Details

sample370.0ms

Algorithm

intervals

Results

172.0ms	68×	body	10240	exit
130.0ms	80×	body	1280	valid
34.0ms	54×	body	640	valid
9.0ms	95×	body	80	valid
5.0ms	1×	body	5120	valid
4.0ms	14×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize18.0ms

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))
37.0b	(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)

series59.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
53.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify120.0ms

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

prune167.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 31.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(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:

2.0ms	(sin (expm1 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)

series63.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sin (expm1 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)

simplify101.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	300
1	26	256
2	32	256
3	40	256
4	68	256
5	142	256
6	643	256
7	2176	256
8	5001	256

prune222.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
36.9b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite18.0ms

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:

16.0ms	(* (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)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series178.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (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)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	104	703
1	308	616
2	1499	509
3	5001	499

prune461.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 30.8b

localize37.0ms

Local error

Found 4 expressions with local error:

37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(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)

simplify92.0ms

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

prune230.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 30.8b

regimes395.0ms

Accuracy

0% (1.6b 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	24	67
1	24	67

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.5s	2602×	body	10240	exit
3.9s	2305×	body	1280	valid
1.2s	1709×	body	640	valid
283.0ms	2757×	body	80	valid
265.0ms	815×	body	320	valid
84.0ms	407×	body	160	valid
27.0ms	6×	body	5120	valid
2.0ms	1×	body	2560	valid