Details

analyze1.5s (16.3%)

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)

sample122.0ms (1.3%)

Algorithm

1×

intervals

Results

42.0ms	83×	body	1024	invalid
31.0ms	239×	body	128	valid
11.0ms	32×	body	512	invalid
5.0ms	8×	body	1024	valid
3.0ms	15×	body	256	invalid
3.0ms	8×	body	512	valid
2.0ms	21×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 87 to 43 computations (50.6% saved)

simplify72.0ms (0.8%)

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 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	37	72
2	62	72
3	105	72
4	245	72
5	968	72
6	2998	72
7	4028	72
8	4444	72
9	4942	72

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

32.4b

Counts

2 → 2

Alt Table

Status	Error	Program
	35.7b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))) y.re) (exp.f64 (.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 y.re (atan2.f64 x.im x.re)))))
▶	32.4b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

Status

Error

Program

35.7b

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

▶

32.4b

(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

Compiler

Compiled 202 to 95 computations (53% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 (atan2.f64 x.im x.re) y.re)
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(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)))

rewrite147.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

32.4b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`

Counts

4 → 56

Calls

4 calls:

13.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 2424 to 343 computations (85.8% saved)

series226.0ms (2.5%)

Error

16.3b

Counts

4 → 47

Calls

4 calls:

82.0ms	(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)))
53.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4533 to 2372 computations (47.7% saved)

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-in_binary64`
384×	`distribute-lft-neg-in_binary64`
304×	`unswap-sqr_binary64`
278×	`distribute-neg-frac_binary64`
253×	`associate-r_binary64`

Counts

103 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	150	2085
1	323	1930
2	781	1930
3	2607	1930
4	4790	1930
5	4990	1930

prune113.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	56	7	63

Error

16.6b

Counts

63 → 7

Alt Table

Status	Error	Program
	35.7b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))) y.re) (exp.f64 (.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 y.re (atan2.f64 x.im x.re)))))
	38.2b	(.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 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (neg.f64 (log.f64 x.re))))))
	45.1b	(.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 (-.f64 (.f64 (/.f64 (pow.f64 x.re 2) x.im) -1/2) x.im)) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
▶	32.4b	(.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))) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))) 3)))
	40.0b	(.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 (neg.f64 x.im)) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
	42.6b	(.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 (neg.f64 x.re)) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
	32.4b	(.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))) (.f64 (.f64 (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))))

Compiler

Compiled 2840 to 1067 computations (62.4% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
28.5b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite185.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 2625 to 1103 computations (58% saved)

series241.0ms (2.6%)

Error

16.3b

Counts

4 → 47

Calls

4 calls:

69.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
57.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
28.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))

Compiler

Compiled 4824 to 2988 computations (38.1% saved)

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

411×	`distribute-rgt-neg-in_binary64`
398×	`neg-mul-1_binary64`
389×	`distribute-lft-neg-in_binary64`
304×	`unswap-sqr_binary64`
279×	`associate-r_binary64`

Counts

105 → 51

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	173	2115
1	343	1960
2	826	1960
3	2730	1960
4	4697	1960
5	5203	1960

prune110.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Error

16.6b

Counts

58 → 6

Alt Table

Status	Error	Program
	35.7b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))) y.re) (exp.f64 (.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 y.re (atan2.f64 x.im x.re)))))
▶	32.4b	(.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))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)) 3)))
	40.7b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 x.im)))) 3)))
	45.1b	(.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 (-.f64 (.f64 (/.f64 (pow.f64 x.re 2) x.im) -1/2) x.im)) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
	40.0b	(.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 (neg.f64 x.im)) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
	32.4b	(.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))) (.f64 (.f64 (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))))

Compiler

Compiled 2437 to 1256 computations (48.5% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 y.re (atan2.f64 x.im x.re))
28.5b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite168.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
7.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 2784 to 1262 computations (54.7% saved)

series258.0ms (2.8%)

Error

16.3b

Counts

4 → 47

Calls

4 calls:

73.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
62.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
36.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
29.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))

Compiler

Compiled 5181 to 3318 computations (36% saved)

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

411×	`distribute-rgt-neg-in_binary64`
398×	`neg-mul-1_binary64`
389×	`distribute-lft-neg-in_binary64`
304×	`unswap-sqr_binary64`
279×	`associate-r_binary64`

Counts

105 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	171	2115
1	343	1960
2	826	1960
3	2730	1960
4	4697	1960
5	5203	1960

prune118.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Error

16.6b

Counts

58 → 6

Alt Table

Status	Error	Program
	35.7b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))) y.re) (exp.f64 (.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 y.re (atan2.f64 x.im x.re)))))
✓	32.4b	(.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))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)) 3)))
	40.7b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 x.im)))) 3)))
	45.1b	(.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 (-.f64 (.f64 (/.f64 (pow.f64 x.re 2) x.im) -1/2) x.im)) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
	40.0b	(.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 (neg.f64 x.im)) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
▶	32.4b	(.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))) (.f64 (.f64 (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))))

Compiler

Compiled 2550 to 1363 computations (46.5% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

28.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
35.2b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
35.2b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite157.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cos-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`

Counts

4 → 39

Calls

4 calls:

7.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3491 to 1729 computations (50.5% saved)

series451.0ms (4.9%)

Error

16.5b

Counts

4 → 54

Calls

4 calls:

89.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
88.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
87.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
76.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 11208 to 6570 computations (41.4% saved)

simplify134.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-in_binary64`
384×	`distribute-lft-neg-in_binary64`
298×	`unswap-sqr_binary64`
278×	`distribute-neg-frac_binary64`
210×	`times-frac_binary64`

Counts

93 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2844
1	269	2604
2	633	2604
3	2411	2604
4	4793	2604
5	4990	2604

prune156.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	58	7	65

Error

16.6b

Counts

65 → 7

Alt Table

Status	Error	Program
	35.7b	(.f64 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))) y.re) (exp.f64 (.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 y.re (atan2.f64 x.im x.re)))))
	32.4b	(.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))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))) y.im) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)) 3)))
	48.9b	(.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))) (.f64 (.f64 (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 x.im)))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))))
	40.7b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 x.im)))) 3)))
	45.1b	(.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 (-.f64 (.f64 (/.f64 (pow.f64 x.re 2) x.im) -1/2) x.im)) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
	40.0b	(.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 (neg.f64 x.im)) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
	32.4b	(.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))) (.f64 (.f64 (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))) (cbrt.f64 (cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))))))

Compiler

Compiled 4114 to 2166 computations (47.4% saved)

regimes749.0ms (8.1%)

Accuracy

Total 0.4b remaining (2%)

Threshold costs 0.4b (2%)

Compiler

Compiled 17597 to 10380 computations (41% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	30	50
2	40	50
3	46	50
4	50	50
5	51	50
6	51	50

end1.0ms (0%)

Compiler: Compiled 29 to 17 computations (41.4% saved)

sample3.8s (41.1%)

Algorithm

1×

intervals

Results

1.3s	2490×	body	1024	invalid
858.0ms	7575×	body	128	valid
359.0ms	1012×	body	512	invalid
100.0ms	427×	body	256	invalid
86.0ms	164×	body	1024	valid
66.0ms	569×	body	128	invalid
60.0ms	172×	body	512	valid
22.0ms	28×	body	2048	invalid
18.0ms	77×	body	256	valid
10.0ms	12×	body	2048	valid

Compiler

Compiled 433 to 258 computations (40.4% saved)

Details

analyze1.5s (16.3%)

sample122.0ms (1.3%)

simplify72.0ms (0.8%)

prune10.0ms (0.1%)

localize22.0ms (0.2%)

rewrite147.0ms (1.6%)

series226.0ms (2.5%)

simplify120.0ms (1.3%)

prune113.0ms (1.2%)

localize32.0ms (0.4%)

rewrite185.0ms (2%)

series241.0ms (2.6%)

simplify122.0ms (1.3%)

prune110.0ms (1.2%)

localize33.0ms (0.4%)

rewrite168.0ms (1.8%)

series258.0ms (2.8%)

simplify122.0ms (1.3%)

prune118.0ms (1.3%)

localize36.0ms (0.4%)

rewrite157.0ms (1.7%)

series451.0ms (4.9%)

simplify134.0ms (1.5%)

prune156.0ms (1.7%)

regimes749.0ms (8.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample3.8s (41.1%)

Profiling