Details

sample856.0ms

Algorithm

intervals

Results

396.0ms	74×	body	1280	valid
174.0ms	260×	body	80	valid
53.0ms	41×	body	640	valid
20.0ms	21×	body	320	valid
6.0ms	9×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	5780
5	821
4	208
3	95
2	62
1	35
0	19

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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×	`cos-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

29.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* y.re (log (hypot x.re x.im)))
28.0ms	(* (atan2 x.im x.re) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)
213.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

93 → 93

Iterations

Iter	Nodes
4	2764
3	1331
2	624
1	284
0	150

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize80.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (atan2 x.im x.re) y.im))
7.1b	(cbrt (* (atan2 x.im x.re) y.im))
7.1b	(cbrt (* (atan2 x.im x.re) y.im))
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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×	`cos-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (* (atan2 x.im x.re) y.im))
62.0ms	(cbrt (* (atan2 x.im x.re) y.im))
67.0ms	(cbrt (* (atan2 x.im x.re) y.im))
157.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

59 → 59

Iterations

Iter	Nodes
5	4921
4	1559
3	588
2	283
1	150
0	83

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize63.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (atan2 x.im x.re) y.im))
7.1b	(cbrt (* (atan2 x.im x.re) y.im))
7.1b	(cbrt (* (atan2 x.im x.re) y.im))
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`cos-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))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cbrt (* (atan2 x.im x.re) y.im))
89.0ms	(cbrt (* (atan2 x.im x.re) y.im))
102.0ms	(cbrt (* (atan2 x.im x.re) y.im))
171.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

59 → 59

Iterations

Iter	Nodes
5	4921
4	1559
3	588
2	283
1	150
0	83

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.7b

localize121.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (atan2 x.im x.re) y.im))
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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

Counts

4 → 45

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
17.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (* (atan2 x.im x.re) y.im))
153.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
147.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
147.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

57 → 57

Iterations

Iter	Nodes
5	4921
4	1559
3	588
2	283
1	150
0	83

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.7b

regimes480.0ms

Accuracy

0% (0.0b remaining)

Error of 3.4b against oracle of 3.4b and baseline of 3.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	32
1	32
0	24

end0.0ms

sample11.0s

Algorithm

intervals

Results

4.3s	2064×	body	1280	valid
2.8s	8007×	body	80	valid
2.6s	1426×	body	640	valid
621.0ms	632×	body	320	valid
253.0ms	303×	body	160	valid