Details

sample558.0ms

Algorithm

intervals

Results

178.0ms	81×	body	1280	valid
93.0ms	259×	body	80	valid
62.0ms	39×	body	640	valid
58.0ms	16×	body	320	valid
7.0ms	2×	body	2560	valid
6.0ms	8×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	5780
5	821
4	208
3	95
2	62
1	35
0	19

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
33.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

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)))
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (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)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* y.re (log (hypot x.re x.im)))
29.0ms	(* (atan2 x.im x.re) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
183.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

93 → 93

Iterations

Iter	Nodes
5	3262
4	1626
3	898
2	525
1	256
0	142

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize118.0ms

Local error

Found 4 expressions with local error:

18.8b	(cos (* (atan2 x.im x.re) y.re))
19.1b	(sin (* (atan2 x.im x.re) y.re))
24.0b	(sin (* y.im (log (hypot x.re x.im))))
24.1b	(cos (* y.im (log (hypot x.re x.im))))

rewrite70.0ms

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:

16.0ms	(cos (* (atan2 x.im x.re) y.re))
16.0ms	(sin (* (atan2 x.im x.re) y.re))
18.0ms	(sin (* y.im (log (hypot x.re x.im))))
18.0ms	(cos (* y.im (log (hypot x.re x.im))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cos (* (atan2 x.im x.re) y.re))
60.0ms	(sin (* (atan2 x.im x.re) y.re))
119.0ms	(sin (* y.im (log (hypot x.re x.im))))
146.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify1.4s

Counts

64 → 64

Iterations

Iter	Nodes
5	2185
4	991
3	492
2	275
1	187
0	134

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize114.0ms

Local error

Found 4 expressions with local error:

18.8b	(cos (* (atan2 x.im x.re) y.re))
19.1b	(sin (* (atan2 x.im x.re) y.re))
24.0b	(sin (* y.im (log (hypot x.re x.im))))
24.1b	(cos (* y.im (log (hypot x.re x.im))))

rewrite61.0ms

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:

15.0ms	(cos (* (atan2 x.im x.re) y.re))
23.0ms	(sin (* (atan2 x.im x.re) y.re))
12.0ms	(sin (* y.im (log (hypot x.re x.im))))
9.0ms	(cos (* y.im (log (hypot x.re x.im))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cos (* (atan2 x.im x.re) y.re))
41.0ms	(sin (* (atan2 x.im x.re) y.re))
122.0ms	(sin (* y.im (log (hypot x.re x.im))))
146.0ms	(cos (* y.im (log (hypot x.re x.im))))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
5	2185
4	991
3	492
2	275
1	187
0	134

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.6b

localize184.0ms

Local error

Found 4 expressions with local error:

24.1b	(cos (* y.im (log (hypot x.re x.im))))
24.1b	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
24.4b	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
24.6b	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

rewrite36.0ms

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:

9.0ms	(cos (* y.im (log (hypot x.re x.im))))
8.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
10.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
8.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

series904.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cos (* y.im (log (hypot x.re x.im))))
252.0ms	(cos (* (log (cbrt (hypot x.re x.im))) y.im))
231.0ms	(cos (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
267.0ms	(sin (* (log (cbrt (hypot x.re x.im))) y.im))

simplify3.4s

Counts

58 → 58

Iterations

Iter	Nodes
5	4818
4	1816
3	780
2	365
1	205
0	138

prune1.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.5b

regimes965.0ms

Accuracy

0% (0.4b remaining)

Error of 3.5b against oracle of 3.2b and baseline of 3.5b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	31
1	31
0	23

end0.0ms

sample11.5s

Algorithm

intervals

Results

4.9s	2254×	body	1280	valid
3.0s	7983×	body	80	valid
2.0s	1375×	body	640	valid
607.0ms	545×	body	320	valid
244.0ms	223×	body	160	valid
174.0ms	52×	body	2560	valid