Details

sample381.0ms

Algorithm

intervals

Results

172.0ms	70×	body	10240	exit
129.0ms	79×	body	1280	valid
37.0ms	57×	body	640	valid
20.0ms	87×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(sin (expm1 a))
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series76.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
64.0ms	(sin (expm1 a))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212

prune162.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

11.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series150.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify57.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	90	935
1	311	852
2	1529	755
3	5001	738

prune282.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 33.2b

localize24.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series9.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	15	352
1	17	300
2	21	300
3	26	300
4	45	300
5	99	300
6	505	300
7	1672	300
8	5001	300

prune238.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 33.2b

localize30.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series9.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify91.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	352
1	17	300
2	21	300
3	26	300
4	45	300
5	99	300
6	505	300
7	1672	300
8	5001	300

prune173.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 33.2b

regimes217.0ms

Accuracy

0% (1.3b remaining)

Error of 33.7b against oracle of 32.4b and baseline of 33.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	12	24

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2596×	body	10240	exit
3.9s	2359×	body	1280	valid
1.1s	1645×	body	640	valid
269.0ms	2776×	body	80	valid
255.0ms	814×	body	320	valid
80.0ms	402×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid