))
4.0ms	(acos (pow (pow (log (exp (fmod (cosh a) (* a a)))) (sqrt (log1p a))) (sqrt (log1p a))))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify113.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	95	369
1	135	320
2	272	320
3	689	319
4	3222	319
5	5001	319

prune162.0ms

Filtered

55 candidates to 39 candidates (70.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	53	12	65

Merged error: 57.5b

Counts

65 → 12

regimes230.0ms

Accuracy

74.9% (0.4b remaining)

Error of 59.0b against oracle of 58.6b and baseline of 60.2b

bsearch131.0ms

Steps

Iters	Range		Point
6	1.003063710064382e-162	1.4643770121535972e-161	1.5952721721417026e-162

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	28

end0.0ms

sample32.7s

Algorithm

intervals

Results

19.1s	7969×	body	5120	exit
5.7s	3160×	body	2560	valid
2.2s	2509×	body	1280	valid
2.0s	2891×	body	1280	nan
982.0ms	2434×	body	640	nan
705.0ms	8783×	body	80	nan
609.0ms	1241×	body	640	valid
344.0ms	1330×	body	320	nan
219.0ms	638×	body	320	valid
114.0ms	646×	body	160	nan
78.0ms	334×	body	160	valid
15.0ms	6×	body	5120	nan
13.0ms	118×	body	80	valid
7.0ms	6×	body	2560	nan