Details

analyze1.8s (13.4%)

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)

sample5.4s (40.5%)

Results

2.3s	2525×	body	1024	invalid
1.8s	7806×	body	128	valid
617.0ms	1005×	body	512	invalid
186.0ms	191×	body	1024	valid
180.0ms	456×	body	256	invalid
127.0ms	575×	body	128	invalid
94.0ms	159×	body	512	valid
48.0ms	36×	body	2048	invalid
34.0ms	84×	body	256	valid
26.0ms	16×	body	2048	valid

Compiler

Compiled 84 to 40 computations (52.4% saved)

preprocess41.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

392×	`times-frac_binary64`
391×	`associate-/l*_binary64`
329×	`associate-/r*_binary64`
280×	`unswap-sqr_binary64`
224×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	280
1	223	266
2	443	266
3	736	266
4	1769	266
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 41 to 19 computations (53.7% saved)

simplify31.0ms (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%)

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

6.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	29.7b	(.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

▶

10.2b

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

29.7b

(*.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 97 computations (52.9% saved)

localize17.0ms (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)
✓	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	33.1b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series509.0ms (3.8%)

Counts

4 → 68

Calls

36 calls:

81.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)	x.im	-inf
69.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)	x.re	-inf
69.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)	x.re	inf
67.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)	x.im	inf
66.0ms	(pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)	x.im	0

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`log-prod_binary64`
253×	`prod-diff_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
219×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	254	40
2	3019	40

Stop Event

1×	node limit

Counts

4 → 87

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
370×	`associate-r_binary64`
225×	`*-commutative_binary64`
218×	`associate-l_binary64`
218×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	3589
1	1022	3343
2	4475	3327

Stop Event

1×	node limit

Counts

155 → 150

prune281.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	140	10	150
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	141	11	152

Error

4.2b

Counts

152 → 11

Alt Table

Status	Error	Program
	10.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cbrt.f64 (pow.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)))
	39.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	18.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) 1) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	29.7b	(.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))))
	23.3b	(.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 (.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)))))) (cos.f64 1)) (.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)))))) (sin.f64 1))))
▶	8.8b	(.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 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 y.im (.f64 (log.f64 (hypot.f64 x.im x.re)) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (*.f64 y.im (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))))))))
	11.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))) (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))))) (log.f64 (cbrt.f64 (exp.f64 (exp.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)))))
	10.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	35.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	11.4b	(.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)))))) (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 8190 to 2763 computations (66.3% 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)))
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
	33.1b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series404.0ms (3%)

Counts

2 → 64

Calls

21 calls:

159.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))	y.im	-inf
155.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))	y.im	inf
11.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))	x.im	inf
11.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))	x.re	-inf
10.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))	x.im	-inf

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	224	25
2	2802	25

Stop Event

1×	node limit

Counts

2 → 56

simplify54.0ms (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

prune404.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	225	10	235

Error

3.4b

Counts

235 → 10

Alt Table

Status	Error	Program
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 y.im (.f64 (log.f64 (hypot.f64 x.im x.re)) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (*.f64 y.im (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))))))))
	10.7b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.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)))))
	18.5b	(.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	11.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))) (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))))) (log.f64 (cbrt.f64 (exp.f64 (exp.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)))))
	35.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	20.3b	(.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) (neg.f64 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)))))
	39.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	23.3b	(.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 (.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)))))) (cos.f64 1)) (.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)))))) (sin.f64 1))))
▶	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 (*.f64 y.re (atan2.f64 x.im x.re))))
	11.4b	(.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)))))) (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 13785 to 4817 computations (65.1% saved)

localize14.0ms (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)))
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
	1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	17.7b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

series14.0ms (0.1%)

Counts

1 → 4

Calls

9 calls:

3.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))	x.re	0
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))	x.re	-inf
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))	x.im	inf
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))	x.im	-inf
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))	x.re	inf

rewrite33.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`pow1_binary64`
578×	`add-log-exp_binary64`
578×	`log1p-expm1-u_binary64`
578×	`expm1-log1p-u_binary64`
70×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	135	9
2	1574	9

Stop Event

1×	node limit

Counts

1 → 17

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

691×	`distribute-rgt-neg-in_binary64`
572×	`distribute-lft-neg-in_binary64`
458×	`fma-def_binary64`
391×	`cancel-sign-sub-inv_binary64`
313×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	110
1	78	106
2	241	102
3	1179	100
4	3905	94

Stop Event

1×	node limit

Counts

21 → 24

prune297.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	167	10	177

Error

3.4b

Counts

177 → 10

Alt Table

Status	Error	Program
	23.3b	(.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 (.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)))))) (cos.f64 1)) (.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)))))) (sin.f64 1))))
	21.0b	(.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) (neg.f64 y.im))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 y.im (.f64 (log.f64 (hypot.f64 x.im x.re)) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (*.f64 y.im (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))))))))
▶	10.7b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.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)))))
	18.5b	(.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	11.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))) (cbrt.f64 (exp.f64 (exp.f64 (atan2.f64 x.im x.re)))))) (log.f64 (cbrt.f64 (exp.f64 (exp.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)))))
	39.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	35.5b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (/.f64 -1 x.im)) (neg.f64 y.re)) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	35.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	11.4b	(.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)))))) (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 8281 to 3043 computations (63.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.8b	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))
✓	3.4b	(pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))
	33.1b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series1.8s (13.3%)

Counts

2 → 84

Calls

21 calls:

302.0ms	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))	y.im	-inf
296.0ms	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))	y.im	inf
98.0ms	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))	x.im	0
98.0ms	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))	y.re	inf
95.0ms	(cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re)))))	y.re	-inf

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`log-prod_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
234×	`log-pow_binary64`
211×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	261	31
2	3222	31

Stop Event

1×	node limit

Counts

2 → 44

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

963×	`associate-/l*_binary64`
696×	`fma-def_binary64`
355×	`*-commutative_binary64`
195×	`associate-r_binary64`
155×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	751	12040
1	2991	10651

Stop Event

1×	node limit

Counts

128 → 121

prune951.0ms (7.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	458	4	462
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	460	12	472

Error

3.4b

Counts

472 → 12

Alt Table

Status	Error	Program
	23.3b	(.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 (.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)))))) (cos.f64 1)) (.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)))))) (sin.f64 1))))
	21.0b	(.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) (neg.f64 y.im))) (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
	39.3b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (cos.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	39.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (fma.f64 (log.f64 x.im) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	29.4b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (pow.f64 (exp.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.re))) 1/3))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.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)))))
	35.5b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (/.f64 -1 x.im)) (neg.f64 y.re)) (.f64 y.im (atan2.f64 x.im x.re)))) (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))))
	35.6b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.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))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 y.im (.f64 (log.f64 (hypot.f64 x.im x.re)) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (*.f64 y.im (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))))))))
	18.5b	(.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	35.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (pow.f64 (exp.f64 (atan2.f64 x.im x.re)) y.im)) (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	39.2b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (log.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))) (cbrt.f64 (exp.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.f64 y.im) (atan2.f64 x.im x.re))))))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (pow.f64 (exp.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)))))
	11.4b	(.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)))))) (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 72225 to 23953 computations (66.8% saved)

regimes597.0ms (4.5%)

Accuracy

Total 2.8b remaining (48%)

Threshold costs 0b (0%)

Counts

64 → 2

Compiler

Compiled 13122 to 6405 computations (51.2% saved)

bsearch4.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(*.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))))

Steps

Iters	Point		Range
-0.0	∈ [	-0.0	,	1.4416658459510789e-8	]

Compiler

Compiled 41 to 19 computations (53.7% saved)

simplify6.0ms (0%)

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	33	159
1	46	159
2	57	159
3	63	159
4	67	159
5	68	159

Stop Event

1×

saturated

end268.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 783 to 312 computations (60.2% saved)

Details

analyze1.8s (13.4%)

sample5.4s (40.5%)

preprocess41.0ms (0.3%)

simplify31.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0.1%)

series509.0ms (3.8%)

rewrite55.0ms (0.4%)

simplify72.0ms (0.5%)

prune281.0ms (2.1%)

localize15.0ms (0.1%)

series404.0ms (3%)

rewrite46.0ms (0.3%)

simplify54.0ms (0.4%)

prune404.0ms (3%)

localize14.0ms (0.1%)

series14.0ms (0.1%)

rewrite33.0ms (0.2%)

simplify27.0ms (0.2%)

prune297.0ms (2.2%)

localize26.0ms (0.2%)

series1.8s (13.3%)

rewrite54.0ms (0.4%)

simplify142.0ms (1.1%)

prune951.0ms (7.1%)

regimes597.0ms (4.5%)

bsearch4.0ms (0%)

simplify6.0ms (0%)

end268.0ms (2%)

Profiling