Details

analyze1.9s (15%)

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)

sample5.8s (47.4%)

Results

2.5s	2552×	body	1024	invalid
1.8s	7809×	body	128	valid
609.0ms	950×	body	512	invalid
243.0ms	175×	body	2048	invalid
190.0ms	189×	body	1024	valid
162.0ms	385×	body	256	invalid
141.0ms	527×	body	128	invalid
98.0ms	147×	body	512	valid
41.0ms	98×	body	256	valid
19.0ms	13×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

892×	`unswap-sqr_binary64`
451×	`associate-/l*_binary64`
320×	`associate-/r*_binary64`
273×	`associate-*l/_binary64`
263×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	39	38
2	76	38
3	126	38
4	286	38
5	1096	38
6	4141	38

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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

8.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))
	29.8b	(.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))))

Status

Error

Program

▶

11.2b

(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))

29.8b

(*.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))))

Compiler

Compiled 206 to 97 computations (52.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(exp.f64 (atan2.f64 x.im x.re))
✓	0.5b	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)
✓	1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	34.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series500.0ms (4.1%)

Counts

4 → 68

Calls

4 calls:

411.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)
79.0ms	(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))
4.0ms	(exp.f64 (atan2.f64 x.im x.re))

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`log-prod_binary64`
252×	`prod-diff_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
230×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	256	40
2	3055	40

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

53.0ms	(exp.f64 (atan2.f64 x.im x.re))
53.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)
53.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
53.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
376×	`associate-r_binary64`
230×	`*-commutative_binary64`
226×	`times-frac_binary64`
214×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	3605
1	997	3323
2	4507	3315

Stop Event

1×	node limit

Counts

154 → 149

prune273.0ms (2.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	134	15	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	16	151

Error

4.8b

Counts

151 → 16

Alt Table

Status	Error	Program
▶	10.2b	(.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)))))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) (+.f64 y.im 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)))))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.re (.f64 (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))))))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))) 1)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.im (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))))
	20.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))))
	34.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	29.8b	(.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))))
	11.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	43.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (sin.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	31.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (exp.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) 1))
	17.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) 1) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.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)))))
	23.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))
	31.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))))))

Compiler

Compiled 8431 to 2899 computations (65.6% saved)

localize17.0ms (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)))
	1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
	34.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series416.0ms (3.4%)

Counts

2 → 64

Calls

2 calls:

409.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite44.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
291×	`prod-diff_binary64`
211×	`log-pow_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	224	25
2	2841	25

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

42.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
42.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

485×	`times-frac_binary64`
415×	`associate-/l*_binary64`
360×	`associate-r_binary64`
271×	`associate-/r*_binary64`
214×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	300	3784
1	1205	3556

Stop Event

1×	node limit

Counts

120 → 125

prune473.0ms (3.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	222	17	239

Error

3.6b

Counts

239 → 17

Alt Table

Status	Error	Program
	23.0b	(.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)))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) (+.f64 y.im 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)))))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.re (.f64 (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))))))
	10.2b	(.f64 (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (exp.f64 (.f64 (neg.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)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.im (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))))
	20.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))))
	34.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	29.8b	(.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))))
	11.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	31.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (exp.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) 1))
▶	4.0b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.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)))))
	43.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (sin.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	10.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (pow.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.im)) 3))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	31.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.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)))))
	17.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (.f64 y.im (.f64 (atan2.f64 x.im x.re) (pow.f64 (hypot.f64 x.im x.re) 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 14156 to 5060 computations (64.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))
	1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
	1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
	34.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series541.0ms (4.4%)

Counts

1 → 36

Calls

1 calls:

541.0ms

(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log1p-expm1-u_binary64`
562×	`expm1-log1p-u_binary64`
324×	`log-prod_binary64`
124×	`pow1/3_binary64`
123×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	135	9
2	1577	9

Stop Event

1×	node limit

Counts

1 → 20

Calls

1 calls:

37.0ms

(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-/l/_binary64`
259×	`times-frac_binary64`
249×	`fma-def_binary64`
217×	`distribute-rgt-neg-in_binary64`
213×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1004
1	276	868
2	787	868
3	2992	847

Stop Event

1×	node limit

Counts

56 → 62

prune394.0ms (3.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	182	16	198

Error

3.6b

Counts

198 → 16

Alt Table

Status	Error	Program
	23.0b	(.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)))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) (+.f64 y.im 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)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.im (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))))
	20.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))))
	34.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	29.8b	(.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))))
	11.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	40.5b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	31.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (exp.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) 1))
▶	4.2b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (pow.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) 3))))
	10.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (pow.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.im)) 3))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	31.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))))))
	10.2b	(.f64 (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (exp.f64 (.f64 (neg.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)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.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)))))
	17.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (.f64 y.im (.f64 (atan2.f64 x.im x.re) (pow.f64 (hypot.f64 x.im x.re) 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 9992 to 3581 computations (64.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
	1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	7.4b	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
✓	34.9b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (pow.f64 (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3)))

series220.0ms (1.8%)

Counts

2 → 63

Calls

2 calls:

141.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (pow.f64 (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3)))
79.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite45.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
348×	`prod-diff_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
214×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	276	27
2	3037	27

Stop Event

1×	node limit

Counts

2 → 53

Calls

2 calls:

44.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
44.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (pow.f64 (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3)))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-def_binary64`
323×	`associate-r_binary64`
226×	`times-frac_binary64`
214×	`associate-/l*_binary64`
206×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	3416
1	913	3156
2	4162	3154

Stop Event

1×	node limit

Counts

116 → 104

prune317.0ms (2.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	143	16	159

Error

3.6b

Counts

159 → 16

Alt Table

Status	Error	Program
	23.0b	(.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)))
	11.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cbrt.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) (+.f64 y.im 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)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (fma.f64 y.im (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))))
	34.8b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.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))))
	20.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))
	29.8b	(.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))))
	11.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))
	40.5b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	31.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (exp.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) 1))
✓	4.2b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (pow.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) 3))))
	10.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (pow.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.im)) 3))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	31.1b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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)))))))))
	10.2b	(.f64 (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (.f64 (sqrt.f64 (pow.f64 (hypot.f64 x.im x.re) y.re)) (exp.f64 (.f64 (neg.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)))))
	12.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.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)))))
	17.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (.f64 y.im (.f64 (atan2.f64 x.im x.re) (pow.f64 (hypot.f64 x.im x.re) 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)))))
	34.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.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))

Compiler

Compiled 7800 to 2689 computations (65.5% saved)

regimes669.0ms (5.4%)

Accuracy

Total 0.4b remaining (9.6%)

Threshold costs 0.4b (9.6%)

Counts

110 → 1

Compiler

Compiled 17812 to 9790 computations (45% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	16	40
1	25	40
2	37	40
3	43	40
4	47	40
5	48	40

Stop Event

1×

saturated

end320.0ms (2.6%)

Compiler: Compiled 648 to 328 computations (49.4% saved)

Details

analyze1.9s (15%)

sample5.8s (47.4%)

simplify24.0ms (0.2%)

prune6.0ms (0.1%)

localize16.0ms (0.1%)

series500.0ms (4.1%)

rewrite55.0ms (0.4%)

simplify65.0ms (0.5%)

prune273.0ms (2.2%)

localize17.0ms (0.1%)

series416.0ms (3.4%)

rewrite44.0ms (0.4%)

simplify50.0ms (0.4%)

prune473.0ms (3.8%)

localize19.0ms (0.2%)

series541.0ms (4.4%)

rewrite38.0ms (0.3%)

simplify38.0ms (0.3%)

prune394.0ms (3.2%)

localize20.0ms (0.2%)

series220.0ms (1.8%)

rewrite45.0ms (0.4%)

simplify63.0ms (0.5%)

prune317.0ms (2.6%)

regimes669.0ms (5.4%)

simplify3.0ms (0%)

end320.0ms (2.6%)

Profiling