Details

sample469.0ms

Algorithm

intervals

Results

260.0ms	104×	body	10240	exit
140.0ms	78×	body	1280	valid
37.0ms	58×	body	640	valid
8.0ms	84×	body	80	valid
7.0ms	22×	body	320	valid
3.0ms	14×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`log1p-expm1-u`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`expm1-log1p` `expm1-udef`

Counts

2 → 20

Calls

2 calls:

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

series104.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(expm1 (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.1s

Counts

26 → 26

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	40	238
1	65	227
2	132	200
3	320	200
4	1009	200
done	5000	200

prune117.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 33.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (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`
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:

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)

series128.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

52 → 52

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	30	673
1	39	669
2	67	555
3	128	552
4	456	552
5	3321	552
done	5000	552

prune238.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 33.3b

localize22.0ms

Local error

Found 4 expressions with local error:

39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(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)

series8.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.6s

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	50	516
6	107	516
7	334	516
8	1169	516
done	5001	516

prune263.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.3b

localize27.0ms

Local error

Found 4 expressions with local error:

39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(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)

series8.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.7s

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	50	516
6	107	516
7	334	516
8	1169	516
done	5001	516

prune217.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.3b

regimes288.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

end0.0ms

sample12.7s

Algorithm

intervals

Results

6.8s	2704×	body	10240	exit
3.8s	2262×	body	1280	valid
1.1s	1672×	body	640	valid
272.0ms	845×	body	320	valid
272.0ms	2777×	body	80	valid
90.0ms	436×	body	160	valid
14.0ms	3×	body	5120	valid
10.0ms	5×	body	2560	valid