Details

sample392.0ms

Algorithm

intervals

Results

216.0ms	85×	body	10240	exit
103.0ms	65×	body	1280	valid
37.0ms	52×	body	640	valid
12.0ms	39×	body	320	valid
8.0ms	84×	body	80	valid
3.0ms	16×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.6b	(sin (expm1 a))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series61.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
56.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

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

prune166.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(sin (expm1 a))
0.7b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
3.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series91.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
34.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify126.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	112	584
1	390	527
2	2787	521
3	5001	521

prune240.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(sin (expm1 a))
0.7b	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
3.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series90.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
30.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify129.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	122	1268
1	402	1141
2	2813	971
3	5002	958

prune288.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

3.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series40.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify127.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	100	1098
1	351	908
2	2713	776
3	5001	741

prune277.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 33.0b

regimes373.0ms

Accuracy

0% (1.7b remaining)

Error of 33.8b against oracle of 32.2b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	23	46

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.7s	2673×	body	10240	exit
3.9s	2332×	body	1280	valid
1.1s	1627×	body	640	valid
283.0ms	883×	body	320	valid
271.0ms	2744×	body	80	valid
83.0ms	410×	body	160	valid
14.0ms	3×	body	5120	valid
2.0ms	1×	body	2560	valid