Details

analyze2.3s (17.2%)

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)

sample129.0ms (1%)

Algorithm

1×

intervals

Results

46.0ms	64×	body	1024	invalid
33.0ms	244×	body	128	valid
14.0ms	33×	body	512	invalid
4.0ms	15×	body	256	invalid
3.0ms	5×	body	1024	valid
3.0ms	18×	body	128	invalid
2.0ms	2×	body	2048	invalid
2.0ms	4×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 87 to 43 computations (50.6% saved)

simplify76.0ms (0.6%)

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	22	52
1	41	50
2	72	50
3	120	50
4	265	50
5	998	50
6	3045	50
7	4087	50
8	4543	50
9	4868	50
10	4934	50

prune9.0ms (0.1%)

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

7.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.4b	(.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)))))
	34.7b	(.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

▶

9.4b

(*.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)))))

34.7b

(*.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)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))
✓	1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	34.5b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 140

Calls

4 calls:

16.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
12.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
10.0ms	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
9.0ms	(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

4 → 96

Calls

4 calls:

367.0ms	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))
105.0ms	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
23.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
20.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify240.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
513×	`associate-r_binary64`
366×	`associate-l_binary64`
242×	`associate-/l*_binary64`
242×	`times-frac_binary64`

Counts

236 → 378

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	482	8670
1	1465	8059
2	4353	8051
3	4940	8051

prune405.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	367	11	378
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	368	12	380

Error

4.7b

Counts

380 → 12

Alt Table

Status	Error	Program
	9.5b	(.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 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (atan2.f64 x.im x.re) y.im))) 1))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	9.6b	(.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 (.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (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)))))))
	34.7b	(.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))))
	24.2b	(.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 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	9.8b	(.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))))
	37.8b	(.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 (sqrt.f64 (.f64 (.f64 (atan2.f64 x.im x.re) y.im) (.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)))))
	36.1b	(.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)))))
	9.4b	(.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)))))))
	24.0b	(.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 (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))
	9.5b	(.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 (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))

Compiler

Compiled 12425 to 3876 computations (68.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	27.8b	(sqrt.f64 (.f64 (.f64 (atan2.f64 x.im x.re) y.im) (*.f64 (atan2.f64 x.im x.re) y.im)))
	34.5b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1/2_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`rem-sqrt-square_binary64`
3×	`pow1_binary64`

Counts

1 → 37

Calls

1 calls:

11.0ms

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

series19.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

19.0ms

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

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

575×	`distribute-rgt-out_binary64`
484×	`associate-+l+_binary64`
482×	`unswap-sqr_binary64`
474×	`fma-def_binary64`
446×	`associate-+r+_binary64`

Counts

73 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	819
1	69	780
2	134	774
3	311	768
4	574	768
5	1013	768
6	3025	768
7	3082	768
8	3272	768
9	4667	768
10	4851	768

prune465.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	344	2	346
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	347	11	358

Error

4.7b

Counts

358 → 11

Alt Table

Status	Error	Program
	9.6b	(.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 (.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (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)))))))
	34.7b	(.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))))
	24.2b	(.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 (expm1.f64 (log1p.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 (sqrt.f64 (.f64 (.f64 (atan2.f64 x.im x.re) y.im) (.f64 (atan2.f64 x.im x.re) y.im))))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	37.8b	(.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 (exp.f64 (log1p.f64 (fabs.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) 1))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	36.1b	(.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)))))
	9.5b	(.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 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.4b	(.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)))))))
	24.0b	(.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 (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))
	9.5b	(.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 (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))

Compiler

Compiled 12043 to 3162 computations (73.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	2.1b	(exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im))))
✓	3.3b	(-.f64 (exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))) 1)
	34.5b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 78

Calls

2 calls:

16.0ms	(-.f64 (exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))) 1)
9.0ms	(exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im))))

series2.7s (20.1%)

Counts

2 → 72

Calls

2 calls:

1.4s	(-.f64 (exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))) 1)
1.3s	(exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im))))

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

809×	`div-sub_binary64`
494×	`fma-neg_binary64`
230×	`cancel-sign-sub-inv_binary64`
203×	`associate--r+_binary64`
156×	`associate--l+_binary64`

Counts

150 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	2653
1	160	2267
2	385	2236
3	1300	2188
4	3553	2188
5	5225	2188

prune500.0ms (3.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	596	1	597
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	597	11	608

Error

4.7b

Counts

608 → 11

Alt Table

Status	Error	Program
	9.6b	(.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 (.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (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 (exp.f64 (log1p.f64 (fabs.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) 1))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	34.7b	(.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))))
	24.2b	(.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 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	37.8b	(.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 (exp.f64 (log1p.f64 (fabs.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) 1))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	36.1b	(.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)))))
	9.5b	(.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 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.4b	(.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)))))))
	24.0b	(.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 (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))
	9.5b	(.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 (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))

Compiler

Compiled 13097 to 4283 computations (67.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.9b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.1b	(exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im))))
	3.3b	(-.f64 (exp.f64 (log1p.f64 (fabs.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))) 1)
✓	20.1b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`log1p-expm1-u_binary64`

Counts

1 → 28

Calls

1 calls:

11.0ms

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

series40.0ms (0.3%)

Counts

1 → 4

Calls

1 calls:

40.0ms

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

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Rules

707×	`distribute-rgt-neg-in_binary64`
572×	`distribute-lft-neg-in_binary64`
460×	`fma-def_binary64`
391×	`cancel-sign-sub-inv_binary64`
357×	`*-commutative_binary64`

Counts

32 → 38

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	48	469
1	105	440
2	254	436
3	971	434
4	2533	428
5	3914	425
6	4822	416
7	4914	416
8	4928	416

prune351.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	495	0	495
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	495	11	506

Error

4.7b

Counts

506 → 11

Alt Table

Status	Error	Program
	9.6b	(.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 (.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (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 (exp.f64 (log1p.f64 (fabs.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) 1))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	34.7b	(.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))))
	24.2b	(.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 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	37.8b	(.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 (exp.f64 (log1p.f64 (fabs.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) 1))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	36.1b	(.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)))))
	9.5b	(.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 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.4b	(.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)))))))
	24.0b	(.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 (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))
	9.5b	(.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 (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))

Compiler

Compiled 6116 to 1922 computations (68.6% saved)

regimes508.0ms (3.8%)

Accuracy

Total 0.8b remaining (16.2%)

Threshold costs 0.8b (16.2%)

Compiler

Compiled 11612 to 6490 computations (44.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 41 to 19 computations (53.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-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	35	193
1	49	193
2	60	193
3	66	193
4	70	193
5	71	193
6	71	193

end1.0ms (0%)

Compiler: Compiled 101 to 29 computations (71.3% saved)

sample4.6s (34.1%)

Algorithm

1×

intervals

Results

1.7s	2378×	body	1024	invalid
1.1s	7567×	body	128	valid
435.0ms	987×	body	512	invalid
166.0ms	191×	body	1024	valid
127.0ms	447×	body	256	invalid
82.0ms	541×	body	128	invalid
62.0ms	140×	body	512	valid
59.0ms	49×	body	2048	invalid
27.0ms	89×	body	256	valid
15.0ms	13×	body	2048	valid

Compiler

Compiled 508 to 248 computations (51.2% saved)

Details

analyze2.3s (17.2%)

sample129.0ms (1%)

simplify76.0ms (0.6%)

prune9.0ms (0.1%)

localize16.0ms (0.1%)

rewrite58.0ms (0.4%)

series515.0ms (3.8%)

simplify240.0ms (1.8%)

prune405.0ms (3%)

localize18.0ms (0.1%)

rewrite13.0ms (0.1%)

series19.0ms (0.1%)

simplify124.0ms (0.9%)

prune465.0ms (3.5%)

localize20.0ms (0.1%)

rewrite30.0ms (0.2%)

series2.7s (20.1%)

simplify135.0ms (1%)

prune500.0ms (3.7%)

localize16.0ms (0.1%)

rewrite12.0ms (0.1%)

series40.0ms (0.3%)

simplify132.0ms (1%)

prune351.0ms (2.6%)

regimes508.0ms (3.8%)

bsearch4.0ms (0%)

simplify11.0ms (0.1%)

end1.0ms (0%)

sample4.6s (34.1%)

Profiling