Details

sample881.0ms

Algorithm

intervals

Results

428.0ms	72×	body	10240	exit
199.0ms	62×	body	1280	valid
95.0ms	48×	body	640	valid
22.0ms	31×	body	320	valid
20.0ms	100×	body	80	valid
7.0ms	15×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

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	(atan2 (expm1 (sin (expm1 a))) (atan a))
4.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series149.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
84.0ms	(sin (expm1 a))
3.0ms	(expm1 (sin (expm1 a)))
57.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
8	4003
7	1217
6	519
5	217
4	84
3	55
2	44
1	39
0	35

prune297.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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:

2.0ms	(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)

series177.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(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)

simplify1.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	1236
3	226
2	85
1	38
0	26

prune408.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.4b

localize91.0ms

Local error

Found 4 expressions with local error:

36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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)

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

simplify1.4s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
8	1013
7	319
6	142
5	64
4	30
3	22
2	17
1	15
0	14

prune413.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.4b

localize83.0ms

Local error

Found 4 expressions with local error:

36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.2b	(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)

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)

simplify1.3s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
8	1013
7	319
6	142
5	64
4	30
3	22
2	17
1	15
0	14

prune306.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 30.4b

regimes310.0ms

Accuracy

0% (1.3b remaining)

Error of 33.7b against oracle of 32.4b and baseline of 33.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample22.6s

Algorithm

intervals

Results

11.4s	2702×	body	10240	exit
7.1s	2195×	body	1280	valid
2.0s	1698×	body	640	valid
1.0s	2772×	body	80	valid
492.0ms	888×	body	320	valid
185.0ms	439×	body	160	valid
17.0ms	6×	body	2560	valid
12.0ms	2×	body	5120	valid