Details

sample751.0ms

Algorithm

intervals

Results

319.0ms	76×	body	10240	exit
225.0ms	64×	body	1280	valid
75.0ms	61×	body	640	valid
18.0ms	91×	body	80	valid
18.0ms	28×	body	320	valid
5.0ms	12×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 29

Calls

3 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series230.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
162.0ms	(expm1 (sin (expm1 a)))
62.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.0s

Counts

38 → 38

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	49	355
1	78	344
2	191	303
3	648	303
4	3273	303
done	5000	303

prune216.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(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` `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)

series219.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(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)

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	30	673
1	42	669
2	94	555
3	257	552
4	1337	552
done	5000	552

prune384.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.0b

localize78.0ms

Local error

Found 4 expressions with local error:

38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(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:

0.0ms	(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)

series18.0ms

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)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

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	32	516
5	66	516
6	147	516
7	321	516
8	917	516
done	5000	516

prune428.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.0b

localize82.0ms

Local error

Found 4 expressions with local error:

38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(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)

simplify1.5s

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	32	516
5	66	516
6	147	516
7	321	516
8	917	516
done	5000	516

prune283.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.0b

regimes292.0ms

Accuracy

0% (1.3b remaining)

Error of 33.6b against oracle of 32.3b and baseline of 33.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample22.2s

Algorithm

intervals

Results

11.2s	2689×	body	10240	exit
6.9s	2224×	body	1280	valid
2.0s	1747×	body	640	valid
1.0s	2783×	body	80	valid
458.0ms	831×	body	320	valid
191.0ms	412×	body	160	valid
10.0ms	2×	body	5120	valid
4.0ms	1×	body	2560	valid