Details

sample428.0ms

Algorithm

intervals

Results

95.0ms	53×	body	1280	valid
84.0ms	35×	body	640	valid
83.0ms	261×	body	80	valid
18.0ms	20×	body	320	valid
7.0ms	10×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize52.0ms

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)
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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×	`cos-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

6.0ms	(* y.re (log (hypot x.re x.im)))
5.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* y.re (log (hypot x.re x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
26.0ms	(* (atan2 x.im x.re) y.re)
208.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

89 → 89

Iterations

Iter	Nodes
4	2993
3	1377
2	631
1	280
0	146

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize86.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
1.2b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
1.7b	(* (atan2 x.im x.re) y.re)
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`cos-sum` `fma-udef`

Counts

4 → 77

Calls

4 calls:

78.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
15.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
5.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
124.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.0ms	(* (atan2 x.im x.re) y.re)
168.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts

89 → 89

Iterations

Iter	Nodes
3	2233
2	860
1	322
0	142

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize83.0ms

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))
32.7b	(cos (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×	`cos-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	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (atan2 x.im x.re))
58.0ms	(cbrt (atan2 x.im x.re))
55.0ms	(cbrt (atan2 x.im x.re))
174.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.7s

Counts

61 → 61

Iterations

Iter	Nodes
5	8193
4	1810
3	552
2	240
1	118
0	66

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize103.0ms

Local error

Found 4 expressions with local error:

5.2b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
5.2b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
5.2b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

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×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

20.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
19.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
19.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
206.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
209.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
154.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

55 → 55

Iterations

Iter	Nodes
5	6561
4	1871
3	673
2	294
1	140
0	75

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

regimes516.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	30
1	30
0	23

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.8s	1996×	body	1280	valid
3.3s	8017×	body	80	valid
2.3s	1536×	body	640	valid
690.0ms	668×	body	320	valid
161.0ms	307×	body	160	valid