Details

sample450.0ms

Algorithm

intervals

Results

162.0ms	71×	body	1280	valid
103.0ms	49×	body	640	valid
66.0ms	256×	body	80	valid
16.0ms	20×	body	320	valid
7.0ms	15×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
1.3b	(* (atan2 x.im x.re) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
29.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite62.0ms

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:

14.0ms	(* y.re (log (hypot x.re x.im)))
24.0ms	(* (atan2 x.im x.re) y.re)
12.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* y.re (log (hypot x.re x.im)))
31.0ms	(* (atan2 x.im x.re) y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
202.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

93 → 93

Iterations

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

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize78.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
29.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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))
4.0ms	(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)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* (atan2 x.im x.re) y.im))
82.0ms	(cbrt (* (atan2 x.im x.re) y.im))
84.0ms	(cbrt (* (atan2 x.im x.re) y.im))
176.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts

59 → 59

Iterations

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

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize69.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
29.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

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))
7.0ms	(cbrt (* (atan2 x.im x.re) y.im))
15.0ms	(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)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(cbrt (* (atan2 x.im x.re) y.im))
68.0ms	(cbrt (* (atan2 x.im x.re) y.im))
80.0ms	(cbrt (* (atan2 x.im x.re) y.im))
151.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

59 → 59

Iterations

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

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize121.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
7.0b	(cbrt (* (atan2 x.im x.re) y.im))
29.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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

series422.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (* (atan2 x.im x.re) y.im))
80.0ms	(cbrt (* (atan2 x.im x.re) y.im))
75.0ms	(cbrt (* (atan2 x.im x.re) y.im))
193.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

59 → 59

Iterations

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

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

regimes484.0ms

Accuracy

0% (0.0b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 3.3b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample10.9s

Algorithm

intervals

Results

4.1s	2034×	body	1280	valid
3.6s	7979×	body	80	valid
2.0s	1428×	body	640	valid
629.0ms	636×	body	320	valid
166.0ms	312×	body	160	valid