Details

sample801.0ms

Algorithm

intervals

Results

361.0ms	96×	body	10240	exit
164.0ms	69×	body	1280	valid
116.0ms	55×	body	640	valid
59.0ms	89×	body	80	valid
16.0ms	30×	body	320	valid
9.0ms	1×	body	5120	valid
4.0ms	12×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series239.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(expm1 (sin (expm1 a)))
108.0ms	(sin (expm1 a))
10.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.9s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
5	2055
4	919
3	408
2	188
1	105
0	61

prune317.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

2.0ms	(sin (expm1 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)

series84.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sin (expm1 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)

simplify4.6s

Counts

49 → 49

Iterations

Iter	Nodes
done	5003
7	4074
6	2123
5	977
4	457
3	214
2	106
1	71
0	44

prune498.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.5b

localize85.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(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)

simplify5.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5008
10	3506
9	1142
8	656
7	371
6	78
5	44
4	32
3	24
2	19
1	17
0	16

prune546.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.5b

localize153.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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)

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(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)

simplify5.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5008
10	3506
9	1142
8	656
7	371
6	78
5	44
4	32
3	24
2	19
1	17
0	16

prune355.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 32.5b

regimes397.0ms

Accuracy

0% (1.1b remaining)

Error of 33.8b against oracle of 32.7b and baseline of 33.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample21.3s

Algorithm

intervals

Results

11.2s	2646×	body	10240	exit
6.7s	2367×	body	1280	valid
1.8s	1564×	body	640	valid
598.0ms	870×	body	320	valid
516.0ms	2758×	body	80	valid
152.0ms	433×	body	160	valid
28.0ms	5×	body	5120	valid
6.0ms	3×	body	2560	valid