Details

sample1.1s

Algorithm

intervals

Results

520.0ms	109×	body	10240	exit
203.0ms	70×	body	1280	valid
88.0ms	29×	body	320	valid
66.0ms	54×	body	640	valid
17.0ms	93×	body	80	valid
4.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize52.0ms

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)

rewrite12.0ms

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))
0.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series261.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
153.0ms	(expm1 (sin (expm1 a)))
94.0ms	(sin (expm1 a))
10.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.8s

Counts

51 → 51

Iterations

Useful iterations: 3 (183.0ms)

Iter	Nodes	Cost
0	70	438
1	109	422
2	200	375
3	407	374
4	937	374
5	2426	374
done	5000	374

prune338.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.4b

localize37.0ms

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)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series195.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	30	673
1	39	669
2	67	555
3	128	552
4	445	552
5	2948	552
done	5001	552

prune405.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 31.4b

localize82.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

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

series21.0ms

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

simplify2.5s

Counts

48 → 48

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	125	516
8	427	516
9	1843	516
done	5001	516

prune441.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

localize87.0ms

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` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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)

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	125	516
8	427	516
9	1843	516
done	5001	516

prune392.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

regimes301.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	33
1	12	33
done	12	33

end0.0ms

sample22.0s

Algorithm

intervals

Results

11.8s	2690×	body	10240	exit
6.6s	2284×	body	1280	valid
1.9s	1664×	body	640	valid
569.0ms	2812×	body	80	valid
471.0ms	786×	body	320	valid
158.0ms	448×	body	160	valid
21.0ms	3×	body	5120	valid
9.0ms	3×	body	2560	valid