Details

sample717.0ms

Algorithm

intervals

Results

364.0ms	95×	body	10240	exit
194.0ms	81×	body	1280	valid
37.0ms	44×	body	640	valid
12.0ms	94×	body	80	valid
11.0ms	25×	body	320	valid
4.0ms	12×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	8	556
done	8	556

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize925.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series30.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
4.0ms	(expm1 (sin (expm1 a)))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify5.8s

Counts

30 → 30

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	28	13130
1	31	13130
2	35	13130
3	44	13130
4	66	13130
5	116	13130
6	246	13130
7	506	13130
8	1231	13130
9	3941	13130
done	5004	13130

prune313.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 31.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `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)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series193.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt (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)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify5.5s

Counts

44 → 44

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	26	27174
1	38	26701
2	68	26662
3	132	26502
4	485	26502
5	2335	26502
done	5003	26502

prune397.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.1b

localize94.0ms

Local error

Found 4 expressions with local error:

37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify6.1s

Counts

40 → 40

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	22640
1	15	22640
2	17	22640
3	22	22640
4	30	22640
5	49	22640
6	83	22640
7	167	22640
8	408	22640
9	1366	22640
done	5000	22640

prune444.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.1b

localize182.0ms

Local error

Found 4 expressions with local error:

37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.6s

Counts

40 → 40

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	22640
1	15	22640
2	17	22640
3	22	22640
4	30	22640
5	49	22640
6	83	22640
7	167	22640
8	408	22640
9	1366	22640
done	5000	22640

prune218.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.1b

regimes251.0ms

Accuracy

0% (1.3b remaining)

Error of 33.5b against oracle of 32.3b and baseline of 33.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	17	1076
1	21	1076
done	21	1076

end0.0ms

sample15.2s

Algorithm

intervals

Results

8.0s	2672×	body	10240	exit
4.1s	2264×	body	1280	valid
1.6s	1686×	body	640	valid
754.0ms	2800×	body	80	valid
392.0ms	831×	body	320	valid
100.0ms	416×	body	160	valid
14.0ms	3×	body	5120	valid