Details

sample406.0ms

Algorithm

intervals

Results

226.0ms	91×	body	10240	exit
110.0ms	59×	body	1280	valid
37.0ms	57×	body	640	valid
9.0ms	29×	body	320	valid
9.0ms	92×	body	80	valid
4.0ms	19×	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: 33.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
38.0b	(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	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series5.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify109.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	212
1	35	181
2	43	181
3	54	181
4	91	181
5	185	181
6	781	181
7	2680	181
8	5001	181

prune135.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

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	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series35.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify98.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 7 (94.0ms)

Iter	Nodes	Cost
0	63	414
1	92	353
2	121	353
3	180	353
4	339	353
5	863	353
6	3913	353
7	5001	349

prune220.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.6b

localize21.0ms

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)))
0.7b	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
38.0b	(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)

rewrite15.0ms

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:

2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
8.0ms	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
1.0ms	(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)

series90.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
28.0ms	(* (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)

simplify224.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (24.0ms)

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

prune348.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 31.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
38.0b	(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)
38.0b	(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)
38.0b	(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)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`unpow-prod-down`
12×	`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` `pow-exp` `add-cbrt-cube`
4×	`pow1` `unpow1/2` `add-log-exp`
1×	`pow2` `sqrt-unprod` `pow-prod-down` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

8.0ms	(* (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1/2))
1.0ms	(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)
1.0ms	(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)
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)

series38.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (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)
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)
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)

simplify223.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	149	1372
1	525	1094
2	4685	1015
3	5001	1015

prune336.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 31.4b

regimes376.0ms

Accuracy

0% (1.7b remaining)

Error of 33.5b against oracle of 31.9b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.4s	2570×	body	10240	exit
3.9s	2295×	body	1280	valid
1.1s	1656×	body	640	valid
268.0ms	2802×	body	80	valid
266.0ms	823×	body	320	valid
84.0ms	418×	body	160	valid
21.0ms	4×	body	5120	valid
4.0ms	2×	body	2560	valid