Details

sample753.0ms

Algorithm

intervals

Results

146.0ms	55×	body	1280	valid
69.0ms	11×	body	160	valid
65.0ms	250×	body	80	valid
44.0ms	40×	body	640	valid
14.0ms	15×	body	320	valid

simplify4.0s

Counts

1 → 1

Iterations

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

prune66.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize230.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.8b	(* (atan2 x.im x.re) y.im)
35.0b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite113.0ms

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:

22.0ms	(* y.re (log (hypot x.re x.im)))
38.0ms	(* (atan2 x.im x.re) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* y.re (log (hypot x.re x.im)))
64.0ms	(* (atan2 x.im x.re) y.re)
57.0ms	(* (atan2 x.im x.re) y.im)
407.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify5.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1996
2	708
1	295
0	150

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize323.0ms

Local error

Found 4 expressions with local error:

4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
34.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

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

series764.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (atan2 x.im x.re))
160.0ms	(cbrt (atan2 x.im x.re))
112.0ms	(cbrt (atan2 x.im x.re))
380.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify5.8s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
4	2558
3	729
2	279
1	129
0	70

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize409.0ms

Local error

Found 4 expressions with local error:

4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
34.6b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

3.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(cbrt (atan2 x.im x.re))
7.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (atan2 x.im x.re))
92.0ms	(cbrt (atan2 x.im x.re))
115.0ms	(cbrt (atan2 x.im x.re))
394.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify7.5s

Counts

65 → 65

Iterations

Iter	Nodes
done	5005
4	3414
3	854
2	310
1	135
0	72

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize488.0ms

Local error

Found 4 expressions with local error:

4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
4.6b	(cbrt (atan2 x.im x.re))
34.8b	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) y.re))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

5.0ms	(cbrt (atan2 x.im x.re))
5.0ms	(cbrt (atan2 x.im x.re))
5.0ms	(cbrt (atan2 x.im x.re))
14.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) y.re))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (atan2 x.im x.re))
114.0ms	(cbrt (atan2 x.im x.re))
162.0ms	(cbrt (atan2 x.im x.re))
437.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) y.re))))

simplify8.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5005
4	3461
3	901
2	321
1	137
0	72

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes1.8s

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.0s	7962×	body	80	valid
2.6s	1988×	body	1280	valid
1.3s	1502×	body	640	valid
485.0ms	609×	body	320	valid
123.0ms	333×	body	160	valid