Details

sample382.0ms

Algorithm

intervals

Results

207.0ms	83×	body	10240	exit
110.0ms	67×	body	1280	valid
34.0ms	56×	body	640	valid
9.0ms	94×	body	80	valid
8.0ms	25×	body	320	valid
3.0ms	14×	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: 32.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
37.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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

series158.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
61.0ms	(sin (expm1 a))
93.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify122.0ms

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	2934	264
4	5001	264

prune207.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 31.4b

localize17.0ms

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)))
37.5b	(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` `log1p-expm1-u` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube`
3×	`log-prod`
1×	`expm1-log1p` `rem-log-exp` `rem-exp-log` `expm1-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series122.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
30.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify58.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	104	472
1	205	410
2	516	410
3	1518	410
4	5002	410

prune266.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.5b	(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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 40

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)

series40.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(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)

simplify78.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	498
1	64	429
2	83	429
3	124	429
4	224	429
5	546	429
6	2617	429
7	5001	429

prune338.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.9b

localize32.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
37.5b	(fmod (log (log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
37.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`rem-log-exp`

Counts

4 → 44

Calls

4 calls:

2.0ms	(log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.0ms	(fmod (log (log (exp (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)

series37.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
2.0ms	(fmod (log (log (exp (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)

simplify91.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	66	566
1	85	483
2	112	483
3	150	483
4	274	483
5	732	483
6	3399	483
7	5002	483

prune279.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.9b

regimes317.0ms

Accuracy

0% (1.8b remaining)

Error of 33.5b against oracle of 31.7b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	30
1	22	30

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.9s	2723×	body	10240	exit
3.7s	2243×	body	1280	valid
1.2s	1719×	body	640	valid
270.0ms	2795×	body	80	valid
267.0ms	819×	body	320	valid
88.0ms	421×	body	160	valid
4.0ms	1×	body	5120	valid
4.0ms	2×	body	2560	valid