Details

sample870.0ms

Algorithm

intervals

Results

611.0ms	260×	body	80	valid
135.0ms	74×	body	1280	valid
40.0ms	41×	body	640	valid
15.0ms	21×	body	320	valid
4.0ms	9×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2030
6	2030
5	823
4	210
3	95
2	62
1	35
0	19

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize48.0ms

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)))

rewrite26.0ms

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:

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

series316.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* y.re (log (hypot x.re x.im)))
18.0ms	(* (atan2 x.im x.re) y.re)
27.0ms	(* (atan2 x.im x.re) y.im)
179.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify944.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
3	2002
2	736
1	298
0	150

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize71.0ms

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)))

rewrite23.0ms

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:

5.0ms	(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)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (* (atan2 x.im x.re) y.im))
104.0ms	(cbrt (* (atan2 x.im x.re) y.im))
106.0ms	(cbrt (* (atan2 x.im x.re) y.im))
173.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify970.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2007
4	2007
3	675
2	293
1	151
0	83

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize75.0ms

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))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
9.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (* (atan2 x.im x.re) y.im))
78.0ms	(cbrt (* (atan2 x.im x.re) y.im))
66.0ms	(cbrt (* (atan2 x.im x.re) y.im))
190.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	2007
4	2007
3	675
2	293
1	151
0	83

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.7b

localize114.0ms

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)))

rewrite29.0ms

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:

13.0ms	(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)))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (* (atan2 x.im x.re) y.im))
187.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
159.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
174.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts

57 → 57

Iterations

Iter	Nodes
done	2007
4	2007
3	675
2	293
1	151
0	83

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.7b

regimes434.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.4s	2064×	body	1280	valid
2.4s	8007×	body	80	valid
2.4s	1426×	body	640	valid
668.0ms	632×	body	320	valid
178.0ms	303×	body	160	valid