Details

sample1.0s

Algorithm

intervals

Results

403.0ms	230×	body	10240	exit
149.0ms	89×	body	2560	valid
61.0ms	106×	body	1280	nan
61.0ms	83×	body	1280	valid
22.0ms	55×	body	640	valid
19.0ms	66×	body	640	nan
14.0ms	277×	body	80	nan
7.0ms	40×	body	320	nan
4.0ms	14×	body	320	valid
3.0ms	24×	body	160	nan
2.0ms	8×	body	160	valid
1.0ms	7×	body	80	valid

simplify46.0ms

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	5002	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p a)
0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
1.6b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.9b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `expm1-log1p-u`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
1×	`acos-asin` `pow-to-exp` `log1p-udef` `pow-pow` `log1p-expm1` `pow-exp` `sqr-pow`

Counts

4 → 49

Calls

4 calls:

1.0ms	(log1p a)
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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(log1p a)
55.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
9.0ms	(fmod (cosh a) (* a a))

simplify160.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	272	496
1	1074	464
2	4780	453
3	5001	453

prune217.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 58.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
1.6b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
8.6b	(log (exp (fmod (cosh a) (* a a))))
58.9b	(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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 59

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))

series52.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(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))

simplify101.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	265	654
1	902	598
2	3697	588
3	5001	580

prune246.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.1b

localize18.0ms

Local error

Found 4 expressions with local error:

8.1b	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))
58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `log-pow`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 43

Calls

4 calls:

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

series145.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (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))

simplify157.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (33.0ms)

Iter	Nodes	Cost
0	61	413
1	114	342
2	274	337
3	731	331
4	3953	311
5	5001	311

prune272.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 58.1b

localize23.0ms

Local error

Found 4 expressions with local error:

58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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`

Counts

4 → 36

Calls

4 calls:

1.0ms	(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	(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))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	228
1	42	200
2	94	200
3	232	200
4	1067	200
5	5001	200

prune292.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 58.1b

regimes180.0ms

Accuracy

84.3% (0.2b remaining)

Error of 58.8b against oracle of 58.6b and baseline of 60.1b

bsearch106.0ms

Steps

Iters	Range		Point
6	1.5912567937714158e-163	1.9638834615483503e-162	1.555092758736906e-162

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	28
1	25	28

end0.0ms

sample25.1s

Algorithm

intervals

Results

13.8s	7882×	body	10240	exit
5.1s	3205×	body	2560	valid
1.8s	2503×	body	1280	valid
1.5s	2918×	body	1280	nan
726.0ms	2538×	body	640	nan
505.0ms	1244×	body	640	valid
410.0ms	8809×	body	80	nan
224.0ms	1276×	body	320	nan
181.0ms	629×	body	320	valid
80.0ms	679×	body	160	nan
62.0ms	305×	body	160	valid
12.0ms	114×	body	80	valid
10.0ms	5×	body	5120	nan
6.0ms	6×	body	2560	nan