Details

sample730.0ms

Algorithm

intervals

Results

362.0ms	80×	body	10240	exit
204.0ms	77×	body	1280	valid
53.0ms	51×	body	640	valid
17.0ms	86×	body	80	valid
17.0ms	27×	body	320	valid
6.0ms	1×	body	5120	valid
5.0ms	13×	body	160	valid
4.0ms	1×	body	2560	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize31.0ms

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)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 43

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
6.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series312.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
158.0ms	(expm1 (sin (expm1 a)))
136.0ms	(sin (expm1 a))
14.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1219
2	309
1	118
0	74

prune430.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 32.4b

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)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

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

series112.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
75.0ms	(sin (expm1 a))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify944.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	777
2	239
1	120
0	81

prune493.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.2b

localize53.0ms

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)

rewrite3.0ms

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 (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)

series88.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify985.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	661
2	170
1	76
0	49

prune679.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 31.9b

localize108.0ms

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)

rewrite7.0ms

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:

5.0ms	(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)
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series134.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(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)

simplify1.3s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	691
2	186
1	90
0	59

prune497.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 31.8b

regimes756.0ms

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

sample25.7s

Algorithm

intervals

Results

13.9s	2624×	body	10240	exit
7.0s	2181×	body	1280	valid
2.4s	1664×	body	640	valid
1.1s	834×	body	320	valid
709.0ms	2882×	body	80	valid
253.0ms	430×	body	160	valid
24.0ms	4×	body	5120	valid
17.0ms	5×	body	2560	valid