Details

sample838.0ms

Algorithm

intervals

Results

361.0ms	85×	body	10240	exit
288.0ms	75×	body	1280	valid
61.0ms	53×	body	640	valid
20.0ms	93×	body	80	valid
19.0ms	29×	body	320	valid
3.0ms	6×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

2 → 14

Calls

2 calls:

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

series16.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(expm1 (sin (expm1 a)))
13.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify937.0ms

Counts: 20 → 20

prune135.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 31.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

3.0ms	(cbrt (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)

series175.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify994.0ms

Counts: 44 → 44

prune277.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 31.9b

localize39.0ms

Local error

Found 4 expressions with local error:

37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(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	(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)

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts: 40 → 40

prune369.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 31.9b

localize44.0ms

Local error

Found 4 expressions with local error:

37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(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	(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)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series23.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
7.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts: 40 → 40

prune288.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 31.9b

regimes459.0ms

Accuracy

0% (0.8b remaining)

Error of 33.6b against oracle of 32.8b and baseline of 33.6b

bsearch0.0ms

simplify12.0ms

end0.0ms

sample23.0s

Algorithm

intervals

Results

11.9s	2696×	body	10240	exit
7.3s	2307×	body	1280	valid
2.0s	1663×	body	640	valid
581.0ms	2786×	body	80	valid
532.0ms	834×	body	320	valid
154.0ms	402×	body	160	valid
17.0ms	2×	body	5120	valid
17.0ms	6×	body	2560	valid