Details

sample333.0ms

Algorithm

intervals

Results

160.0ms	65×	body	10240	exit
111.0ms	65×	body	1280	valid
30.0ms	46×	body	640	valid
10.0ms	106×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	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: 29.9b

localize19.0ms

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))
34.2b	(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)

series62.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
56.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify119.0ms

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

prune164.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series92.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
28.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify99.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 7 (95.0ms)

Iter	Nodes	Cost
0	63	401
1	92	342
2	121	342
3	180	342
4	339	342
5	863	342
6	3913	342
7	5001	338

prune206.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 28.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
34.1b	(fmod (log (* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))) a)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`unpow-prod-down`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `sqr-pow`
9×	`prod-exp` `unswap-sqr`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-to-exp` `exp-prod` `pow-exp` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `unpow1/2`
2×	`rem-exp-log`
1×	`pow2` `sqrt-unprod` `pow-prod-down` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
11.0ms	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
0.0ms	(fmod (log (* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))) a)

series95.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
29.0ms	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
3.0ms	(fmod (log (* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))) a)

simplify227.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	161	1188
1	553	947
2	4758	884
3	5001	884

prune329.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 28.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.1b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	430
1	60	361
2	78	361
3	118	361
4	218	361
5	534	361
6	2589	361
7	5001	361

prune191.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 28.4b

regimes324.0ms

Accuracy

0% (1.7b remaining)

Error of 33.0b against oracle of 31.2b and baseline of 33.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	21	45

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.5s	2598×	body	10240	exit
3.7s	2217×	body	1280	valid
1.1s	1609×	body	640	valid
286.0ms	855×	body	320	valid
275.0ms	2887×	body	80	valid
91.0ms	422×	body	160	valid
18.0ms	4×	body	5120	valid
11.0ms	6×	body	2560	valid