Details

sample481.0ms

Algorithm

intervals

Results

260.0ms	95×	body	10240	exit
147.0ms	79×	body	1280	valid
38.0ms	53×	body	640	valid
11.0ms	87×	body	80	valid
9.0ms	24×	body	320	valid
3.0ms	13×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
39.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 14

Calls

2 calls:

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

series3.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify103.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	137
1	26	117
2	32	117
3	40	117
4	68	117
5	142	117
6	643	117
7	2176	117
8	5001	117

prune164.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (expm1 (sin (expm1 a))))
21.0ms	(cbrt (expm1 (sin (expm1 a))))
20.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	39	474
1	69	412
2	146	406
3	479	395
4	2429	395
5	5001	395

prune575.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 33.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
20×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`pow1/3` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

0.0ms	(cbrt (expm1 (sin (expm1 a))))
7.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series63.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (expm1 (sin (expm1 a))))
20.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
19.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify84.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 4 (76.0ms)

Iter	Nodes	Cost
0	123	1193
1	359	1063
2	926	1055
3	2677	1032
4	5003	912

prune1.1s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 32.7b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (* (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
20.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
19.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (* (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify123.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 6 (116.0ms)

Iter	Nodes	Cost
0	71	1092
1	108	964
2	224	958
3	502	958
4	1121	958
5	2965	955
6	5001	937

prune900.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 32.5b

regimes1.6s

Accuracy

0% (1.7b remaining)

Error of 32.8b against oracle of 31.1b and baseline of 32.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	22	45

end0.0ms

sample13.3s

Algorithm

intervals

Results

7.1s	2657×	body	10240	exit
3.9s	2210×	body	1280	valid
1.3s	1679×	body	640	valid
344.0ms	2908×	body	80	valid
312.0ms	788×	body	320	valid
109.0ms	407×	body	160	valid
24.0ms	5×	body	5120	valid
6.0ms	3×	body	2560	valid