Details

sample565.0ms

Algorithm

intervals

Results

225.0ms	79×	body	10240	exit
156.0ms	76×	body	1280	valid
90.0ms	54×	body	640	valid
11.0ms	90×	body	80	valid
9.0ms	22×	body	320	valid
4.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize18.0ms

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))
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite42.0ms

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)))
38.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series102.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
78.0ms	(sin (expm1 a))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	59	293
3	120	293
4	430	293
5	1759	293
done	5000	293

prune257.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite7.0ms

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:

4.0ms	(cbrt (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)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series219.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (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)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.7s

Counts

44 → 44

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	26	591
1	49	547
2	431	470
done	5000	470

prune399.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.5b

localize69.0ms

Local error

Found 4 expressions with local error:

38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(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)

series19.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify7.6s

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	23	436
3	48	436
4	159	436
5	687	436
6	4431	436
done	5000	436

prune384.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.5b

localize104.0ms

Local error

Found 4 expressions with local error:

38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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)
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)

simplify7.8s

Counts

40 → 40

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	23	436
3	48	436
4	159	436
5	687	436
6	4431	436
done	5000	436

prune266.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.5b

regimes315.0ms

Accuracy

0% (1.3b remaining)

Error of 33.4b against oracle of 32.1b and baseline of 33.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	58
1	16	58
done	16	58

end0.0ms

sample22.4s

Algorithm

intervals

Results

11.3s	2610×	body	10240	exit
7.4s	2286×	body	1280	valid
2.0s	1638×	body	640	valid
534.0ms	2821×	body	80	valid
515.0ms	810×	body	320	valid
160.0ms	439×	body	160	valid
18.0ms	5×	body	2560	valid
9.0ms	1×	body	5120	valid