Details

sample264.0ms

Algorithm

intervals

Results

94.0ms	56×	body	1280	valid
37.0ms	256×	body	80	valid
27.0ms	41×	body	640	valid
7.0ms	20×	body	320	valid
1.0ms	4×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize68.0ms

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.re)
2.4b	(* (atan2 x.im x.re) y.im)
34.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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` `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 → 77

Calls

4 calls:

7.0ms	(* y.re (log (hypot x.re x.im)))
10.0ms	(* (atan2 x.im x.re) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* y.re (log (hypot x.re x.im)))
27.0ms	(* (atan2 x.im x.re) y.re)
34.0ms	(* (atan2 x.im x.re) y.im)
195.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1097
1	298
0	146

prune779.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize77.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
34.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
12.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (atan2 x.im x.re))
61.0ms	(cbrt (atan2 x.im x.re))
76.0ms	(cbrt (atan2 x.im x.re))
206.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1255
2	313
1	119
0	66

prune744.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize109.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
34.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite7.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(cbrt (atan2 x.im x.re))
69.0ms	(cbrt (atan2 x.im x.re))
43.0ms	(cbrt (atan2 x.im x.re))
204.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1255
2	313
1	119
0	66

prune713.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize170.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
5.5b	(cbrt (atan2 x.im x.re))
34.5b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite5.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (atan2 x.im x.re))
59.0ms	(cbrt (atan2 x.im x.re))
63.0ms	(cbrt (atan2 x.im x.re))
210.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1255
2	313
1	119
0	66

prune627.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.0b

regimes423.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.3s	2015×	body	1280	valid
1.7s	1389×	body	640	valid
1.6s	8005×	body	80	valid
693.0ms	648×	body	320	valid
108.0ms	319×	body	160	valid