Details

analyze1.5s (0.8%)

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 38 to 20 computations (47.4% saved)

sample131.0ms (0.1%)

Algorithm

1×

intervals

Results

43.0ms	80×	body	1024	invalid
29.0ms	239×	body	128	valid
17.0ms	38×	body	512	invalid
4.0ms	7×	body	1024	valid
3.0ms	2×	body	2048	invalid
2.0ms	19×	body	128	invalid
2.0ms	9×	body	256	invalid
2.0ms	5×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 78 to 50 computations (35.9% saved)

simplify156.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	75
1	4944	75

prune6.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

4.6b

Counts

8 → 5

Compiler

Compiled 39 to 22 computations (43.6% saved)

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.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))
0.0b	(.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 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.7b	(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)))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

8 calls:

8.0ms	(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)))
5.0ms	(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.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series587.0ms (0.3%)

Counts

4 → 50

Calls

4 calls:

292.0ms	(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)))
143.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
78.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
73.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3428 to 2241 computations (34.6% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5075	2052

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(.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)))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.7b	(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))))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

8 calls:

7.0ms	(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))))
5.0ms	(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.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series565.0ms (0.3%)

Counts

4 → 50

Calls

4 calls:

270.0ms	(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))))
141.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
79.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
75.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3345 to 2176 computations (34.9% saved)

simplify72.0ms (0%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5075	2052

prune1.5s (0.8%)

Pruning

81 alts after pruning (79 fresh and 2 done)

	Pruned	Kept	Total
New	136	76	212
Fresh	0	3	3
Picked	0	0	0
Done	0	2	2
Total	136	81	217

Error

4.6b

Counts

217 → 81

Compiler

Compiled 9595 to 3776 computations (60.6% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.0b	(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)))
0.0b	(-.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))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
1.0b	(*.f64 (atan2.f64 x.im x.re) y.re)
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
13.9b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 58

Calls

8 calls:

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.im)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
2.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series399.0ms (0.2%)

Counts

4 → 46

Calls

4 calls:

135.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
126.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2114 to 1494 computations (29.3% saved)

simplify52.0ms (0%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5041	1497

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(*.f64 y.re (atan2.f64 x.im x.re))
0.0b	(/.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)))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
1.0b	(*.f64 y.re (atan2.f64 x.im x.re))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
13.9b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 58

Calls

8 calls:

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))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
1.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series402.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

137.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
126.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
70.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2036 to 1416 computations (30.5% saved)

simplify83.0ms (0%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	1597
1	4953	1597

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.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))
0.0b	(-.f64 (.f64 (log.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
6.6b	(/.f64 (pow.f64 x.re 2) x.im)
6.8b	(log.f64 (+.f64 x.im (*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.7b	(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)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64` `times-frac_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
10×	`add-exp-log_binary64`
8×	`associate-/l*_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64`
3×	`associate-/r*_binary64` `log-prod_binary64` `div-exp_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `log-div_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `cos-sum_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 86

Calls

8 calls:

7.0ms	(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)))
6.0ms	(/.f64 (pow.f64 x.re 2) x.im)
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
3.0ms	(log.f64 (+.f64 x.im (*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series486.0ms (0.3%)

Counts

4 → 35

Calls

4 calls:

241.0ms	(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)))
126.0ms	(log.f64 (+.f64 x.im (*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
77.0ms	(/.f64 (pow.f64 x.re 2) x.im)
41.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 2643 to 1873 computations (29.1% saved)

simplify78.0ms (0%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4949	2343
1	4949	2343

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 (log.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))
0.0b	(*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))
0.0b	(*.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
14.7b	(cos.f64 (+.f64 (.f64 (log.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
14.8b	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
14.9b	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite70.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
63×	`unpow-prod-down_binary64`
57×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`cube-prod_binary64`
21×	`sqr-pow_binary64`
16×	`add-exp-log_binary64`
12×	`associate-/r*_binary64`
9×	`add-log-exp_binary64` `div-exp_binary64`
8×	`unpow3_binary64` `cube-mult_binary64`
7×	`associate-/l*_binary64`
6×	`pow-to-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `associate-*r/_binary64` `flip-+_binary64` `frac-sub_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `cos-sum_binary64` `div-inv_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 164

Calls

8 calls:

18.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
9.0ms	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
7.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) 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)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series1.1s (0.6%)

Counts

4 → 52

Calls

4 calls:

421.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
414.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))) (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))))
129.0ms	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
117.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4108 to 2894 computations (29.6% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5273	5438

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(-.f64 (cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))) (.f64 1/2 (/.f64 (.f64 (pow.f64 x.re 2) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (pow.f64 x.im 2))))
7.2b	(/.f64 (.f64 (pow.f64 x.re 2) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (pow.f64 x.im 2))
16.6b	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
16.6b	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite47.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-exp-log_binary64`
27×	`prod-exp_binary64`
21×	`div-exp_binary64`
13×	`pow-to-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-/r*_binary64` `times-frac_binary64`
6×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
2×	`sub-neg_binary64` `unpow2_binary64` `sin-sum_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `cos-sum_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `cos-diff_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

8 calls:

14.0ms	(/.f64 (.f64 (pow.f64 x.re 2) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (pow.f64 x.im 2))
5.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
4.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
0.0ms	(-.f64 (cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))) (.f64 1/2 (/.f64 (.f64 (pow.f64 x.re 2) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (pow.f64 x.im 2))))

series1.5s (0.8%)

Counts

4 → 49

Calls

4 calls:

678.0ms	(/.f64 (.f64 (pow.f64 x.re 2) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (pow.f64 x.im 2))
370.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
352.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
116.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5438 to 3678 computations (32.4% saved)

simplify92.0ms (0%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5178	4553

prune13.2s (7%)

Pruning

281 alts after pruning (274 fresh and 7 done)

	Pruned	Kept	Total
New	482	200	682
Fresh	0	74	74
Picked	0	0	0
Done	0	7	7
Total	482	281	763

Error

3.9b

Counts

763 → 281

Compiler

Compiled 30060 to 15755 computations (47.6% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.0b	(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)))
0.0b	(-.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))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(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)))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 69

Calls

8 calls:

7.0ms	(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)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
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.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series738.0ms (0.4%)

Counts

4 → 58

Calls

4 calls:

281.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
257.0ms	(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)))
132.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2420 to 1981 computations (18.1% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4953	2670
1	4953	2670

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
0.0b	(/.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)))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(/.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)))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
24×	`unpow-prod-down_binary64`
15×	`sqrt-prod_binary64`
10×	`associate-/l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`sqr-pow_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `div-exp_binary64`
2×	`sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `exp-to-pow_binary64` `flip-+_binary64` `pow-exp_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

8 calls:

11.0ms	(/.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)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series695.0ms (0.4%)

Counts

4 → 57

Calls

4 calls:

411.0ms	(/.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)))
134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
80.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2228 to 1785 computations (19.9% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4955	4880
1	4955	4880

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.0b	(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)))
0.0b	(-.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))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.7b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
13.9b	(cos.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64` `add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`unswap-sqr_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 59

Calls

8 calls:

8.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)))
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.im)
3.0ms	(cos.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series651.0ms (0.3%)

Counts

4 → 46

Calls

4 calls:

311.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)))
141.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
132.0ms	(cos.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re)))
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2558 to 1752 computations (31.5% saved)

simplify73.0ms (0%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5160	1640

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.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))
0.0b	(-.f64 (.f64 (log.f64 (+.f64 x.im (.f64 1/2 (/.f64 (/.f64 (pow.f64 x.re 2) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im))))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(.f64 1/2 (/.f64 (/.f64 (pow.f64 x.re 2) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
3.5b	(/.f64 (pow.f64 x.re 2) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
6.8b	(log.f64 (+.f64 x.im (.f64 1/2 (/.f64 (/.f64 (pow.f64 x.re 2) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.7b	(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)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-/l*_binary64` `times-frac_binary64`
7×	`add-cbrt-cube_binary64`
6×	`pow1_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64`
3×	`log-prod_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `log-div_binary64` `flip-+_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `cos-sum_binary64` `div-inv_binary64`

Counts

4 → 72

Calls

8 calls:

8.0ms	(/.f64 (pow.f64 x.re 2) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
7.0ms	(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	(log.f64 (+.f64 x.im (.f64 1/2 (/.f64 (/.f64 (pow.f64 x.re 2) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series686.0ms (0.4%)

Counts

4 → 35

Calls

4 calls:

269.0ms	(/.f64 (pow.f64 x.re 2) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
238.0ms	(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)))
132.0ms	(log.f64 (+.f64 x.im (.f64 1/2 (/.f64 (/.f64 (pow.f64 x.re 2) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))))
46.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3018 to 2092 computations (30.7% saved)

simplify78.0ms (0%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5025	2244

localize42.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.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))
0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
6.6b	(/.f64 (pow.f64 x.re 2) x.im)
16.6b	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
16.6b	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
9×	`add-exp-log_binary64`
8×	`associate-/l*_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64`
3×	`associate-/r*_binary64` `div-exp_binary64` `sqrt-prod_binary64`
2×	`sub-neg_binary64` `sin-sum_binary64` `cancel-sign-sub-inv_binary64` `cos-sum_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sin-diff_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `cos-diff_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 84

Calls

8 calls:

5.0ms	(/.f64 (pow.f64 x.re 2) x.im)
5.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
4.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series880.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

369.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
364.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
90.0ms	(/.f64 (pow.f64 x.re 2) x.im)
56.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4404 to 2952 computations (33% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4929	2412
1	4929	2412

prune29.6s (15.7%)

Pruning

470 alts after pruning (458 fresh and 12 done)

	Pruned	Kept	Total
New	406	210	616
Fresh	21	248	269
Picked	0	0	0
Done	0	12	12
Total	427	470	897

Error

3.9b

Counts

897 → 470

Compiler

Compiled 35750 to 20255 computations (43.3% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
0.0b	(exp.f64 (neg.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(exp.f64 (neg.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`rem-exp-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `exp-diff_binary64` `unswap-sqr_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `prod-exp_binary64` `exp-neg_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(exp.f64 (neg.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0ms	(exp.f64 (neg.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series164.0ms (0.1%)

Counts

2 → 19

Calls

2 calls:

101.0ms	(exp.f64 (neg.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
63.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 341 to 377 computations (-10.6% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4917	667
1	4917	667

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 26

Calls

4 calls:

4.0ms	(+.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)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series228.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

128.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
100.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

Compiler

Compiled 726 to 726 computations (0% saved)

simplify56.0ms (0%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5048	1184

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(*.f64 y.re (atan2.f64 x.im x.re))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))
0.0b	(*.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))
13.9b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
14.4b	(-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))))
14.8b	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
15.2b	(pow.f64 (-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))) y.re)

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
66×	`unpow-prod-down_binary64`
56×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`cube-prod_binary64`
22×	`sqr-pow_binary64`
17×	`add-exp-log_binary64`
12×	`associate-/r*_binary64`
9×	`add-log-exp_binary64` `div-exp_binary64`
8×	`unpow3_binary64` `cube-mult_binary64`
7×	`pow-to-exp_binary64` `associate-/l*_binary64` `pow-exp_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`pow-unpow_binary64`
2×	`diff-log_binary64` `associate-*r/_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `cancel-sign-sub-inv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 163

Calls

8 calls:

9.0ms	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
8.0ms	(-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))))
8.0ms	(pow.f64 (-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))) y.re)
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
0.0ms	(*.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))

series941.0ms (0.5%)

Counts

4 → 44

Calls

4 calls:

425.0ms	(-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))))
257.0ms	(pow.f64 (-.f64 (+.f64 x.im (.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))) (.f64 1/8 (/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3)))) y.re)
130.0ms	(/.f64 (pow.f64 x.re 4) (pow.f64 x.im 3))
128.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2605 to 1966 computations (24.5% saved)

simplify128.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4933	5146
1	4933	5146

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im)))
0.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 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))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
2.1b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.7b	(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)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
6×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`associate-r_binary64` `unswap-sqr_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

8 calls:

8.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
7.0ms	(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)))
5.0ms	(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)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series809.0ms (0.4%)

Counts

4 → 50

Calls

4 calls:

305.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
279.0ms	(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)))
144.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
81.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4019 to 2554 computations (36.5% saved)

simplify71.0ms (0%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4997	2195
1	4997	2195

localize45.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))
0.0b	(-.f64 (cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im))))) (.f64 1/2 (/.f64 (.f64 (/.f64 (pow.f64 x.re 2) (fabs.f64 x.im)) (.f64 y.im (sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (sqrt.f64 (pow.f64 x.im 2)))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
16.6b	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
16.6b	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
27.1b	(sqrt.f64 (pow.f64 x.im 2))
28.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`sqrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64` `rem-sqrt-square_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `unpow2_binary64` `sin-sum_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `cos-sum_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `cos-diff_binary64` `flip-+_binary64`

Counts

4 → 56

Calls

8 calls:

5.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
5.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(sqrt.f64 (pow.f64 x.im 2))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series889.0ms (0.5%)

Counts

4 → 40

Calls

4 calls:

383.0ms	(cos.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
363.0ms	(sin.f64 (-.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 (/.f64 -1 x.im)))))
118.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.0ms	(sqrt.f64 (pow.f64 x.im 2))

Compiler

Compiled 4631 to 3145 computations (32.1% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4917	1921
1	4917	1921

prune31.2s (16.5%)

Pruning

633 alts after pruning (617 fresh and 16 done)

	Pruned	Kept	Total
New	347	179	526
Fresh	15	438	453
Picked	0	0	0
Done	1	16	17
Total	363	633	996

Error

3.9b

Counts

996 → 633

Compiler

Compiled 13386 to 5878 computations (56.1% saved)

simplify1.5s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5021	98061

regimes47.3s (25%)

Compiler: Compiled 240596 to 166847 computations (30.7% saved)

bsearch229.0ms (0.1%)

Steps

Iters	Range		Point
10	3.050723552348764e-09	10355269.626937324	1.283027228318879
9	-1.5578992213074374	-5.6890314433992626e-08	-0.09612485582958105

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes648.0ms (0.3%)

Compiler: Compiled 2188 to 2264 computations (-3.5% saved)

bsearch142.0ms (0.1%)

Steps

Iters	Range		Point
10	3.050723552348764e-09	10355269.626937324	1.2326399240224684
9	-1.5578992213074374	-5.6890314433992626e-08	-0.12742787824649954

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes287.0ms (0.2%)

Compiler: Compiled 528 to 652 computations (-23.5% saved)

bsearch142.0ms (0.1%)

Steps

Iters	Range		Point
10	3.050723552348764e-09	10355269.626937324	1.0310907068368254
9	-1.5578992213074374	-5.6890314433992626e-08	-1.004260088703933

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes199.0ms (0.1%)

Compiler: Compiled 176 to 284 computations (-61.4% saved)

bsearch297.0ms (0.2%)

Steps

Iters	Range		Point
10	6.654413549334293e-21	3.360813302179667e-07	5.7069940823255305e-11
8	2.049193016602682e-249	2.660094616028826e-246	2.3595511341950196e-249
9	3.894192710684878e-287	1.7680999765633104e-280	9.883152837860138e-282
8	-2.9889729204483913e-77	-1.020412279260504e-79	-4.0101416291592097e-78
8	-2.1648341132595568e-35	-1.4080751851230472e-38	-1.8683306389997372e-37
6	-3.1543382781247202e-09	-3.778943519298702e-10	-3.109657661637387e-09

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes185.0ms (0.1%)

Compiler: Compiled 140 to 244 computations (-74.3% saved)

bsearch333.0ms (0.2%)

Steps

Iters	Range		Point
10	6.654413549334293e-21	3.360813302179667e-07	1.8086140243412983e-17
8	2.049193016602682e-249	2.660094616028826e-246	4.1627783980696043e-249
9	3.894192710684878e-287	1.7680999765633104e-280	8.515675588535299e-283
10	-9.57283209781698e-244	-9.351841186595983e-255	-3.011769076518427e-249
8	-7.999829410350478e-105	-4.952483514244431e-109	-2.4008345045284037e-107
8	-3.778943519298702e-10	-4.70903816938075e-14	-3.248272526850449e-10

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes183.0ms (0.1%)

Compiler: Compiled 108 to 204 computations (-88.9% saved)

bsearch216.0ms (0.1%)

Steps

Iters	Range		Point
10	6.654413549334293e-21	3.360813302179667e-07	3.3436903475398154e-14
10	-9.57283209781698e-244	-9.351841186595983e-255	-3.916832953433798e-254
8	-7.999829410350478e-105	-4.952483514244431e-109	-6.440102143888612e-105
8	-3.778943519298702e-10	-4.70903816938075e-14	-3.7199800756933404e-10

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes186.0ms (0.1%)

Compiler: Compiled 76 to 164 computations (-115.8% saved)

bsearch216.0ms (0.1%)

Steps

Iters	Range		Point
10	3.050723552348764e-09	10355269.626937324	3.0314203917512626e-06
9	8.788983934924534e-257	2.731793206933175e-251	4.3106573132595196e-256
8	1.011089848595497e-292	6.294625286891897e-290	4.188528826746926e-290
7	-5.6890314433992626e-08	-4.2790894681004497e-10	-2.0708852731958088e-08

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes32.0ms (0%)

Accuracy

Total 2.2b remaining (42.7%)

Threshold costs 0b (0%)

Compiler

Compiled 16 to 72 computations (-350% saved)

bsearch13.0ms (0%)

Compiler: Compiled 249 to 225 computations (9.6% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	192	356
1	192	356

end0.0ms (0%)

sample45.5s (24.1%)

Algorithm

1×

intervals

Results

1.6s	2459×	body	1024	invalid
884.0ms	7597×	body	128	valid
373.0ms	1009×	body	512	invalid
97.0ms	409×	body	256	invalid
90.0ms	164×	body	1024	valid
69.0ms	567×	body	128	invalid
49.0ms	135×	body	512	valid
29.0ms	37×	body	2048	invalid
22.0ms	90×	body	256	valid
11.0ms	14×	body	2048	valid

Compiler

Compiled 48528 to 33727 computations (30.5% saved)

Pareto

0.7713698250579906