Details

analyze1.8s (11.6%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample145.0ms (0.9%)

Algorithm

1×

intervals

Results

47.0ms	70×	body	1024	invalid
36.0ms	247×	body	128	valid
18.0ms	29×	body	512	invalid
4.0ms	4×	body	2048	invalid
3.0ms	5×	body	1024	valid
2.0ms	6×	body	256	invalid
1.0ms	2×	body	512	valid
1.0ms	6×	body	128	invalid
1.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify187.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.6b	(sin.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)))

rewrite119.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

31.6b

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`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

15.0ms	(sin.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)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series1.0s (6.5%)

Error

20.0b

Counts

4 → 62

Calls

4 calls:

489.0ms	(sin.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)))
174.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
154.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
88.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6605 to 3384 computations (48.8% saved)

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5187	2488

prune232.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Error

19.9b

Counts

119 → 7

Compiler

Compiled 5130 to 1434 computations (72% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
16.5b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
28.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite83.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

19.9b

Rules

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

Counts

4 → 58

Calls

4 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)
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series501.0ms (3.3%)

Error

10.8b

Counts

4 → 45

Calls

4 calls:

148.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
126.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
94.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
89.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3282 to 1722 computations (47.5% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5145	1456

prune151.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Error

10.8b

Counts

110 → 10

Compiler

Compiled 3277 to 871 computations (73.4% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

28.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.6b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
32.6b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
32.6b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))

rewrite188.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

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×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 39

Calls

4 calls:

11.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
7.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
7.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (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)))

Compiler

Compiled 3576 to 1765 computations (50.6% saved)

series1.8s (12.1%)

Error

10.8b

Counts

4 → 69

Calls

4 calls:

517.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
465.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
421.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
207.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 15438 to 9074 computations (41.2% saved)

simplify164.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4953	3543
1	4953	3543

prune493.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	106	12	118

Error

10.8b

Counts

118 → 12

Compiler

Compiled 9347 to 4661 computations (50.1% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

16.4b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
16.5b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
28.1b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
28.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite153.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

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

Counts

4 → 46

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2418 to 747 computations (69.1% saved)

series738.0ms (4.8%)

Error

10.8b

Counts

4 → 54

Calls

4 calls:

195.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
168.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
160.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
143.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 6474 to 3400 computations (47.5% saved)

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5084	1645

prune169.0ms (1.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	100	12	112

Error

10.8b

Counts

112 → 12

Compiler

Compiled 4728 to 1531 computations (67.6% saved)

regimes895.0ms (5.8%)

Accuracy

Total 7.5b remaining (41.6%)

Threshold costs 0b (0%)

Compiler

Compiled 7907 to 4850 computations (38.7% saved)

bsearch265.0ms (1.7%)

Steps

Iters	Range	Point
8	3.4555507721665676e+151	1.1158112536071319e+156	1.353620561619206e+154
7	-1.6521557630999177e-306	3.1462273592031e-309	-5.103978518472407e-309
8	-1.0954685597694892e+129	-2.071338797913988e+125	-3.657601472007926e+126

Iters

Range

Point

3.4555507721665676e+151

1.1158112536071319e+156

1.353620561619206e+154

-1.6521557630999177e-306

3.1462273592031e-309

-5.103978518472407e-309

-1.0954685597694892e+129

-2.071338797913988e+125

-3.657601472007926e+126

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	116	218
1	116	218

end0.0ms (0%)

sample5.8s (38%)

Algorithm

1×

intervals

Results

1.6s	2509×	body	1024	invalid
1.1s	7619×	body	128	valid
411.0ms	926×	body	512	invalid
194.0ms	185×	body	2048	invalid
110.0ms	169×	body	1024	valid
93.0ms	336×	body	256	invalid
72.0ms	517×	body	128	invalid
62.0ms	137×	body	512	valid
18.0ms	64×	body	256	valid
14.0ms	11×	body	2048	valid

Compiler

Compiled 1714 to 1027 computations (40.1% saved)

Details

analyze1.8s (11.6%)

sample145.0ms (0.9%)

simplify187.0ms (1.2%)

prune8.0ms (0.1%)

localize50.0ms (0.3%)

rewrite119.0ms (0.8%)

series1.0s (6.5%)

simplify86.0ms (0.6%)

prune232.0ms (1.5%)

localize35.0ms (0.2%)

rewrite83.0ms (0.5%)

series501.0ms (3.3%)

simplify70.0ms (0.5%)

prune151.0ms (1%)

localize39.0ms (0.3%)

rewrite188.0ms (1.2%)

series1.8s (12.1%)

simplify164.0ms (1.1%)

prune493.0ms (3.2%)

localize31.0ms (0.2%)

rewrite153.0ms (1%)

series738.0ms (4.8%)

simplify62.0ms (0.4%)

prune169.0ms (1.1%)

regimes895.0ms (5.8%)

bsearch265.0ms (1.7%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample5.8s (38%)

Profiling