Details

sample419.0ms

Algorithm

intervals

Results

217.0ms	81×	body	10240	exit
109.0ms	61×	body	1280	valid
42.0ms	50×	body	640	valid
18.0ms	41×	body	320	valid
17.0ms	89×	body	80	valid
5.0ms	15×	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: 33.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.2b	(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	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series60.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
54.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify123.0ms

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

prune160.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.3b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `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 → 69

Calls

4 calls:

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

series493.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (sin (expm1 a)))
155.0ms	(cbrt (sin (expm1 a)))
177.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify78.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	99	673
1	366	578
2	2587	543
3	5002	526

prune342.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 31.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
38.2b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

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`
3×	`cbrt-prod` `pow1/3`

Counts

4 → 34

Calls

4 calls:

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

series527.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
174.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
175.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify90.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 5 (85.0ms)

Iter	Nodes	Cost
0	45	698
1	70	578
2	141	572
3	323	572
4	1214	572
5	5001	544

prune290.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 31.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.4b	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
38.3b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `log-prod` `exp-sum` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`log-pow`
1×	`rem-exp-log`

Counts

4 → 42

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series540.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
179.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
175.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify116.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 5 (110.0ms)

Iter	Nodes	Cost
0	85	806
1	130	682
2	234	648
3	567	640
4	2411	640
5	5002	610

prune203.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 31.1b

regimes732.0ms

Accuracy

0% (2.3b remaining)

Error of 33.5b against oracle of 31.2b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	114
1	22	114

end0.0ms

sample13.8s

Algorithm

intervals

Results

7.0s	2597×	body	10240	exit
4.2s	2321×	body	1280	valid
1.3s	1658×	body	640	valid
504.0ms	2808×	body	80	valid
356.0ms	820×	body	320	valid
122.0ms	387×	body	160	valid
10.0ms	2×	body	5120	valid
9.0ms	4×	body	2560	valid