Details

analyze90.0ms (0.7%)

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
74.9%	25%	0.2%	3
74.9%	25%	0.2%	4
74.9%	25%	0.2%	5
87.3%	12.5%	0.2%	6
93.6%	6.2%	0.2%	7
93.6%	6.2%	0.2%	8
93.6%	6.2%	0.2%	9
96.7%	3.1%	0.2%	10
98.2%	1.6%	0.2%	11
98.2%	1.6%	0.2%	12
98.2%	1.6%	0.2%	13
99%	0.8%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample3.9s (31.2%)

Results

1.7s	1716×	body	1024	valid
1.2s	5411×	body	128	valid
683.0ms	753×	body	512	valid
131.0ms	355×	body	256	valid
109.0ms	21×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify68.0ms (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

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

14.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	38.6b	(.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))))
▶	17.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Status

Error

Program

38.6b

(*.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))))

▶

17.2b

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

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
✓	1.8b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	2.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	40.0b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series726.0ms (5.8%)

Counts

4 → 96

Calls

4 calls:

604.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
108.0ms	(cos.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)
7.0ms	(*.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	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

simplify214.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

723×	`times-frac_binary64`
676×	`fma-def_binary64`
672×	`associate-/l*_binary64`
276×	`*-commutative_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

193 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	704	9231
1	2205	8440
2	4490	8380
3	4964	8380
4	4875	8380

prune518.0ms (4.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	260	11	271
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	262	11	273

Error

3.4b

Counts

273 → 11

Alt Table

Status	Error	Program
	23.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	32.8b	(.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (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)))))
▶	16.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	40.5b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	17.2b	(.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 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	22.8b	(.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)))))
	16.3b	(.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))))
	17.2b	(.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 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	17.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 y.re (*.f64 (cbrt.f64 (atan2.f64 x.im x.re)) (cbrt.f64 (atan2.f64 x.im x.re)))) (cbrt.f64 (atan2.f64 x.im x.re))))))
	49.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (exp.f64 (+.f64 (log.f64 (atan2.f64 x.im x.re)) (log.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)))))
	17.7b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))

Compiler

Compiled 15449 to 4936 computations (68% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	2.4b	(.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))
✓	26.1b	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))
✓	26.3b	(cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))

series1.0s (8%)

Counts

3 → 120

Calls

3 calls:

823.0ms

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

96.0ms

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

90.0ms

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`distribute-lft-in_binary64`
42×	`distribute-rgt-in_binary64`
36×	`log-prod_binary64`
30×	`sin-sum_binary64`
16×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms

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

2.0ms

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

2.0ms

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

simplify171.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

622×	`times-frac_binary64`
533×	`fma-def_binary64`
467×	`*-commutative_binary64`
258×	`associate-r_binary64`
174×	`sub-neg_binary64`

Counts

194 → 281

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	947	11791
1	2646	10991
2	4969	10991

prune634.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	308	4	312
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	311	12	323

Error

3.4b

Counts

323 → 12

Alt Table

Status	Error	Program
	23.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	32.8b	(.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (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)))))
	22.8b	(.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)))))
	17.2b	(.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 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	17.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 y.re (*.f64 (cbrt.f64 (atan2.f64 x.im x.re)) (cbrt.f64 (atan2.f64 x.im x.re)))) (cbrt.f64 (atan2.f64 x.im x.re))))))
	49.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (exp.f64 (+.f64 (log.f64 (atan2.f64 x.im x.re)) (log.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)))))
	17.7b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	16.1b	(.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 (.f64 (cos.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (cos.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im))) (.f64 (sin.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (sin.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
▶	15.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	40.5b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	24.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 -1/6 (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.re x.im)) 3))))))))
	16.3b	(.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 (.f64 (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))

Compiler

Compiled 22301 to 7573 computations (66% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
	2.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
	2.4b	(.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))
	26.1b	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))

prune696.0ms (5.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	372	2	374
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	374	12	386

Error

2.2b

Counts

386 → 12

Alt Table

Status	Error	Program
	23.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	32.8b	(.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (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)))))
	22.8b	(.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)))))
	17.2b	(.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 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	17.7b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	15.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (log.f64 (exp.f64 (sin.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))))))))
	16.1b	(.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 (.f64 (cos.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (cos.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im))) (.f64 (sin.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (sin.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	40.5b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	49.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (exp.f64 (+.f64 (log.f64 (atan2.f64 x.im x.re)) (log.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)))))
	24.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 -1/6 (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.re x.im)) 3))))))))
▶	10.6b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 y.im (atan2.f64 x.im x.re)))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	16.3b	(.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 (.f64 (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))

Compiler

Compiled 23676 to 8464 computations (64.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))
✓	2.4b	(*.f64 y.im (atan2.f64 x.im x.re))
	2.4b	(.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))
	26.1b	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))

series670.0ms (5.3%)

Counts

2 → 48

Calls

2 calls:

662.0ms	(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))
8.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`
7×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

3.0ms	(*.f64 y.re (log.f64 (hypot.f64 x.im x.re)))
3.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1029×	`fma-neg_binary64`
481×	`times-frac_binary64`
368×	`associate-l_binary64`
311×	`fma-def_binary64`
241×	`associate-/l*_binary64`

Counts

95 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	1741
1	407	1491
2	1121	1491
3	3320	1491
4	4735	1455
5	5008	1455

prune621.0ms (4.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	309	12	321

Error

2.2b

Counts

321 → 12

Alt Table

Status	Error	Program
	23.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 (.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2))) (.f64 (log.f64 (hypot.f64 x.im x.re)) (.f64 y.im (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	22.0b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 y.im (atan2.f64 x.im x.re)))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 -1/6 (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.re x.im)) 3))))))))
	17.7b	(.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 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	15.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (log.f64 (exp.f64 (sin.f64 (*.f64 (log.f64 (hypot.f64 x.re x.im)) y.im))))))))
	16.1b	(.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 (.f64 (cos.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (cos.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im))) (.f64 (sin.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 x.im x.re)) (cbrt.f64 (hypot.f64 x.im x.re)))) y.im)) (sin.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x.im x.re))) y.im)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	16.1b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 y.im (atan2.f64 x.im x.re)))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (.f64 (log.f64 (hypot.f64 x.re x.im)) y.im)))))
	40.5b	(.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 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	17.2b	(.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 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	49.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (exp.f64 (+.f64 (log.f64 (atan2.f64 x.im x.re)) (log.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)))))
	24.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 -1/6 (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.re x.im)) 3))))))))
✓	10.6b	(.f64 (exp.f64 (-.f64 (.f64 y.re (log.f64 (hypot.f64 x.im x.re))) (.f64 y.im (atan2.f64 x.im x.re)))) (-.f64 1 (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
	16.3b	(.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 (.f64 (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (.f64 y.re (.f64 (atan2.f64 x.im x.re) (sin.f64 (.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))

Compiler

Compiled 18147 to 6615 computations (63.5% saved)

regimes2.6s (20.7%)

Accuracy

Total 11.1b remaining (83.2%)

Threshold costs 0b (0%)

Counts

274 → 3

Compiler

Compiled 53357 to 30550 computations (42.7% saved)

bsearch112.0ms (0.9%)

Steps

Iters	Range		Point
8	1.8249058563034673e-207	3.755867358904482e-200	2.711595358633846e-202
8	-2.6179988326730864e+70	-4.971090745481741e+66	-5.379883987355033e+66

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
11×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	139
1	73	139
2	93	139
3	112	139
4	123	139
5	127	139
6	128	139
7	127	139

end288.0ms (2.3%)

Compiler: Compiled 699 to 348 computations (50.2% saved)

Details

analyze90.0ms (0.7%)

sample3.9s (31.2%)

simplify68.0ms (0.5%)

prune6.0ms (0%)

localize16.0ms (0.1%)

series726.0ms (5.8%)

rewrite17.0ms (0.1%)

simplify214.0ms (1.7%)

prune518.0ms (4.1%)

localize25.0ms (0.2%)

series1.0s (8%)

rewrite19.0ms (0.1%)

simplify171.0ms (1.4%)

prune634.0ms (5%)

localize24.0ms (0.2%)

prune696.0ms (5.5%)

localize17.0ms (0.1%)

series670.0ms (5.3%)

rewrite8.0ms (0.1%)

simplify88.0ms (0.7%)

prune621.0ms (4.9%)

regimes2.6s (20.7%)

bsearch112.0ms (0.9%)

simplify7.0ms (0.1%)

end288.0ms (2.3%)

Profiling