Details

sample722.0ms

Algorithm

intervals

Results

359.0ms	76×	body	10240	exit
159.0ms	64×	body	1280	valid
81.0ms	61×	body	640	valid
18.0ms	91×	body	80	valid
15.0ms	28×	body	320	valid
4.0ms	12×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize33.0ms

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

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

3 → 21

Calls

3 calls:

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

series76.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
68.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

30 → 30

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	28	290
1	31	290
2	35	250
3	44	250
4	66	250
5	166	250
6	423	250
7	957	250
8	3088	250
done	5001	250

prune242.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.0b

localize46.0ms

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)

rewrite5.0ms

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)

series174.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(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)

simplify2.1s

Counts

44 → 44

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	26	591
1	38	587
2	85	473
3	228	470
4	1222	470
done	5000	470

prune288.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.0b

localize51.0ms

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)

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)

series11.0ms

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)

simplify1.6s

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	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune341.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.0b

localize86.0ms

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` `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)
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)

series21.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.8s

Counts

40 → 40

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune289.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.0b

regimes290.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample23.0s

Algorithm

intervals

Results

12.3s	2689×	body	10240	exit
6.4s	2224×	body	1280	valid
2.1s	1747×	body	640	valid
1.0s	2783×	body	80	valid
535.0ms	831×	body	320	valid
153.0ms	412×	body	160	valid
13.0ms	2×	body	5120	valid
2.0ms	1×	body	2560	valid