Details

analyze1.8s (13.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample5.8s (42.4%)

Results

2.3s	2432×	body	1024	invalid
1.9s	7828×	body	128	valid
750.0ms	993×	body	512	invalid
183.0ms	564×	body	128	invalid
181.0ms	425×	body	256	invalid
167.0ms	166×	body	1024	valid
84.0ms	142×	body	512	valid
47.0ms	24×	body	2048	invalid
42.0ms	102×	body	256	valid
29.0ms	18×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

373×	`rules-1_binary64`
365×	`rules-6-rev_binary64`
344×	`rules-20_binary64`
313×	`rules-33_binary64`
295×	`rules-1-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	46	38
2	123	38
3	324	38
4	1182	38
5	4091	38
6	4883	38
7	4981	38

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

5.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	31.2b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

Status

Error

Program

▶

7.0b

(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

31.2b

(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

Compiler

Compiled 206 to 96 computations (53.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.7b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
✓	1.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	31.6b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series581.0ms (4.3%)

Counts

4 → 96

Calls

4 calls:

481.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
86.0ms	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

rewrite95.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

625×	`prod-diff_binary64`
190×	`egg-rr`
148×	`add-sqr-sqrt_binary64`
136×	`add-log-exp_binary64`
136×	`log1p-expm1-u_binary64`

Counts

4 → 190

Calls

4 calls:

87.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
87.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
87.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
87.0ms	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	335	50
2	4189	50
3	5478	50
0	0	0
1	0	0

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
411×	`rules-13_binary64`
400×	`rules-14-rev_binary64`
307×	`rules-21_binary64`
255×	`rules-20_binary64`

Counts

286 → 321

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	558	7070
1	2234	6584
2	5342	6584

prune680.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	309	12	321
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	311	12	323

Error

2.1b

Counts

323 → 12

Alt Table

Status	Error	Program
	18.9b	(.f64 (fma.f64 (log.f64 (hypot.f64 x.im x.re)) (/.f64 y.re (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) (exp.f64 (neg.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	7.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	19.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (sqrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	36.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	7.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fabs.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))
	17.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
▶	2.3b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	34.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (log1p.f64 (expm1.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2)))
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (log.f64 (exp.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 17989 to 6112 computations (66% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (log.f64 (hypot.f64 x.re x.im)) y.re)
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	1.4b	(*.f64 y.im (atan2.f64 x.im x.re))
	31.6b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series515.0ms (3.8%)

Counts

2 → 48

Calls

2 calls:

509.0ms	(*.f64 (log.f64 (hypot.f64 x.re x.im)) y.re)
6.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

rewrite72.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
248×	`prod-diff_binary64`
126×	`egg-rr`
99×	`add-sqr-sqrt_binary64`

Counts

2 → 126

Calls

2 calls:

70.0ms	(*.f64 (log.f64 (hypot.f64 x.re x.im)) y.re)
70.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	223	16
2	2749	16
3	6540	16
0	0	0
1	0	0

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-neg_binary64`
579×	`rules-11_binary64`
416×	`fma-def_binary64`
393×	`rules-20_binary64`
324×	`rules-15-rev_binary64`

Counts

174 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1092
1	302	992
2	1403	976
3	6126	976

prune1.4s (10.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	331	11	342

Error

2.1b

Counts

342 → 11

Alt Table

Status	Error	Program
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (log1p.f64 (expm1.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
▶	3.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	7.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fabs.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))
	17.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	18.9b	(.f64 (fma.f64 (log.f64 (hypot.f64 x.im x.re)) (/.f64 y.re (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) (exp.f64 (neg.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	19.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (sqrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	34.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	34.2b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2)))
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (log.f64 (exp.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 16149 to 5097 computations (68.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (log.f64 (hypot.f64 x.re x.im)) y.re)
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
	1.4b	(*.f64 y.im (atan2.f64 x.im x.re))
✓	18.2b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

series14.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

14.0ms

(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite72.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

651×	`log1p-expm1-u_binary64`
651×	`expm1-log1p-u_binary64`
383×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
64×	`add-cbrt-cube_binary64`

Counts

1 → 31

Calls

1 calls:

71.0ms

(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	157	9
2	1951	9
3	5021	9
0	0	0
1	0	0

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

739×	`rules-11_binary64`
482×	`fma-neg_binary64`
442×	`rules-20_binary64`
415×	`fma-def_binary64`
286×	`rules-13_binary64`

Counts

35 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	110
1	73	106
2	266	106
3	1388	106
4	5444	106

prune656.0ms (4.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	273	11	284

Error

2.1b

Counts

284 → 11

Alt Table

Status	Error	Program
▶	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (log1p.f64 (expm1.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
✓	3.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	7.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fabs.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))
	17.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	18.9b	(.f64 (fma.f64 (log.f64 (hypot.f64 x.im x.re)) (/.f64 y.re (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) (exp.f64 (neg.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	19.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (sqrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	34.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	34.2b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2)))
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (log.f64 (exp.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 9508 to 3157 computations (66.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.7b	(log1p.f64 (expm1.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
	1.4b	(*.f64 y.im (atan2.f64 x.im x.re))
	31.6b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series10.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(log1p.f64 (expm1.f64 (*.f64 y.im (atan2.f64 x.im x.re))))

rewrite47.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

637×	`expm1-log1p-u_binary64`
636×	`log1p-expm1-u_binary64`
210×	`prod-diff_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Counts

1 → 76

Calls

1 calls:

45.0ms

(log1p.f64 (expm1.f64 (*.f64 y.im (atan2.f64 x.im x.re))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	157	7
2	1920	7
3	4991	7
0	0	0
1	0	0

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`rules-20_binary64`

Counts

112 → 76

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	252
1	7	252
2	7	252

prune694.0ms (5.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	298	11	309

Error

2.1b

Counts

309 → 11

Alt Table

Status	Error	Program
	19.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (sqrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (log1p.f64 (expm1.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))))
✓	7.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (log1p.f64 (expm1.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
✓	3.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	7.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fabs.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))
	17.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	18.9b	(.f64 (fma.f64 (log.f64 (hypot.f64 x.im x.re)) (/.f64 y.re (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) (exp.f64 (neg.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	34.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	34.2b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.re) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
	7.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2)))

Compiler

Compiled 14344 to 4307 computations (70% saved)

regimes544.0ms (4%)

Accuracy

Total 0.4b remaining (11.7%)

Threshold costs 0.4b (11.7%)

Counts

81 → 1

Compiler

Compiled 12707 to 7050 computations (44.5% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	16	40

end263.0ms (1.9%)

Compiler: Compiled 441 to 232 computations (47.4% saved)

Details

analyze1.8s (13.5%)

sample5.8s (42.4%)

simplify60.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series581.0ms (4.3%)

rewrite95.0ms (0.7%)

simplify105.0ms (0.8%)

prune680.0ms (5%)

localize16.0ms (0.1%)

series515.0ms (3.8%)

rewrite72.0ms (0.5%)

simplify45.0ms (0.3%)

prune1.4s (10.6%)

localize13.0ms (0.1%)

series14.0ms (0.1%)

rewrite72.0ms (0.5%)

simplify28.0ms (0.2%)

prune656.0ms (4.8%)

localize18.0ms (0.1%)

series10.0ms (0.1%)

rewrite47.0ms (0.3%)

simplify13.0ms (0.1%)

prune694.0ms (5.1%)

regimes544.0ms (4%)

simplify1.0ms (0%)

end263.0ms (1.9%)

Profiling