Details

sample419.0ms

Algorithm

intervals

Results

229.0ms	94×	body	10240	exit
121.0ms	77×	body	1280	valid
34.0ms	51×	body	640	valid
10.0ms	30×	body	320	valid
8.0ms	85×	body	80	valid
3.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

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:

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

series7.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify109.0ms

Counts

30 → 30

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	212
1	35	181
2	43	181
3	54	181
4	91	181
5	185	181
6	781	181
7	2680	181
8	5001	181
done	5001	181

prune131.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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:

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)

series130.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(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)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify251.0ms

Counts

44 → 44

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	34	413
1	63	335
2	140	333
3	584	333
4	4641	333
5	5001	333
done	5001	333

prune204.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 33.0b

localize20.0ms

Local error

Found 4 expressions with local error:

39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(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)

simplify94.0ms

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	352
1	17	300
2	21	300
3	26	300
4	45	300
5	99	300
6	505	300
7	1672	300
8	5001	300
done	5001	300

prune219.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 33.0b

localize27.0ms

Local error

Found 4 expressions with local error:

39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(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)

simplify95.0ms

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	352
1	17	300
2	21	300
3	26	300
4	45	300
5	99	300
6	505	300
7	1672	300
8	5001	300
done	5001	300

prune172.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 33.0b

regimes204.0ms

Accuracy

0% (1.2b remaining)

Error of 33.8b against oracle of 32.6b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	12	24
done	12	24

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2556×	body	10240	exit
3.8s	2297×	body	1280	valid
1.1s	1704×	body	640	valid
271.0ms	2744×	body	80	valid
265.0ms	816×	body	320	valid
89.0ms	434×	body	160	valid
18.0ms	4×	body	5120	valid
2.0ms	1×	body	2560	valid