Details

sample503.0ms

Algorithm

intervals

Results

219.0ms	75×	body	1280	valid
74.0ms	45×	body	640	valid
56.0ms	257×	body	80	valid
11.0ms	18×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.8s

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: 3.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
29.6b	(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)))
10.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* y.re (log (hypot x.re x.im)))
19.0ms	(* (atan2 x.im x.re) y.re)
21.0ms	(* (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)))

simplify1.7s

Counts

89 → 89

Iterations

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

prune822.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize95.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

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

Counts

4 → 43

Calls

4 calls:

3.0ms	(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))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt (* (atan2 x.im x.re) y.im))
87.0ms	(cbrt (* (atan2 x.im x.re) y.im))
114.0ms	(cbrt (* (atan2 x.im x.re) y.im))
218.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
6	4989
5	1818
4	753
3	351
2	194
1	121
0	72

prune651.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize160.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cbrt (* (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)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* (atan2 x.im x.re) y.im))
65.0ms	(cbrt (* (atan2 x.im x.re) y.im))
96.0ms	(cbrt (* (atan2 x.im x.re) y.im))
166.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
6	4989
5	1818
4	753
3	351
2	194
1	121
0	72

prune773.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize192.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

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

Counts

4 → 43

Calls

4 calls:

3.0ms	(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))
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (* (atan2 x.im x.re) y.im))
81.0ms	(cbrt (* (atan2 x.im x.re) y.im))
98.0ms	(cbrt (* (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)))

simplify3.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
6	4989
5	1818
4	753
3	351
2	194
1	121
0	72

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

regimes788.0ms

Accuracy

0% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.0s	2239×	body	1280	valid
2.3s	7959×	body	80	valid
2.0s	1448×	body	640	valid
338.0ms	580×	body	320	valid
194.0ms	40×	body	2560	valid
134.0ms	219×	body	160	valid