Details

analyze1.6s (1%)

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)

sample161.0ms (0.1%)

Algorithm

1×

intervals

Results

53.0ms	66×	body	1024	invalid
43.0ms	244×	body	128	valid
18.0ms	33×	body	512	invalid
4.0ms	11×	body	256	invalid
3.0ms	4×	body	1024	valid
3.0ms	5×	body	512	valid
3.0ms	15×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify231.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (0%)

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

34.3b

Counts

2 → 2

Compiler

Compiled 36 to 19 computations (47.2% saved)

localize37.0ms (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))
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(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)))

rewrite52.0ms (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:

22.0ms	(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	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series584.0ms (0.3%)

Counts

4 → 49

Calls

4 calls:

307.0ms	(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)))
105.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
103.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3316 to 2169 computations (34.6% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4945	1979
1	4945	1979

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

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	(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	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(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))))

rewrite24.0ms (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:

6.0ms	(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))))
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	(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))

series545.0ms (0.3%)

Counts

4 → 53

Calls

4 calls:

229.0ms	(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))))
142.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
102.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
72.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3442 to 2253 computations (34.5% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4945	2077
1	4945	2077

prune1.3s (0.8%)

Pruning

75 alts after pruning (73 fresh and 2 done)

	Pruned	Kept	Total
New	141	73	214
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	141	75	216

Error

19.5b

Counts

216 → 75

Compiler

Compiled 9224 to 3565 computations (61.4% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
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))
1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
15.8b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite20.0ms (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)
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
1.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series397.0ms (0.2%)

Counts

4 → 45

Calls

4 calls:

134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
127.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
70.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
67.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2114 to 1494 computations (29.3% saved)

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5121	1447

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

1.1b	(*.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))
1.1b	(*.f64 y.re (atan2.f64 x.im x.re))
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
15.8b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite18.0ms (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)
3.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series387.0ms (0.2%)

Counts

4 → 45

Calls

4 calls:

131.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
122.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
68.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
66.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2036 to 1416 computations (30.5% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	1447

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) 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 (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 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
7.8b	(log.f64 (+.f64 x.re (*.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
7.8b	(/.f64 (pow.f64 x.im 2) x.re)
15.8b	(cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite29.0ms (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:

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

series496.0ms (0.3%)

Counts

4 → 38

Calls

4 calls:

252.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
103.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
75.0ms	(/.f64 (pow.f64 x.im 2) x.re)
66.0ms	(log.f64 (+.f64 x.re (*.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))

Compiler

Compiled 2872 to 2009 computations (30% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5009	2452

localize42.0ms (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 (pow.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(.f64 (/.f64 (pow.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) 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))
12.4b	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
19.4b	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(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))))

rewrite60.0ms (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:

16.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
8.0ms	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
6.0ms	(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))))
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))

series837.0ms (0.5%)

Counts

4 → 42

Calls

4 calls:

411.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
244.0ms	(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))))
133.0ms	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
48.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3329 to 2368 computations (28.9% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4968	4769
1	4968	4769

localize29.0ms (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 y.re (atan2.f64 x.im x.re)))
0.0b	(exp.f64 (.f64 (.f64 (sqrt.f64 (atan2.f64 x.im x.re)) (sqrt.f64 y.im)) (*.f64 (sqrt.f64 (atan2.f64 x.im x.re)) (sqrt.f64 y.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))
4.1b	(sqrt.f64 (atan2.f64 x.im x.re))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(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))))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`cos-sum_binary64`

Counts

4 → 51

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))))
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)))
1.0ms	(sqrt.f64 (atan2.f64 x.im x.re))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series445.0ms (0.3%)

Counts

4 → 38

Calls

4 calls:

239.0ms	(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))))
114.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
50.0ms	(sqrt.f64 (atan2.f64 x.im x.re))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3282 to 1899 computations (42.1% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4947	1642
1	4947	1642

prune11.4s (6.8%)

Pruning

268 alts after pruning (261 fresh and 7 done)

	Pruned	Kept	Total
New	431	194	625
Fresh	1	67	68
Picked	0	0	0
Done	0	7	7
Total	432	268	700

Error

2.8b

Counts

700 → 268

Compiler

Compiled 27390 to 13242 computations (51.7% saved)

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
15.8b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
31.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
31.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
31.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
15×	`sqrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64` `unpow-prod-down_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 58

Calls

8 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
1.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
0.0ms	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))

series515.0ms (0.3%)

Counts

4 → 51

Calls

4 calls:

150.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
125.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
121.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
119.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 3884 to 3012 computations (22.5% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4957	1781
1	4957	1781

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b	(*.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 (.f64 x.re x.re) (.f64 x.im x.im))
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `+-commutative_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 54

Calls

8 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)))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.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))

series367.0ms (0.2%)

Counts

4 → 51

Calls

4 calls:

131.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
93.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
82.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
61.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1692 to 1405 computations (17% saved)

simplify75.0ms (0%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4979	1515
1	4979	1515

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im))
0.0b	(.f64 (exp.f64 (-.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))) (cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) 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 x.im (*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im)))
7.8b	(log.f64 (+.f64 x.re (*.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
7.8b	(/.f64 (pow.f64 x.im 2) x.re)
8.0b	(/.f64 (pow.f64 x.re 2) x.im)
15.8b	(cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

8 calls:

8.0ms	(/.f64 (pow.f64 x.re 2) x.im)
5.0ms	(/.f64 (pow.f64 x.im 2) x.re)
5.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
3.0ms	(log.f64 (+.f64 x.re (*.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
0.0ms	(+.f64 x.im (*.f64 1/2 (/.f64 (pow.f64 x.re 2) x.im)))

series487.0ms (0.3%)

Counts

4 → 30

Calls

4 calls:

266.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
82.0ms	(/.f64 (pow.f64 x.re 2) x.im)
72.0ms	(/.f64 (pow.f64 x.im 2) x.re)
67.0ms	(log.f64 (+.f64 x.re (*.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))

Compiler

Compiled 2540 to 1823 computations (28.2% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5066	2711

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 y.im (cbrt.f64 (atan2.f64 x.im x.re)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (.f64 (cbrt.f64 (atan2.f64 x.im x.re)) (cbrt.f64 (atan2.f64 x.im x.re))) (.f64 y.im (cbrt.f64 (atan2.f64 x.im x.re)))))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
4.5b	(cbrt.f64 (atan2.f64 x.im x.re))
4.5b	(cbrt.f64 (atan2.f64 x.im x.re))
15.8b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

8 calls:

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

series573.0ms (0.3%)

Counts

4 → 39

Calls

4 calls:

158.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
150.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
137.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
128.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

Compiler

Compiled 2564 to 1536 computations (40.1% saved)

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5069	1159

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (/.f64 (pow.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (log.f64 (exp.f64 (cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.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 (pow.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
12.4b	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
19.4b	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
31.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.4b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite70.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
65×	`unpow-prod-down_binary64`
60×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
56×	`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` `sqrt-prod_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `distribute-lft-out_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 → 166

Calls

8 calls:

19.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
7.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
0.0ms	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))

series839.0ms (0.5%)

Counts

4 → 42

Calls

4 calls:

416.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
239.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
133.0ms	(/.f64 (pow.f64 x.im 4) (pow.f64 x.re 3))
50.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 3473 to 2584 computations (25.6% saved)

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4938	4733
1	4938	4733

prune25.6s (15.2%)

Pruning

431 alts after pruning (419 fresh and 12 done)

	Pruned	Kept	Total
New	482	173	655
Fresh	10	246	256
Picked	0	0	0
Done	0	12	12
Total	492	431	923

Error

2.8b

Counts

923 → 431

Compiler

Compiled 35653 to 21989 computations (38.3% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
0.3b	(.f64 (log.f64 (fabs.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))) y.re)
0.0b	(-.f64 (.f64 (log.f64 (fabs.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))
1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
15.8b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
31.2b	(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))

series335.0ms (0.2%)

Counts

4 → 39

Calls

4 calls:

119.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
75.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
73.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 1910 to 1356 computations (29% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5119	1249

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

31.2b	(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))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite10.0ms (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)))

series203.0ms (0.1%)

Counts

2 → 33

Calls

2 calls:

121.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
81.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

Compiler

Compiled 726 to 726 computations (0% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4947	1034
1	4947	1034

localize25.0ms (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 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im)))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
25.1b	(cos.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_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-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

8 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
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)
2.0ms	(cos.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series484.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

197.0ms	(cos.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im))
111.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
100.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
75.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2750 to 2152 computations (21.7% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4996	1736
1	4996	1736

localize45.0ms (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 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im (/.f64 4 2)) (/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2)))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) 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 (pow.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im (/.f64 4 2)) (/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2)))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re)))) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
12.4b	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im (/.f64 4 2)) (/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2)))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
15.3b	(/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.4b	(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))))

rewrite118.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
66×	`unpow-prod-down_binary64`
60×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`cube-prod_binary64`
22×	`sqr-pow_binary64`
16×	`add-exp-log_binary64`
13×	`unpow2_binary64`
12×	`associate-/l*_binary64`
9×	`add-log-exp_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
8×	`associate-/r*_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 → 177

Calls

8 calls:

69.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im (/.f64 4 2)) (/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2)))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
8.0ms	(/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2))
6.0ms	(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))))
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))

series824.0ms (0.5%)

Counts

4 → 42

Calls

4 calls:

409.0ms	(-.f64 (.f64 1/8 (/.f64 (pow.f64 x.im (/.f64 4 2)) (/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2)))) (+.f64 x.re (.f64 1/2 (/.f64 (pow.f64 x.im 2) x.re))))
253.0ms	(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))))
110.0ms	(/.f64 (pow.f64 x.re 3) (pow.f64 x.im 2))
51.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3617 to 2608 computations (27.9% saved)

simplify114.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	4810
1	4971	4810

localize37.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 x.im 2)) (cbrt.f64 (pow.f64 x.im 2))) (sqrt.f64 x.re)) (/.f64 (cbrt.f64 (pow.f64 x.im 2)) (sqrt.f64 x.re)))
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	(.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 x.re (.f64 1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 x.im 2)) (cbrt.f64 (pow.f64 x.im 2))) (sqrt.f64 x.re)) (/.f64 (cbrt.f64 (pow.f64 x.im 2)) (sqrt.f64 x.re)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))
31.2b	(cbrt.f64 (pow.f64 x.im 2))
31.2b	(cbrt.f64 (pow.f64 x.im 2))
31.2b	(cbrt.f64 (pow.f64 x.im 2))
31.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

8 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(cbrt.f64 (pow.f64 x.im 2))
2.0ms	(cbrt.f64 (pow.f64 x.im 2))
2.0ms	(cbrt.f64 (pow.f64 x.im 2))
0.0ms	(.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 x.re (.f64 1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 x.im 2)) (cbrt.f64 (pow.f64 x.im 2))) (sqrt.f64 x.re)) (/.f64 (cbrt.f64 (pow.f64 x.im 2)) (sqrt.f64 x.re)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))))

series376.0ms (0.2%)

Counts

4 → 23

Calls

4 calls:

127.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
89.0ms	(cbrt.f64 (pow.f64 x.im 2))
82.0ms	(cbrt.f64 (pow.f64 x.im 2))
79.0ms	(cbrt.f64 (pow.f64 x.im 2))

Compiler

Compiled 2120 to 1522 computations (28.2% saved)

simplify55.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5055	1028

prune28.8s (17.1%)

Pruning

591 alts after pruning (575 fresh and 16 done)

	Pruned	Kept	Total
New	383	183	566
Fresh	22	392	414
Picked	0	0	0
Done	1	16	17
Total	406	591	997

Error

2.8b

Counts

997 → 591

Compiler

Compiled 14475 to 6682 computations (53.8% saved)

simplify1.8s (1.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5053	99575

regimes27.5s (16.3%)

Compiler: Compiled 245971 to 174222 computations (29.2% saved)

bsearch188.0ms (0.1%)

Steps

Iters	Range		Point
3	7.485832770081977e-56	1.0011540738404607e-55	8.213506235332776e-56
7	-6.6478224099761884e+103	-9.301590631095428e+101	-9.437066424131207e+101

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes608.0ms (0.4%)

Compiler: Compiled 4264 to 3860 computations (9.5% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
3	-112325087553573.72	-78864955021725.7	-80956213304966.22

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes1.1s (0.6%)

Compiler: Compiled 4188 to 3804 computations (9.2% saved)

bsearch197.0ms (0.1%)

Steps

Iters	Range		Point
3	7.485832770081977e-56	1.0011540738404607e-55	8.213506235332776e-56
9	1.9095769352958856e-140	1.8833972208446976e-135	6.050372847421959e-137
8	-3.915659362676596e-306	3.3491533533387655e-307	-2.6615346232889e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes888.0ms (0.5%)

Compiler: Compiled 3284 to 2984 computations (9.1% saved)

bsearch252.0ms (0.1%)

Steps

Iters	Range		Point
3	7.485832770081977e-56	1.0011540738404607e-55	7.585723575808189e-56
9	1.9095769352958856e-140	1.8833972208446976e-135	5.2362255579481547e-138
8	-3.915659362676596e-306	3.3491533533387655e-307	8.8604533274285e-310
8	-3.9015081324143217e-29	-3.646830102185637e-33	-1.9239150977086479e-31

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes870.0ms (0.5%)

Compiler: Compiled 2920 to 2720 computations (6.8% saved)

bsearch426.0ms (0.3%)

Steps

Iters	Range		Point
8	1.127764409763547e-91	8.970418581825754e-88	1.0099943610527774e-89
9	1.0494697433290072e-163	1.2520286740487143e-157	1.1180088059793839e-163
10	-1.7491402500417026e-304	9.280213698582033e-299	2.107910171741242e-304
8	-3.0635695679673836e-270	-1.4176318963701347e-274	-3.0103639225785356e-270
7	-2.0146251141338312e-215	-8.031731115918593e-217	-3.337876888210069e-216
3	-1.5078487050365128e-191	-1.2536460616856681e-191	-1.432227224093284e-191
7	-2.311849759883921e+66	-7.266055324680505e+64	-6.236497842777764e+65

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes508.0ms (0.3%)

Compiler: Compiled 1448 to 1472 computations (-1.7% saved)

bsearch239.0ms (0.1%)

Steps

Iters	Range		Point
9	3.0659979301545097e-06	0.38767664572984284	0.383540112365557
7	1.849725606459231e-151	2.005130727836764e-149	2.2969899053499743e-151
2	-4.825978818016433e-270	-4.033641851884393e-270	-4.528852455716918e-270
8	-9.202900525937869e-117	-7.237486307090217e-120	-3.250382936462931e-117
8	-1.8660232343950614e+35	-3.930779446528964e+32	-3.987264733662572e+32

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes472.0ms (0.3%)

Compiler: Compiled 1220 to 1292 computations (-5.9% saved)

bsearch234.0ms (0.1%)

Steps

Iters	Range		Point
9	3.0659979301545097e-06	0.38767664572984284	0.2511710447084123
7	1.849725606459231e-151	2.005130727836764e-149	1.749782679206405e-150
2	-4.825978818016433e-270	-4.033641851884393e-270	-4.3307682141839085e-270
8	-9.202900525937869e-117	-7.237486307090217e-120	-4.159872953407092e-119
8	-1.8660232343950614e+35	-3.930779446528964e+32	-3.987264733662572e+32

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes162.0ms (0.1%)

Accuracy

Total 2.3b remaining (42.3%)

Threshold costs 0b (0%)

Compiler

Compiled 140 to 244 computations (-74.3% saved)

bsearch212.0ms (0.1%)

Steps

Iters	Range		Point
9	3.0659979301545097e-06	0.38767664572984284	1.1269981410690433e-05
6	2.0653943270987655e-131	8.510787908268941e-131	2.0834915756950648e-131
7	1.849725606459231e-151	2.005130727836764e-149	1.7459411491827386e-149
8	-1.8660232343950614e+35	-3.930779446528964e+32	-3.987264733662572e+32

Compiler

Compiled 555 to 298 computations (46.3% saved)

simplify17.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	241	896
1	241	896

end0.0ms (0%)

sample52.6s (31.2%)

Algorithm

1×

intervals

Results

1.2s	2371×	body	1024	invalid
853.0ms	7576×	body	128	valid
370.0ms	1019×	body	512	invalid
105.0ms	205×	body	1024	valid
97.0ms	420×	body	256	invalid
64.0ms	547×	body	128	invalid
40.0ms	114×	body	512	valid
28.0ms	33×	body	2048	invalid
20.0ms	86×	body	256	valid
15.0ms	19×	body	2048	valid

Compiler

Compiled 50606 to 35611 computations (29.6% saved)

Pareto

0.3631703024591112