Details

sample458.0ms

Algorithm

intervals

Results

251.0ms	94×	body	10240	exit
123.0ms	67×	body	1280	valid
43.0ms	52×	body	640	valid
16.0ms	39×	body	320	valid
12.0ms	87×	body	80	valid
3.0ms	11×	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: 34.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

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

series61.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	173
1	35	148
2	43	148
3	54	148
4	91	148
5	185	148
6	781	148
7	2680	148
8	5001	148

prune112.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 33.4b

localize20.0ms

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))))
39.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite2.0ms

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)

series314.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (expm1 (sin (expm1 a))))
103.0ms	(cbrt (expm1 (sin (expm1 a))))
106.0ms	(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)

simplify91.0ms

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

prune237.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
39.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
19×	`add-sqr-sqrt`
10×	`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 → 62

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
8.0ms	(* (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 (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series346.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
107.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
110.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify50.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	131	1236
1	379	1094
2	1391	1067
3	5002	971

prune416.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 32.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.3b	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
39.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-exp-log`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow-pow` `associate-r` `unswap-sqr`
8×	`pow1/3`
6×	`prod-exp`
5×	`unpow-prod-down` `associate-l` `add-cbrt-cube` `sqr-pow`
4×	`pow-exp` `add-log-exp`
3×	`pow-unpow` `pow-prod-down`
2×	`pow-to-exp` `unpow1/3` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `pow-plus` `*-commutative`

Counts

4 → 84

Calls

4 calls:

8.0ms	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series453.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
105.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
240.0ms	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify180.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	211	1477
1	786	1291
2	4501	1121
3	5001	1121

prune372.0ms

Pruning

45 alts after pruning (44 fresh and 1 done)

Merged error: 31.8b

regimes801.0ms

Accuracy

0% (2.3b remaining)

Error of 34.1b against oracle of 31.8b and baseline of 34.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	20	43

end0.0ms

sample14.0s

Algorithm

intervals

Results

7.2s	2706×	body	10240	exit
4.4s	2405×	body	1280	valid
1.3s	1622×	body	640	valid
356.0ms	2715×	body	80	valid
353.0ms	855×	body	320	valid
109.0ms	398×	body	160	valid
14.0ms	3×	body	5120	valid
4.0ms	2×	body	2560	valid