Details

sample1.5s

Algorithm

intervals

Results

587.0ms	77×	body	1280	valid
570.0ms	80×	body	10240	exit
192.0ms	51×	body	640	valid
28.0ms	27×	body	320	valid
27.0ms	86×	body	80	valid
11.0ms	13×	body	160	valid
9.0ms	1×	body	5120	valid
5.0ms	1×	body	2560	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.5b	(sin (expm1 a))
39.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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

series100.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
85.0ms	(sin (expm1 a))
8.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
8	3857
7	1265
6	537
5	221
4	88
3	59
2	48
1	43
0	39

prune365.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.5b	(sin (expm1 a))
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(sin (expm1 a))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series125.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
81.0ms	(sin (expm1 a))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify2.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
6	1481
5	548
4	269
3	152
2	103
1	71
0	55

prune408.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

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:

4.0ms	(sin (expm1 a))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series133.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sin (expm1 a))
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.3s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
8	1925
7	634
6	279
5	120
4	53
3	38
2	31
1	28
0	26

prune576.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 31.9b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
39.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

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:

4.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series107.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sin (expm1 a))
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify2.1s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
8	2157
7	643
6	272
5	133
4	66
3	51
2	44
1	40
0	34

prune389.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 31.9b

regimes806.0ms

Accuracy

0% (2.1b remaining)

Error of 32.9b against oracle of 30.8b and baseline of 32.9b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample25.9s

Algorithm

intervals

Results

13.2s	2624×	body	10240	exit
7.5s	2181×	body	1280	valid
2.7s	1664×	body	640	valid
755.0ms	834×	body	320	valid
741.0ms	2882×	body	80	valid
657.0ms	430×	body	160	valid
28.0ms	4×	body	5120	valid
17.0ms	5×	body	2560	valid