Details

sample883.0ms

Algorithm

intervals

Results

370.0ms	75×	body	10240	exit
211.0ms	64×	body	1280	valid
90.0ms	35×	body	320	valid
82.0ms	54×	body	640	valid
19.0ms	90×	body	80	valid
6.0ms	13×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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:

43.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series210.0ms

Counts

2 → 6

Calls

2 calls:

190.0ms	(expm1 (sin (expm1 a)))
19.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.5s

Counts

26 → 26

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	40	238
1	67	227
2	179	200
3	637	200
4	3457	200
done	5000	200

prune283.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.3b

localize54.0ms

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)

rewrite4.0ms

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

series262.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(cbrt (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)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.6s

Counts

52 → 52

Iterations

Useful iterations: 3 (77.0ms)

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

prune583.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 32.3b

localize73.0ms

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

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.8s

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

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

prune659.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.3b

localize103.0ms

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

series24.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.8s

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

prune526.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.3b

regimes483.0ms

Accuracy

0% (0.8b remaining)

Error of 33.5b against oracle of 32.7b and baseline of 33.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample28.7s

Algorithm

intervals

Results

14.9s	2708×	body	10240	exit
8.7s	2271×	body	1280	valid
2.6s	1662×	body	640	valid
901.0ms	2791×	body	80	valid
669.0ms	860×	body	320	valid
185.0ms	412×	body	160	valid
11.0ms	3×	body	2560	valid
8.0ms	1×	body	5120	valid