Details

sample590.0ms

Algorithm

intervals

Results

207.0ms	58×	body	1280	valid
99.0ms	260×	body	80	valid
59.0ms	37×	body	640	valid
20.0ms	15×	body	320	valid
6.0ms	9×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

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

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.6b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.re)
33.2b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

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:

6.0ms	(* y.re (log (hypot x.re x.im)))
7.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* y.re (log (hypot x.re x.im)))
19.0ms	(* (atan2 x.im x.re) y.im)
31.0ms	(* (atan2 x.im x.re) y.re)
201.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

89 → 89

Iterations

Iter	Nodes
5	3315
4	1685
3	961
2	525
1	252
0	138

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize68.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
4.9b	(cbrt (atan2 x.im x.re))
4.9b	(cbrt (atan2 x.im x.re))
33.2b	(sin (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×	`sin-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	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (atan2 x.im x.re))
50.0ms	(cbrt (atan2 x.im x.re))
43.0ms	(cbrt (atan2 x.im x.re))
177.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify9.2s

Counts

61 → 61

Iterations

Iter	Nodes
6	9638
5	1881
4	534
3	237
2	146
1	90
0	57

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize97.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
4.9b	(cbrt (atan2 x.im x.re))
4.9b	(cbrt (atan2 x.im x.re))
33.2b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite9.0ms

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×	`sin-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))
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (atan2 x.im x.re))
42.0ms	(cbrt (atan2 x.im x.re))
40.0ms	(cbrt (atan2 x.im x.re))
165.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify8.3s

Counts

61 → 61

Iterations

Iter	Nodes
6	9638
5	1881
4	534
3	237
2	146
1	90
0	57

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
1.6b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
1.6b	(* (atan2 x.im x.re) y.im)
33.2b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`sin-sum` `pow1/3` `fma-udef`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt y.re)
26.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
8.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(cbrt y.re)
122.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
24.0ms	(* (atan2 x.im x.re) y.im)
166.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify3.6s

Counts

76 → 76

Iterations

Iter	Nodes
4	5269
3	1630
2	645
1	268
0	126

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

regimes537.0ms

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	27
1	27
0	21

end0.0ms

sample12.1s

Algorithm

intervals

Results

4.8s	2174×	body	1280	valid
3.5s	7993×	body	80	valid
2.4s	1484×	body	640	valid
584.0ms	576×	body	320	valid
216.0ms	58×	body	2560	valid
170.0ms	239×	body	160	valid