Details

sample521.0ms

Algorithm

intervals

Results

293.0ms	109×	body	10240	exit
119.0ms	70×	body	1280	valid
68.0ms	54×	body	640	valid
11.0ms	93×	body	80	valid
10.0ms	29×	body	320	valid
2.0ms	10×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `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)))
3.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series83.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
75.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify109.0ms

Counts: 40 → 40

prune158.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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:

1.0ms	(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)

series131.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(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)

simplify241.0ms

Counts: 44 → 44

prune207.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 31.4b

localize33.0ms

Local error

Found 4 expressions with local error:

38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `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)

series17.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(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)

simplify84.0ms

Counts: 40 → 40

prune225.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

localize56.0ms

Local error

Found 4 expressions with local error:

38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `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)

simplify87.0ms

Counts: 40 → 40

prune179.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

regimes198.0ms

Accuracy

0% (1.3b remaining)

Error of 33.4b against oracle of 32.2b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample15.8s

Algorithm

intervals

Results

8.5s	2690×	body	10240	exit
4.6s	2284×	body	1280	valid
1.5s	1664×	body	640	valid
364.0ms	786×	body	320	valid
356.0ms	2812×	body	80	valid
108.0ms	448×	body	160	valid
14.0ms	3×	body	5120	valid
7.0ms	3×	body	2560	valid