Details

analyze2.3s (15.1%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample258.0ms (1.7%)

Algorithm

1×

intervals

Results

67.0ms	82×	body	1024	invalid
38.0ms	243×	body	128	valid
13.0ms	9×	body	2048	invalid
9.0ms	19×	body	512	invalid
3.0ms	7×	body	512	valid
3.0ms	4×	body	1024	valid
3.0ms	9×	body	256	invalid
3.0ms	17×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 87 to 43 computations (50.6% saved)

simplify65.0ms (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

7.3b

Counts

3 → 2

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))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	35.8b	(.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

▶

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

35.8b

(*.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 96 computations (53.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
✓	1.2b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	33.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series692.0ms (4.5%)

Counts

4 → 96

Calls

4 calls:

572.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
104.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
12×	`unpow-prod-down_binary64`

Counts

4 → 97

Calls

4 calls:

4.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
3.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
1.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

simplify229.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary64`
680×	`associate-/l*_binary64`
644×	`fma-def_binary64`
277×	`*-commutative_binary64`
143×	`cancel-sign-sub-inv_binary64`

Counts

193 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	699	9245
1	2181	8424
2	4520	8364
3	4956	8364
4	4880	8364

prune451.0ms (2.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	259	14	273
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	261	14	275

Error

3.3b

Counts

275 → 14

Alt Table

Status	Error	Program
	9.7b	(.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 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	10.3b	(.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 (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)))))
	35.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.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))))) (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)))))))
	24.8b	(.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 y.re (atan2.f64 x.im x.re))))
	10.0b	(.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 (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))))) (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)))))) (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)))))))
	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))))
	9.6b	(.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.f64 (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)))))
	21.5b	(.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 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
▶	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	30.7b	(.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 (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)))))))
	41.2b	(.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 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	17.5b	(.f64 (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)))))
	20.4b	(.f64 (/.f64 1 (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)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.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 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.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 15995 to 5100 computations (68.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re))
	1.2b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
	33.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series646.0ms (4.2%)

Counts

1 → 32

Calls

1 calls:

646.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
24×	`unpow-prod-down_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

1 → 59

Calls

1 calls:

5.0ms

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

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

480×	`cancel-sign-sub-inv_binary64`
301×	`times-frac_binary64`
274×	`unswap-sqr_binary64`
259×	`associate-/l*_binary64`
255×	`associate-r_binary64`

Counts

91 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	4255
1	829	4107
2	3660	4102
3	5253	4102

prune600.0ms (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	253	14	267

Error

3.3b

Counts

267 → 14

Alt Table

Status	Error	Program
	9.7b	(.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 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	10.3b	(.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 (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)))))
	35.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.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))))) (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)))))))
	24.8b	(.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 y.re (atan2.f64 x.im x.re))))
	10.0b	(.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 (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))))) (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)))))) (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)))))))
	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))))
	9.6b	(.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.f64 (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)))))
	21.5b	(.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 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	20.4b	(.f64 (/.f64 1 (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)))))
	41.2b	(.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 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	17.5b	(.f64 (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)))))
▶	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (/.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re))) (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.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 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.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 16411 to 4339 computations (73.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)) (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))
	1.2b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
	33.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series721.0ms (4.7%)

Counts

1 → 32

Calls

1 calls:

721.0ms

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`sqrt-prod_binary64`
39×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`

Counts

1 → 69

Calls

1 calls:

6.0ms

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

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
347×	`fma-neg_binary64`
274×	`cancel-sign-sub-inv_binary64`
217×	`unswap-sqr_binary64`
191×	`associate-r_binary64`

Counts

101 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	284	4710
1	694	4460
2	2359	4227
3	4642	4199
4	4965	4199
5	4974	4199

prune702.0ms (4.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	264	14	278

Error

3.3b

Counts

278 → 14

Alt Table

Status	Error	Program
	9.7b	(.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 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	10.3b	(.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 (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)))))
	35.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.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))))) (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)))))))
	24.8b	(.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 y.re (atan2.f64 x.im x.re))))
	10.0b	(.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 (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))))) (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)))))) (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)))))))
	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))))
▶	9.6b	(.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.f64 (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)))))
	21.5b	(.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 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	20.4b	(.f64 (/.f64 1 (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)))))
	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (/.f64 (/.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (sqrt.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (sqrt.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	41.2b	(.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 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	17.5b	(.f64 (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)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.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 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.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 18890 to 4512 computations (76.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))))
	1.2b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
	33.5b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series1.4s (9.1%)

Counts

1 → 48

Calls

1 calls:

1.4s	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
7×	`associate-/l*_binary64`
7×	`times-frac_binary64`
6×	`unpow-prod-down_binary64`
6×	`div-exp_binary64`

Counts

1 → 35

Calls

1 calls:

6.0ms

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

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-r_binary64`
442×	`associate-l_binary64`
307×	`fma-def_binary64`
289×	`fma-neg_binary64`
229×	`times-frac_binary64`

Counts

83 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	396	5989
1	1221	4988
2	4888	4976
3	5148	4976

prune782.0ms (5.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	313	14	327

Error

3.3b

Counts

327 → 14

Alt Table

Status	Error	Program
	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (/.f64 (/.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (sqrt.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (sqrt.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (sqrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	6.8b	(.f64 (/.f64 (exp.f64 (fma.f64 y.re (log.f64 (hypot.f64 x.im x.re)) (.f64 -2 (log.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))))) (cbrt.f64 (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)))))
	9.6b	(.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (.f64 (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.f64 (exp.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 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)))))
	9.7b	(.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 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	10.3b	(.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 (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)))))
	35.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.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))))) (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)))))))
	24.8b	(.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 y.re (atan2.f64 x.im x.re))))
	10.0b	(.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 (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))))) (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)))))) (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)))))))
	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))))
	21.5b	(.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 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	41.2b	(.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 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	17.5b	(.f64 (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)))))
	9.6b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re) (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) y.re)))) (cbrt.f64 (/.f64 (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)) (pow.f64 (sqrt.f64 (hypot.f64 x.re x.im)) 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)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.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 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))))) (cbrt.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 22031 to 6301 computations (71.4% saved)

regimes600.0ms (3.9%)

Accuracy

Total 1.6b remaining (35.4%)

Threshold costs 0b (0%)

Counts

85 → 2

Compiler

Compiled 18412 to 8205 computations (55.4% saved)

bsearch6.0ms (0%)

Steps

Iters	Range		Point
0	-2.2640823595479625e+127	-2.261306351947414e+127	-2.2626943557476885e+127

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	93
1	34	93
2	34	93

end1.0ms (0%)

Compiler: Compiled 64 to 27 computations (57.8% saved)

sample5.4s (34.8%)

Algorithm

1×

intervals

Results

1.8s	2455×	body	1024	invalid
1.1s	7605×	body	128	valid
707.0ms	306×	body	256	invalid
430.0ms	917×	body	512	invalid
181.0ms	164×	body	2048	invalid
115.0ms	157×	body	1024	valid
80.0ms	502×	body	128	invalid
55.0ms	125×	body	512	valid
30.0ms	98×	body	256	valid
19.0ms	15×	body	2048	valid

Compiler

Compiled 695 to 305 computations (56.1% saved)

Details

analyze2.3s (15.1%)

sample258.0ms (1.7%)

simplify65.0ms (0.4%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series692.0ms (4.5%)

rewrite18.0ms (0.1%)

simplify229.0ms (1.5%)

prune451.0ms (2.9%)

localize19.0ms (0.1%)

series646.0ms (4.2%)

rewrite10.0ms (0.1%)

simplify133.0ms (0.9%)

prune600.0ms (3.9%)

localize21.0ms (0.1%)

series721.0ms (4.7%)

rewrite15.0ms (0.1%)

simplify160.0ms (1%)

prune702.0ms (4.6%)

localize20.0ms (0.1%)

series1.4s (9.1%)

rewrite9.0ms (0.1%)

simplify124.0ms (0.8%)

prune782.0ms (5.1%)

regimes600.0ms (3.9%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end1.0ms (0%)

sample5.4s (34.8%)

Profiling