Details

sample2.3s

Algorithm

intervals

Results

1.3s	99×	body	10240	exit
364.0ms	66×	body	1280	valid
207.0ms	62×	body	640	valid
60.0ms	99×	body	80	valid
37.0ms	17×	body	320	valid
5.0ms	12×	body	160	valid

simplify271.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize113.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.5b	(sin (expm1 a))
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

1.0ms	(expm1 a)
1.0ms	(expm1 (sin (expm1 a)))
6.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series1.6s

Counts

4 → 12

Calls

4 calls:

34.0ms	(expm1 a)
571.0ms	(expm1 (sin (expm1 a)))
642.0ms	(sin (expm1 a))
390.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify14.6s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
5	3918
4	1687
3	638
2	252
1	131
0	73

prune813.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.7b

localize131.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

8.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series558.0ms

Counts

4 → 12

Calls

4 calls:

520.0ms	(sin (expm1 a))
8.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify11.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
7	3240
6	1914
5	957
4	458
3	216
2	106
1	71
0	44

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.5b

localize183.0ms

Local error

Found 4 expressions with local error:

35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

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)
18.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify7.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	1146
8	356
7	152
6	81
5	51
4	32
3	24
2	19
1	17
0	16

prune778.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 30.5b

localize212.0ms

Local error

Found 4 expressions with local error:

35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify12.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	1146
8	356
7	152
6	81
5	51
4	32
3	24
2	19
1	17
0	16

prune1.2s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

regimes760.0ms

Accuracy

0% (1.1b remaining)

Error of 33.6b against oracle of 32.5b and baseline of 33.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample1.1m

Algorithm

intervals

Results

36.2s	2650×	body	10240	exit
16.3s	2305×	body	1280	valid
5.7s	1602×	body	640	valid
3.4s	850×	body	320	valid
2.9s	2781×	body	80	valid
310.0ms	458×	body	160	valid
15.0ms	2×	body	5120	valid
14.0ms	2×	body	2560	valid