Details

analyze2.2s (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.9%	0.2%	13
50%	49.7%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample6.4s (46.1%)

Results

2.6s	2535×	body	1024	invalid
2.1s	7813×	body	128	valid
696.0ms	900×	body	512	invalid
267.0ms	178×	body	2048	invalid
172.0ms	177×	body	1024	valid
171.0ms	381×	body	256	invalid
140.0ms	529×	body	128	invalid
91.0ms	144×	body	512	valid
49.0ms	107×	body	256	valid
23.0ms	15×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify70.0ms (0.5%)

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
	34.3b	(.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))))
▶	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))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Status

Error

Program

34.3b

(*.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))))

▶

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

Compiler

Compiled 206 to 96 computations (53.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
✓	1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	35.2b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series542.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

419.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
109.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

rewrite17.0ms (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:

5.0ms	(/.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 y.re (atan2.f64 x.im x.re))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
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))))

simplify203.0ms (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

prune434.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	261	12	273
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	263	12	275

Error

4.5b

Counts

275 → 12

Alt Table

Status	Error	Program
	10.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (.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)))))))
	22.9b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	39.8b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	10.5b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	19.7b	(.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)))
	10.5b	(.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 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
	51.6b	(.f64 (-.f64 (fma.f64 1/2 (.f64 (/.f64 (.f64 (.f64 x.re x.re) y.re) (.f64 x.im x.im)) (/.f64 (pow.f64 (/.f64 -1 x.im) (neg.f64 y.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (fma.f64 1/8 (.f64 (/.f64 (.f64 (pow.f64 x.re 4) (.f64 y.re y.re)) (pow.f64 x.im 4)) (/.f64 (pow.f64 (/.f64 -1 x.im) (neg.f64 y.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (/.f64 (pow.f64 (/.f64 -1 x.im) (neg.f64 y.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))))) (.f64 1/4 (.f64 (/.f64 (.f64 (pow.f64 x.re 4) y.re) (pow.f64 x.im 4)) (/.f64 (pow.f64 (/.f64 -1 x.im) (neg.f64 y.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))
	42.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	30.2b	(.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)))))))
	48.2b	(.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 x.re x.re) (.f64 y.re (pow.f64 x.im y.re))) (.f64 (.f64 x.im x.im) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (/.f64 (pow.f64 x.im y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
▶	4.8b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
	11.4b	(.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)))))

Compiler

Compiled 16021 to 5144 computations (67.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (log.f64 (hypot.f64 x.re x.im)) y.re)
	1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
	35.2b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series554.0ms (4%)

Counts

1 → 36

Calls

1 calls:

554.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 21

Calls

1 calls:

3.0ms

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

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

583×	`associate-/r/_binary64`
506×	`associate-/l/_binary64`
259×	`times-frac_binary64`
249×	`fma-def_binary64`
217×	`distribute-rgt-neg-in_binary64`

Counts

57 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1306
1	335	1108
2	828	1108
3	2818	1087
4	5391	1087

prune422.0ms (3.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	203	12	215

Error

4.5b

Counts

215 → 12

Alt Table

Status	Error	Program
	10.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (.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)))))))
	22.9b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	39.8b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	39.6b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
▶	10.5b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	19.7b	(.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)))
	30.2b	(.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)))))))
	48.2b	(.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 x.re x.re) (.f64 y.re (pow.f64 x.im y.re))) (.f64 (.f64 x.im x.im) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (/.f64 (pow.f64 x.im y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	50.3b	(.f64 (exp.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 y.re (.f64 x.re x.re)) (.f64 x.im x.im)) (.f64 y.re (-.f64 (/.f64 (.f64 (pow.f64 x.re 4) -1/4) (pow.f64 x.im 4)) (log.f64 (/.f64 -1 x.im))))) (.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)))))
✓	4.8b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
	11.4b	(.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)))))
	10.5b	(.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 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 10736 to 3565 computations (66.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))
✓	1.2b	(*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))
	2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	35.2b	(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)))))

series533.0ms (3.9%)

Counts

3 → 120

Calls

3 calls:

420.0ms

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

90.0ms

(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)))))

22.0ms

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
17×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
9×	`cbrt-unprod_binary64`

Counts

3 → 58

Calls

3 calls:

7.0ms

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

4.0ms

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

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
487×	`associate-r_binary64`
344×	`associate-l_binary64`
271×	`*-commutative_binary64`
256×	`unswap-sqr_binary64`

Counts

178 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	5027
1	1105	4594
2	3816	4587
3	5071	4587

prune310.0ms (2.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	176	12	188

Error

4.5b

Counts

188 → 12

Alt Table

Status	Error	Program
	10.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (.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)))))))
	22.9b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	39.8b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	39.6b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
✓	10.5b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	19.7b	(.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)))
	30.2b	(.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)))))))
	48.2b	(.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 x.re x.re) (.f64 y.re (pow.f64 x.im y.re))) (.f64 (.f64 x.im x.im) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (/.f64 (pow.f64 x.im y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	50.3b	(.f64 (exp.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 y.re (.f64 x.re x.re)) (.f64 x.im x.im)) (.f64 y.re (-.f64 (/.f64 (.f64 (pow.f64 x.re 4) -1/4) (pow.f64 x.im 4)) (log.f64 (/.f64 -1 x.im))))) (.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)))))
✓	4.8b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
	11.4b	(.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)))))
▶	10.5b	(.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 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 9730 to 2885 computations (70.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
	2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	9.2b	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
✓	35.1b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))))))

series739.0ms (5.4%)

Counts

2 → 84

Calls

2 calls:

653.0ms

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

86.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 21

Calls

2 calls:

2.0ms

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

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
531×	`cancel-sign-sub-inv_binary64`
360×	`associate-r_binary64`
232×	`*-commutative_binary64`
226×	`sub-neg_binary64`

Counts

105 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	350	4369
1	1030	4050
2	3390	4014
3	4931	4014

prune327.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	231	12	243

Error

4.5b

Counts

243 → 12

Alt Table

Status	Error	Program
	10.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (.f64 (.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)))))))
	22.9b	(.f64 (fma.f64 (/.f64 (log.f64 (hypot.f64 x.im x.re)) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re)))) y.re (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	39.8b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	39.6b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
✓	10.5b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	19.7b	(.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)))
	30.2b	(.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)))))))
	48.2b	(.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 x.re x.re) (.f64 y.re (pow.f64 x.im y.re))) (.f64 (.f64 x.im x.im) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (/.f64 (pow.f64 x.im y.re) (exp.f64 (.f64 y.im (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	50.3b	(.f64 (exp.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 y.re (.f64 x.re x.re)) (.f64 x.im x.im)) (.f64 y.re (-.f64 (/.f64 (.f64 (pow.f64 x.re 4) -1/4) (pow.f64 x.im 4)) (log.f64 (/.f64 -1 x.im))))) (.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)))))
✓	4.8b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (hypot.f64 x.re x.im)) y.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)))))
	11.4b	(.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)))))
✓	10.5b	(.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 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 12791 to 3050 computations (76.2% saved)

regimes438.0ms (3.2%)

Accuracy

Total 0.3b remaining (7%)

Threshold costs 0.3b (7%)

Counts

63 → 1

Compiler

Compiled 11132 to 6160 computations (44.7% 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	35	40
3	41	40
4	45	40
5	46	40
6	46	40

end252.0ms (1.8%)

Compiler: Compiled 522 to 262 computations (49.8% saved)

Details

analyze2.2s (16%)

sample6.4s (46.1%)

simplify70.0ms (0.5%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series542.0ms (3.9%)

rewrite17.0ms (0.1%)

simplify203.0ms (1.5%)

prune434.0ms (3.1%)

localize21.0ms (0.1%)

series554.0ms (4%)

rewrite4.0ms (0%)

simplify57.0ms (0.4%)

prune422.0ms (3.1%)

localize22.0ms (0.2%)

series533.0ms (3.9%)

rewrite15.0ms (0.1%)

simplify110.0ms (0.8%)

prune310.0ms (2.3%)

localize21.0ms (0.2%)

series739.0ms (5.4%)

rewrite4.0ms (0%)

simplify104.0ms (0.8%)

prune327.0ms (2.4%)

regimes438.0ms (3.2%)

simplify3.0ms (0%)

end252.0ms (1.8%)

Profiling