Details

sample582.0ms

Algorithm

intervals

Results

150.0ms	73×	body	1280	valid
70.0ms	21×	body	320	valid
51.0ms	252×	body	80	valid
32.0ms	39×	body	640	valid
6.0ms	2×	body	2560	valid
4.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
31.0b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

13.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* y.re (log (hypot x.re x.im)))
25.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
193.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5003
3	1877
2	640
1	270
0	138

prune880.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
31.0b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite49.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

21.0ms	(* 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)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* y.re (log (hypot x.re x.im)))
19.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
165.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

89 → 89

Iterations

Iter	Nodes
done	5003
3	1877
2	640
1	270
0	138

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
31.0b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 77

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

series389.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* y.re (log (hypot x.re x.im)))
32.0ms	(* (atan2 x.im x.re) y.re)
34.0ms	(* (atan2 x.im x.re) y.im)
188.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	5003
3	1877
2	640
1	270
0	138

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize137.0ms

Local error

Found 4 expressions with local error:

15.9b	(cos (* (atan2 x.im x.re) y.re))
16.2b	(sin (* (atan2 x.im x.re) y.re))
20.8b	(sin (* y.im (log (hypot x.re x.im))))
21.0b	(cos (* y.im (log (hypot x.re x.im))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

11.0ms	(cos (* (atan2 x.im x.re) y.re))
7.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(sin (* y.im (log (hypot x.re x.im))))
8.0ms	(cos (* y.im (log (hypot x.re x.im))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cos (* (atan2 x.im x.re) y.re))
47.0ms	(sin (* (atan2 x.im x.re) y.re))
129.0ms	(sin (* y.im (log (hypot x.re x.im))))
136.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify3.5s

Counts

60 → 60

Iterations

Iter	Nodes
done	5010
5	4249
4	1435
3	567
2	274
1	182
0	130

prune857.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

regimes620.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.5s	2141×	body	1280	valid
1.8s	1418×	body	640	valid
1.7s	7945×	body	80	valid
787.0ms	621×	body	320	valid
185.0ms	228×	body	160	valid
115.0ms	51×	body	2560	valid