Details

sample662.0ms

Algorithm

intervals

Results

269.0ms	77×	body	10240	exit
175.0ms	73×	body	1280	valid
94.0ms	55×	body	640	valid
21.0ms	89×	body	80	valid
14.0ms	24×	body	320	valid
6.0ms	15×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`expm1-udef`
2×	`expm1-log1p`
1×	`sin-diff`

Counts

4 → 45

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)

series310.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(expm1 a)
154.0ms	(expm1 (sin (expm1 a)))
116.0ms	(sin (expm1 a))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify5.8s

Counts

57 → 57

Iterations

Iter	Nodes
5	4128
4	1492
3	551
2	243
1	128
0	78

prune979.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 32.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 a))
0.5b	(cbrt (expm1 a))
0.5b	(cbrt (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (expm1 a))
1.0ms	(cbrt (expm1 a))
1.0ms	(cbrt (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

series405.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (expm1 a))
116.0ms	(cbrt (expm1 a))
130.0ms	(cbrt (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
5	2496
4	806
3	366
2	177
1	90
0	54

prune1.2s

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 32.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 41

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)

series99.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.7s

Counts

53 → 53

Iterations

Iter	Nodes
6	2636
5	1471
4	630
3	238
2	115
1	71
0	46

prune1.2s

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 31.8b

localize51.0ms

Local error

Found 4 expressions with local error:

38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

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)

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify8.8s

Counts

52 → 52

Iterations

Iter	Nodes
10	7575
9	1469
8	467
7	191
6	92
5	53
4	33
3	25
2	20
1	18
0	17

prune773.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 31.8b

regimes707.0ms

Accuracy

0% (1.7b remaining)

Error of 33.5b against oracle of 31.8b and baseline of 33.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample25.7s

Algorithm

intervals

Results

12.7s	2630×	body	10240	exit
7.4s	2298×	body	1280	valid
3.5s	1623×	body	640	valid
825.0ms	2803×	body	80	valid
701.0ms	860×	body	320	valid
201.0ms	409×	body	160	valid
40.0ms	5×	body	5120	valid
5.0ms	2×	body	2560	valid