Details

analyze3.8s (23.5%)

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%	50.9%	0.2%	13
50%	49.7%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample6.0s (37.2%)

Results

2.5s	2575×	body	1024	invalid
1.8s	7833×	body	128	valid
661.0ms	907×	body	512	invalid
303.0ms	213×	body	2048	invalid
157.0ms	359×	body	256	invalid
154.0ms	161×	body	1024	valid
129.0ms	497×	body	128	invalid
96.0ms	152×	body	512	valid
38.0ms	92×	body	256	valid
29.0ms	18×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

892×	`unswap-sqr_binary64`
461×	`associate-/l*_binary64`
323×	`associate-/r*_binary64`
296×	`associate-*l/_binary64`
286×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	39	38
2	70	38
3	118	38
4	263	38
5	996	38
6	3043	38
7	4085	38
8	4541	38
9	4866	38
10	4932	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
	31.0b	(.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))) (sin.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))))
▶	7.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Status

Error

Program

31.0b

(*.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))) (sin.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))))

▶

7.3b

(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.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
✓	0.3b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
✓	1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	27.6b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series611.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

499.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
99.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
6.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
6.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite70.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

552×	`prod-diff_binary64`
276×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
143×	`add-log-exp_binary64`
142×	`log1p-expm1-u_binary64`

Counts

4 → 85

Calls

4 calls:

68.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
68.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
68.0ms	(sin.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	300	50
2	3609	50
3	5164	50
0	0	0
1	0	0

simplify168.0ms (1%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
629×	`associate-/l*_binary64`
622×	`fma-def_binary64`
417×	`associate-/r*_binary64`
256×	`*-commutative_binary64`

Counts

181 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	553	7028
1	1945	6350
2	4446	6290
3	4989	6290
4	4912	6290

prune294.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	193	11	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	11	206

Error

3.5b

Counts

206 → 11

Alt Table

Status	Error	Program
	33.7b	(.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 (+.f64 1 (expm1.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))))
	20.0b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.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 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	25.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (*.f64 (pow.f64 y.re 3) (pow.f64 (atan2.f64 x.im x.re) 3))))))
	39.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	20.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	25.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2)))
	33.5b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	7.8b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	19.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 1/2 (.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (.f64 (.f64 y.im y.im) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))) (.f64 1/6 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 3)))))))
	25.9b	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.re)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Compiler

Compiled 12998 to 4760 computations (63.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))))
✓	1.7b	(*.f64 y.im (atan2.f64 x.im x.re))
	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
	27.6b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series512.0ms (3.2%)

Counts

2 → 60

Calls

2 calls:

505.0ms	(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))))
7.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

rewrite60.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

604×	`log-prod_binary64`
291×	`prod-diff_binary64`
226×	`log-pow_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`

Counts

2 → 70

Calls

2 calls:

58.0ms	(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))))
58.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	240	25
2	2856	25
3	5502	25
0	0	0
1	0	0

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

491×	`times-frac_binary64`
403×	`associate-/l*_binary64`
366×	`associate-r_binary64`
268×	`associate-/r*_binary64`
240×	`fma-neg_binary64`

Counts

130 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	3762
1	1085	3534
2	4915	3532
3	5119	3532

prune387.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	229	11	240

Error

3.5b

Counts

240 → 11

Alt Table

Status	Error	Program
	33.7b	(.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 (+.f64 1 (expm1.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))))
	20.0b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	20.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	7.9b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (fma.f64 (.f64 y.re (atan2.f64 x.im x.re)) (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))
	25.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2)))
	33.5b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
▶	7.8b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	8.3b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	25.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (*.f64 (pow.f64 y.re 3) (pow.f64 (atan2.f64 x.im x.re) 3))))))
	39.6b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))
	25.9b	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.re)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Compiler

Compiled 14199 to 5027 computations (64.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3)
	1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
	27.6b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series1.3s (7.8%)

Counts

1 → 48

Calls

1 calls:

1.3s	(pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3)

rewrite51.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

578×	`log-prod_binary64`
252×	`prod-diff_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
214×	`log-pow_binary64`

Counts

1 → 30

Calls

1 calls:

50.0ms

(pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	260	18
2	2854	18
3	5273	18
0	0	0
1	0	0

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
528×	`cancel-sign-sub-inv_binary64`
355×	`associate-r_binary64`
226×	`times-frac_binary64`
220×	`*-commutative_binary64`

Counts

78 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	3528
1	954	3246
2	3252	3242
3	4911	3242

prune300.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	191	14	205

Error

3.4b

Counts

205 → 14

Alt Table

Status	Error	Program
	47.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (sin.f64 1))))
	20.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	33.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))))))
	20.0b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	33.5b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	25.6b	(.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 (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2))) 3))
	39.6b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))
▶	7.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (sin.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.im)) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (cos.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.im)) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))))
	25.9b	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.re)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	34.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) 2/3)) 3) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	8.0b	(.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 (pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3)) 3))
	25.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2)))
	8.3b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	25.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (*.f64 (pow.f64 y.re 3) (pow.f64 (atan2.f64 x.im x.re) 3))))))

Compiler

Compiled 13071 to 4926 computations (62.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.1b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
✓	14.3b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
✓	19.5b	(sin.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))
✓	19.5b	(cos.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))

series246.0ms (1.5%)

Counts

4 → 64

Calls

4 calls:

93.0ms	(cos.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))
86.0ms	(sin.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))
52.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
14.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite86.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

601×	`prod-diff_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
237×	`log-pow_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

4 → 78

Calls

4 calls:

84.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
84.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
84.0ms	(sin.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))
84.0ms	(cos.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	268	40
2	3024	40
3	4981	40
4	5225	40
0	0	0
1	0	0

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
370×	`times-frac_binary64`
359×	`associate-/l*_binary64`
310×	`associate-l_binary64`
220×	`associate-/r*_binary64`

Counts

142 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	499	4884
1	1649	4604
2	4871	4604
3	5108	4604

prune364.0ms (2.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	200	14	214

Error

3.4b

Counts

214 → 14

Alt Table

Status	Error	Program
	47.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (sin.f64 1))))
	20.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	33.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))))))
	20.0b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	33.5b	(.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 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 2))
	25.6b	(.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 (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2))) 3))
	39.6b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))
✓	7.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (sin.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.im)) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (cos.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.im)) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))))
	25.9b	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.re)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	34.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) 2/3)) 3) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	8.0b	(.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 (pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3)) 3))
	25.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (pow.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 2)))
	8.3b	(.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (pow.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))
	25.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (*.f64 (pow.f64 y.re 3) (pow.f64 (atan2.f64 x.im x.re) 3))))))

Compiler

Compiled 14684 to 4902 computations (66.6% saved)

regimes1.1s (7.1%)

Accuracy

Total 0.3b remaining (8.7%)

Threshold costs 0.3b (8.7%)

Counts

183 → 1

Compiler

Compiled 30172 to 16935 computations (43.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	30	40
2	39	40
3	45	40
4	49	40
5	50	40
6	49	40

end301.0ms (1.9%)

Compiler: Compiled 600 to 314 computations (47.7% saved)

Details

analyze3.8s (23.5%)

sample6.0s (37.2%)

simplify67.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series611.0ms (3.8%)

rewrite70.0ms (0.4%)

simplify168.0ms (1%)

prune294.0ms (1.8%)

localize18.0ms (0.1%)

series512.0ms (3.2%)

rewrite60.0ms (0.4%)

simplify90.0ms (0.6%)

prune387.0ms (2.4%)

localize20.0ms (0.1%)

series1.3s (7.8%)

rewrite51.0ms (0.3%)

simplify79.0ms (0.5%)

prune300.0ms (1.9%)

localize21.0ms (0.1%)

series246.0ms (1.5%)

rewrite86.0ms (0.5%)

simplify133.0ms (0.8%)

prune364.0ms (2.3%)

regimes1.1s (7.1%)

simplify3.0ms (0%)

end301.0ms (1.9%)

Profiling