Details

sample376.0ms

Algorithm

intervals

Results

172.0ms	68×	body	10240	exit
135.0ms	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
3.0ms	12×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize12.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

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)

series150.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
83.0ms	(expm1 (sin (expm1 a)))
62.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune196.0ms

Pruning

11 alts after pruning (11 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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

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)

series65.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(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)

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	67	360
1	138	315
2	360	315
3	1390	315
4	5001	315

prune267.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.9b

localize30.0ms

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)

rewrite19.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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:

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)

series152.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (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)

simplify67.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	151	788
1	447	697
2	1900	571
3	5001	561

prune494.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 30.7b

localize38.0ms

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)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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)

simplify95.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356

prune269.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 30.7b

regimes369.0ms

Accuracy

0% (1.6b remaining)

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

bsearch0.0ms

simplify2.0ms

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

6.6s	2602×	body	10240	exit
3.9s	2305×	body	1280	valid
1.1s	1709×	body	640	valid
270.0ms	2757×	body	80	valid
266.0ms	815×	body	320	valid
89.0ms	407×	body	160	valid
27.0ms	6×	body	5120	valid
2.0ms	1×	body	2560	valid