Details

sample361.0ms

Algorithm

intervals

Results

96.0ms	38×	body	640	valid
89.0ms	59×	body	1280	valid
55.0ms	260×	body	80	valid
13.0ms	19×	body	320	valid
3.0ms	1×	body	2560	valid
3.0ms	6×	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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
34.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

19.0ms	(* y.re (log (hypot x.re x.im)))
15.0ms	(* (atan2 x.im x.re) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* y.re (log (hypot x.re x.im)))
32.0ms	(* (atan2 x.im x.re) y.re)
32.0ms	(* (atan2 x.im x.re) y.im)
209.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	3768
3	1505
2	616
1	270
0	142

prune956.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
34.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

9.0ms	(* y.re (log (hypot x.re x.im)))
13.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* y.re (log (hypot x.re x.im)))
30.0ms	(* (atan2 x.im x.re) y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
187.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	3768
3	1505
2	616
1	270
0	142

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize115.0ms

Local error

Found 4 expressions with local error:

16.0b	(sin (* (atan2 x.im x.re) y.re))
16.1b	(cos (* (atan2 x.im x.re) y.re))
25.8b	(cos (* y.im (log (hypot x.re x.im))))
25.9b	(sin (* y.im (log (hypot x.re x.im))))

rewrite52.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

8.0ms	(sin (* (atan2 x.im x.re) y.re))
8.0ms	(cos (* (atan2 x.im x.re) y.re))
12.0ms	(cos (* y.im (log (hypot x.re x.im))))
23.0ms	(sin (* y.im (log (hypot x.re x.im))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (* (atan2 x.im x.re) y.re))
55.0ms	(cos (* (atan2 x.im x.re) y.re))
156.0ms	(cos (* y.im (log (hypot x.re x.im))))
119.0ms	(sin (* y.im (log (hypot x.re x.im))))

simplify2.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	1483
3	553
2	278
1	186
0	134

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize135.0ms

Local error

Found 4 expressions with local error:

25.7b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
25.8b	(cos (* y.im (log (hypot x.re x.im))))
26.0b	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
26.0b	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `cos-sum` `log-prod` `*-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×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 46

Calls

4 calls:

8.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
17.0ms	(cos (* y.im (log (hypot x.re x.im))))
20.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
18.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))

series914.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))
180.0ms	(cos (* y.im (log (hypot x.re x.im))))
246.0ms	(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
216.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))

simplify2.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
4	2629
3	921
2	403
1	216
0	142

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

regimes842.0ms

Accuracy

0% (0.3b remaining)

Error of 3.4b against oracle of 3.1b and baseline of 3.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.4s	2158×	body	1280	valid
2.0s	1379×	body	640	valid
2.0s	7928×	body	80	valid
573.0ms	207×	body	160	valid
317.0ms	550×	body	320	valid
114.0ms	40×	body	2560	valid