Details

sample1.2s

Algorithm

intervals

Results

811.0ms	96×	body	10240	exit
164.0ms	69×	body	1280	valid
58.0ms	55×	body	640	valid
17.0ms	89×	body	80	valid
16.0ms	30×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	12×	body	160	valid

simplify10.0ms

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

localize41.0ms

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)

rewrite48.0ms

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:

1.0ms	(expm1 (sin (expm1 a)))
43.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series286.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(expm1 (sin (expm1 a)))
95.0ms	(sin (expm1 a))
19.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
3	1219
2	298
1	105
0	61

prune336.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.7b

localize72.0ms

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)

rewrite6.0ms

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:

4.0ms	(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)

series92.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(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)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify5.8s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4871
3	673
2	166
1	71
0	44

prune569.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.5b

localize105.0ms

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)

simplify4.6s

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

prune554.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.5b

localize146.0ms

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)

rewrite1.0ms

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)

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)

simplify4.6s

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

prune463.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 32.5b

regimes410.0ms

Accuracy

0% (1.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample21.8s

Algorithm

intervals

Results

11.7s	2646×	body	10240	exit
6.3s	2367×	body	1280	valid
2.3s	1564×	body	640	valid
544.0ms	2758×	body	80	valid
494.0ms	870×	body	320	valid
157.0ms	433×	body	160	valid
35.0ms	5×	body	5120	valid
10.0ms	3×	body	2560	valid