Details

sample705.0ms

Algorithm

intervals

Results

296.0ms	72×	body	10240	exit
217.0ms	62×	body	1280	valid
59.0ms	48×	body	640	valid
21.0ms	31×	body	320	valid
16.0ms	100×	body	80	valid
5.0ms	15×	body	160	valid

simplify11.0ms

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

localize36.0ms

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)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series307.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
82.0ms	(sin (expm1 a))
182.0ms	(expm1 (sin (expm1 a)))
40.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	1268
2	312
1	115
0	70

prune380.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.4b

localize56.0ms

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×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

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)

series189.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
13.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
4	1143
3	237
2	91
1	42
0	30

prune449.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.4b

localize77.0ms

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)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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)

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify4.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
9	4827
8	944
7	327
6	146
5	66
4	32
3	24
2	19
1	17
0	16

prune471.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 30.4b

localize74.0ms

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` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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)

simplify4.4s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
9	4827
8	944
7	327
6	146
5	66
4	32
3	24
2	19
1	17
0	16

prune329.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 30.4b

regimes329.0ms

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

sample21.9s

Algorithm

intervals

Results

11.5s	2702×	body	10240	exit
6.4s	2195×	body	1280	valid
2.4s	1698×	body	640	valid
610.0ms	888×	body	320	valid
452.0ms	2772×	body	80	valid
162.0ms	439×	body	160	valid
19.0ms	6×	body	2560	valid
12.0ms	2×	body	5120	valid