Details

sample1.0s

Algorithm

intervals

Results

498.0ms	89×	body	10240	exit
285.0ms	89×	body	1280	valid
72.0ms	50×	body	640	valid
24.0ms	30×	body	320	valid
20.0ms	78×	body	80	valid
5.0ms	9×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

3 → 24

Calls

3 calls:

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

series22.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify825.0ms

Counts

33 → 33

Iterations

Iter	Nodes
done	2024
8	1246
7	493
6	231
5	124
4	69
3	47
2	38
1	34
0	31

prune347.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 34.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

3.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series173.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify918.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2002
4	585
3	141
2	70
1	40
0	28

prune482.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.9b

localize74.0ms

Local error

Found 4 expressions with local error:

41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

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)

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.5s

Counts

44 → 44

Iterations

Iter	Nodes
done	2000
9	1400
8	417
7	168
6	84
5	50
4	31
3	23
2	18
1	16
0	15

prune444.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.9b

localize86.0ms

Local error

Found 4 expressions with local error:

41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.4s

Counts

44 → 44

Iterations

Iter	Nodes
done	2000
9	1400
8	417
7	168
6	84
5	50
4	31
3	23
2	18
1	16
0	15

prune383.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.9b

regimes358.0ms

Accuracy

0% (1.6b remaining)

Error of 34.0b against oracle of 32.4b and baseline of 34.0b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample26.8s

Algorithm

intervals

Results

13.9s	2660×	body	10240	exit
8.3s	2343×	body	1280	valid
2.5s	1649×	body	640	valid
784.0ms	2721×	body	80	valid
693.0ms	838×	body	320	valid
265.0ms	446×	body	160	valid
19.0ms	3×	body	5120	valid