Details

sample269.0ms

Algorithm

intervals

Results

66.0ms	66×	body	1280	valid
39.0ms	253×	body	80	valid
28.0ms	42×	body	640	valid
5.0ms	11×	body	320	valid
2.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	823
4	210
3	95
2	62
1	35
0	19

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
6×	`log-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

7.0ms	(* y.re (log (hypot x.re x.im)))
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* y.re (log (hypot x.re x.im)))
29.0ms	(* (atan2 x.im x.re) y.im)
31.0ms	(* (atan2 x.im x.re) y.re)
208.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	3524
3	1362
2	599
1	268
0	142

prune776.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize105.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

4.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (* (atan2 x.im x.re) y.im))
80.0ms	(cbrt (* (atan2 x.im x.re) y.im))
78.0ms	(cbrt (* (atan2 x.im x.re) y.im))
180.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
5	1854
4	772
3	360
2	196
1	123
0	74

prune723.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize104.0ms

Local error

Found 4 expressions with local error:

18.0b	(sin (* (atan2 x.im x.re) y.re))
18.1b	(cos (* (atan2 x.im x.re) y.re))
23.8b	(sin (* y.im (log (hypot x.re x.im))))
24.4b	(cos (* y.im (log (hypot x.re x.im))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

13.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (atan2 x.im x.re) y.re))
9.0ms	(sin (* y.im (log (hypot x.re x.im))))
9.0ms	(cos (* y.im (log (hypot x.re x.im))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sin (* (atan2 x.im x.re) y.re))
50.0ms	(cos (* (atan2 x.im x.re) y.re))
157.0ms	(sin (* y.im (log (hypot x.re x.im))))
141.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify2.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	1441
3	559
2	280
1	188
0	134

prune1.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.1b

localize52.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

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`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (* (atan2 x.im x.re) y.im))
76.0ms	(cbrt (* (atan2 x.im x.re) y.im))
74.0ms	(cbrt (* (atan2 x.im x.re) y.im))
157.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
5	1854
4	772
3	360
2	196
1	123
0	74

prune717.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.4s	2232×	body	1280	valid
2.2s	7967×	body	80	valid
1.8s	1424×	body	640	valid
451.0ms	584×	body	320	valid
154.0ms	45×	body	2560	valid
88.0ms	244×	body	160	valid