Details

sample425.0ms

Algorithm

intervals

Results

94.0ms	72×	body	1280	valid
56.0ms	257×	body	80	valid
52.0ms	26×	body	320	valid
39.0ms	44×	body	640	valid
1.0ms	4×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
0.7b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
35.3b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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:

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

series339.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* y.re (log (hypot x.re x.im)))
19.0ms	(* (atan2 x.im x.re) y.im)
21.0ms	(* (atan2 x.im x.re) y.re)
186.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
4	2933
3	1309
2	630
1	284
0	150

prune830.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize96.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot x.re x.im))
0.7b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
35.3b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt (hypot x.re x.im))
10.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(* (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)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (hypot x.re x.im))
31.0ms	(* (atan2 x.im x.re) y.im)
22.0ms	(* (atan2 x.im x.re) y.re)
180.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

79 → 79

Iterations

Iter	Nodes
4	3426
3	1497
2	614
1	261
0	134

prune851.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize108.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.7b	(* (atan2 x.im x.re) y.im)
0.8b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
35.4b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`cos-sum` `pow1/3` `fma-udef`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt y.re)
12.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series653.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(cbrt y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
112.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
190.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
3	2016
2	756
1	300
0	138

prune947.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize109.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re)))))
0.7b	(* (atan2 x.im x.re) y.im)
0.9b	(* y.re (atan2 x.im x.re))
35.3b	(cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cos-sum` `expm1-log1p` `fma-udef` `expm1-udef`

Counts

4 → 65

Calls

4 calls:

0.0ms	(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re)))))
13.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(* y.re (atan2 x.im x.re))
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re)))))
18.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(* y.re (atan2 x.im x.re))
239.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* y.re (atan2 x.im x.re))))

simplify1.6s

Counts

77 → 77

Iterations

Iter	Nodes
5	2062
4	1118
3	686
2	397
1	200
0	111

prune768.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

regimes629.0ms

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 3.0b and baseline of 3.4b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	33
1	33
0	26

end0.0ms

sample11.4s

Algorithm

intervals

Results

4.8s	1909×	body	1280	valid
3.0s	8008×	body	80	valid
2.1s	1502×	body	640	valid
657.0ms	641×	body	320	valid
252.0ms	327×	body	160	valid