Details

sample788.0ms

Algorithm

intervals

Results

447.0ms	109×	body	10240	exit
188.0ms	70×	body	1280	valid
49.0ms	54×	body	640	valid
16.0ms	29×	body	320	valid
15.0ms	93×	body	80	valid
4.0ms	10×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize68.0ms

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)

rewrite14.0ms

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)))
9.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
4.0ms	(expm1 (sin (expm1 a)))
104.0ms	(sin (expm1 a))
18.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts

40 → 40

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	176	293
7	436	293
8	1564	293
done	5001	293

prune289.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.4b

localize60.0ms

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)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

3.0ms	(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)

series214.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
4.0ms	(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)

simplify4.4s

Counts

44 → 44

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	26	591
1	35	587
2	63	473
3	117	470
4	434	470
5	2941	470
done	5001	470

prune302.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 31.4b

localize43.0ms

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)

rewrite1.0ms

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	(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)

simplify2.4s

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	59	436
7	125	436
8	406	436
9	1820	436
done	5000	436

prune338.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

localize97.0ms

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` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

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)

series13.0ms

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)

simplify2.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	59	436
7	125	436
8	406	436
9	1820	436
done	5000	436

prune252.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 31.4b

regimes332.0ms

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

sample23.4s

Algorithm

intervals

Results

12.5s	2690×	body	10240	exit
6.4s	2284×	body	1280	valid
2.1s	1664×	body	640	valid
687.0ms	2812×	body	80	valid
643.0ms	448×	body	160	valid
571.0ms	786×	body	320	valid
16.0ms	3×	body	5120	valid
10.0ms	3×	body	2560	valid