Details

sample678.0ms

Algorithm

intervals

Results

346.0ms	85×	body	10240	exit
149.0ms	64×	body	1280	valid
57.0ms	61×	body	640	valid
17.0ms	33×	body	320	valid
15.0ms	85×	body	80	valid
4.0ms	13×	body	160	valid

simplify24.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
39.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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

series157.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
140.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts: 40 → 40

prune185.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite9.0ms

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:

2.0ms	(sin (expm1 a))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series187.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sin (expm1 a))
61.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.2s

Counts: 52 → 52

prune339.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 33.3b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

3.0ms	(log (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)

series12.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify931.0ms

Counts: 48 → 48

prune498.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.1b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.8b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

5.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series49.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify2.5s

Counts: 56 → 56

prune353.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 32.9b

regimes477.0ms

Accuracy

0% (1.8b remaining)

Error of 33.6b against oracle of 31.8b and baseline of 33.6b

bsearch0.0ms

simplify2.4s

end0.0ms

sample22.4s

Algorithm

intervals

Results

12.1s	2671×	body	10240	exit
6.6s	2277×	body	1280	valid
2.0s	1668×	body	640	valid
594.0ms	2774×	body	80	valid
468.0ms	809×	body	320	valid
161.0ms	466×	body	160	valid
30.0ms	4×	body	5120	valid
7.0ms	2×	body	2560	valid