Details

analyze2.1s (13.9%)

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)

sample5.7s (37.4%)

Results

2.5s	2428×	body	1024	invalid
1.9s	7838×	body	128	valid
615.0ms	1018×	body	512	invalid
181.0ms	422×	body	256	invalid
171.0ms	194×	body	1024	valid
122.0ms	540×	body	128	invalid
82.0ms	136×	body	512	valid
41.0ms	31×	body	2048	invalid
41.0ms	79×	body	256	valid
13.0ms	9×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify67.0ms (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
	32.8b	(.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))) (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))))
▶	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))) (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

32.8b

(*.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))) (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))))

▶

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))) (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)

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)))
✓	0.4b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.4b	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series620.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

502.0ms	(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
104.0ms	(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 y.re (atan2.f64 x.im x.re))
6.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite15.0ms (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	(cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

simplify208.0ms (1.4%)

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

prune482.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	261	10	271
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	263	10	273

Error

3.8b

Counts

273 → 10

Alt Table

Status	Error	Program
	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 (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)))))))
	10.7b	(.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 (*.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))) (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)))
	36.4b	(.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))))
	38.0b	(.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 x.im) y.im (*.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))) (expm1.f64 (log1p.f64 (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 (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)))))
	20.8b	(.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)))))
	24.9b	(.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 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (sqrt.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.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))) (log.f64 (exp.f64 (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 15311 to 4870 computations (68.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.4b	(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)
	2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.4b	(cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))

series538.0ms (3.5%)

Counts

2 → 64

Calls

2 calls:

437.0ms	(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)
101.0ms	(cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
3×	`cube-prod_binary64`
3×	`pow-unpow_binary64`

Counts

2 → 35

Calls

2 calls:

2.0ms	(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)
1.0ms	(cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))

simplify225.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
621×	`times-frac_binary64`
345×	`*-commutative_binary64`
166×	`associate-r_binary64`
160×	`cancel-sign-sub-inv_binary64`

Counts

99 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	772	10827
1	2539	9961
2	4558	9945
3	4997	9945
4	4845	9945

prune495.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	219	12	231

Error

3.8b

Counts

231 → 12

Alt Table

Status	Error	Program
	38.0b	(.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 x.im) y.im (*.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))) (cbrt.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.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) (pow.f64 (cbrt.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))))
	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))) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.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))) (cbrt.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.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)))
	16.3b	(.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)))))
▶	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))) (cbrt.f64 (pow.f64 (log1p.f64 (expm1.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)))
	36.4b	(.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))))
	10.1b	(.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 (log.f64 (exp.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)))))
	20.8b	(.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)))))
	36.4b	(.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 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))) 3)))
	10.7b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	24.9b	(.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 (sqrt.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) (pow.f64 (sqrt.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))))

Compiler

Compiled 18406 to 7359 computations (60% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (log1p.f64 (expm1.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)
✓	0.6b	(expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))
	2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
	32.4b	(cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))

series760.0ms (5%)

Counts

2 → 96

Calls

2 calls:

487.0ms

(pow.f64 (log1p.f64 (expm1.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)

273.0ms

(expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
3×	`cube-prod_binary64`
3×	`pow-unpow_binary64`

Counts

2 → 36

Calls

2 calls:

1.0ms

(pow.f64 (log1p.f64 (expm1.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)

0.0ms

(expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))

simplify239.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

836×	`times-frac_binary64`
770×	`fma-def_binary64`
530×	`*-commutative_binary64`
299×	`associate-r_binary64`
190×	`+-commutative_binary64`

Counts

132 → 174

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1085	15665
1	3399	14992
2	5555	14992

prune736.0ms (4.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	273	4	277
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	276	13	289

Error

3.8b

Counts

289 → 13

Alt Table

Status	Error	Program
	38.0b	(.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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 y.re (atan2.f64 x.im x.re) (*.f64 y.im (log.f64 x.im)))))) 3)))
	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))) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.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))) (cbrt.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.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)))
	16.3b	(.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)))))
✓	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))) (cbrt.f64 (pow.f64 (log1p.f64 (expm1.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)))
	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))) (cbrt.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))))) (cbrt.f64 (log1p.f64 (expm1.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) (pow.f64 (cbrt.f64 (log1p.f64 (expm1.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))))
	10.7b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	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))) (cbrt.f64 (pow.f64 (log1p.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))))) (cbrt.f64 (expm1.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)))
	36.4b	(.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))))
	10.1b	(.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 (log.f64 (exp.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)))))
	36.4b	(.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 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im)))) 1)) 3)))
	20.8b	(.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)))))
	24.9b	(.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 (sqrt.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) (pow.f64 (sqrt.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))))

Compiler

Compiled 29363 to 11924 computations (59.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.4b	(pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.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)
	2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
	32.4b	(cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))

series450.0ms (2.9%)

Counts

1 → 48

Calls

1 calls:

450.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
15×	`pow-pow_binary64`
9×	`pow-prod-up_binary64`
9×	`pow1/3_binary64`
7×	`add-exp-log_binary64`

Counts

1 → 39

Calls

1 calls:

7.0ms

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

simplify148.0ms (1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
408×	`times-frac_binary64`
379×	`associate-/l*_binary64`
288×	`associate-/r*_binary64`
270×	`*-commutative_binary64`

Counts

87 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	595	7604
1	1869	6838
2	4597	6819
3	4932	6819

prune1.1s (7.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	419	5	424
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	422	15	437

Error

3.8b

Counts

437 → 15

Alt Table

Status	Error	Program
	16.3b	(.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)))))
✓	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))) (cbrt.f64 (pow.f64 (log1p.f64 (expm1.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)))
	36.4b	(.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 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im)))) 1)) 3)))
	10.9b	(.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 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))))) 3)))
	10.1b	(.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 (log.f64 (exp.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.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)))))
	20.8b	(.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)))))
	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))) (cbrt.f64 (log1p.f64 (expm1.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.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)))))
	38.0b	(.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 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (fma.f64 y.re (atan2.f64 x.im x.re) (*.f64 y.im (log.f64 x.im)))))) 3)))
	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))) (cbrt.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))))) (cbrt.f64 (log1p.f64 (expm1.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) (pow.f64 (cbrt.f64 (log1p.f64 (expm1.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))))
	10.7b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	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))) (cbrt.f64 (pow.f64 (log1p.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (expm1.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))))) (cbrt.f64 (expm1.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)))
	36.4b	(.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))))
	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))) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	36.4b	(.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 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (cos.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (cos.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))) 3)))
	24.9b	(.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 (sqrt.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) (pow.f64 (sqrt.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))))

Compiler

Compiled 40677 to 12179 computations (70.1% saved)

regimes797.0ms (5.2%)

Accuracy

Total 3.6b remaining (56%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 17907 to 8935 computations (50.1% saved)

bsearch66.0ms (0.4%)

Steps

Iters	Range		Point
6	-1.7103626419907514e+101	-2.866752857954457e+100	-2.937387267079664e+100

Compiler

Compiled 5 to 4 computations (20% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	76
1	33	76
2	33	76

end383.0ms (2.5%)

Compiler: Compiled 794 to 376 computations (52.6% saved)

Details

analyze2.1s (13.9%)

sample5.7s (37.4%)

simplify67.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series620.0ms (4.1%)

rewrite15.0ms (0.1%)

simplify208.0ms (1.4%)

prune482.0ms (3.1%)

localize20.0ms (0.1%)

series538.0ms (3.5%)

rewrite4.0ms (0%)

simplify225.0ms (1.5%)

prune495.0ms (3.2%)

localize22.0ms (0.1%)

series760.0ms (5%)

rewrite4.0ms (0%)

simplify239.0ms (1.6%)

prune736.0ms (4.8%)

localize23.0ms (0.2%)

series450.0ms (2.9%)

rewrite14.0ms (0.1%)

simplify148.0ms (1%)

prune1.1s (7.3%)

regimes797.0ms (5.2%)

bsearch66.0ms (0.4%)

simplify2.0ms (0%)

end383.0ms (2.5%)

Profiling