Details

analyze2.3s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample152.0ms (0.8%)

Algorithm

1×

intervals

Results

48.0ms	70×	body	1024	invalid
43.0ms	247×	body	128	valid
14.0ms	29×	body	512	invalid
4.0ms	4×	body	2048	invalid
3.0ms	5×	body	1024	valid
2.0ms	6×	body	256	invalid
1.0ms	6×	body	128	invalid
1.0ms	2×	body	512	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify224.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune18.0ms (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)

localize46.0ms (0.2%)

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 (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))) (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))))
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))
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)))

rewrite53.0ms (0.3%)

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

8 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)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series1.0s (5.1%)

Counts

4 → 62

Calls

4 calls:

519.0ms	(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)))
217.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
177.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
128.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 4212 to 2768 computations (34.3% saved)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5187	2488

prune342.0ms (1.7%)

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 1433 computations (72.1% saved)

localize20.0ms (0.1%)

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

rewrite28.0ms (0.1%)

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:

6.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
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))) (sin.f64 (.f64 (atan2.f64 x.im x.re) y.re)))

series485.0ms (2.4%)

Counts

4 → 45

Calls

4 calls:

184.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
133.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
90.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
78.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 2122 to 1494 computations (29.6% saved)

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5121	1456

prune233.0ms (1.1%)

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)

localize67.0ms (0.3%)

Local error

Found 8 expressions with local error:

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))
0.0b	(+.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 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.6b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.6b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_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×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

8 calls:

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

series1.9s (9.5%)

Counts

4 → 69

Calls

4 calls:

596.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
541.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
515.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
271.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 9939 to 6498 computations (34.6% saved)

simplify153.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4953	3543
1	4953	3543

prune606.0ms (3%)

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)

localize54.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (sin.f64 (.f64 (atan2.f64 x.im x.re) y.re)) (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (.f64 y.im (cos.f64 (.f64 (atan2.f64 x.im x.re) 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 x.re x.re) (.f64 x.im x.im))
0.0b	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
16.4b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
16.5b	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.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)))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `flip-+_binary64`

Counts

4 → 46

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)))
2.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
2.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
0.0ms	(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))

series794.0ms (3.9%)

Counts

4 → 54

Calls

4 calls:

220.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
197.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
191.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
186.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

Compiler

Compiled 4032 to 2676 computations (33.6% saved)

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5084	1645

prune263.0ms (1.3%)

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)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	290	2096
1	290	2096

regimes801.0ms (3.9%)

Accuracy

Total 11.6b remaining (53.5%)

Threshold costs 0b (0%)

Compiler

Compiled 4284 to 2868 computations (33.1% saved)

bsearch325.0ms (1.6%)

Steps

Iters	Range	Point
5	6.2732264945086444e-46	2.0967248840614313e-45	6.5533082775056296e-46
9	1.6200153387709363e-193	2.853343438117141e-188	9.075984131776858e-190
9	-2.6846170462999737e-266	-8.267531271069666e-273	-5.76352593355014e-271

Iters

Range

Point

6.2732264945086444e-46

2.0967248840614313e-45

6.5533082775056296e-46

1.6200153387709363e-193

2.853343438117141e-188

9.075984131776858e-190

-2.6846170462999737e-266

-8.267531271069666e-273

-5.76352593355014e-271

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	89	194
1	89	194

end0.0ms (0%)

sample9.9s (48.7%)

Algorithm

1×

intervals

Results

2.0s	2509×	body	1024	invalid
1.3s	7619×	body	128	valid
511.0ms	926×	body	512	invalid
237.0ms	185×	body	2048	invalid
132.0ms	169×	body	1024	valid
125.0ms	336×	body	256	invalid
90.0ms	517×	body	128	invalid
74.0ms	137×	body	512	valid
23.0ms	64×	body	256	valid
15.0ms	11×	body	2048	valid

Compiler

Compiled 3443 to 2233 computations (35.1% saved)

Pareto

-0.09325968107776186

Details

analyze2.3s (11.3%)

sample152.0ms (0.8%)

simplify224.0ms (1.1%)

prune18.0ms (0.1%)

localize46.0ms (0.2%)

rewrite53.0ms (0.3%)

series1.0s (5.1%)

simplify142.0ms (0.7%)

prune342.0ms (1.7%)

localize20.0ms (0.1%)

rewrite28.0ms (0.1%)

series485.0ms (2.4%)

simplify118.0ms (0.6%)

prune233.0ms (1.1%)

localize67.0ms (0.3%)

rewrite37.0ms (0.2%)

series1.9s (9.5%)

simplify153.0ms (0.8%)

prune606.0ms (3%)

localize54.0ms (0.3%)

rewrite28.0ms (0.1%)

series794.0ms (3.9%)

simplify104.0ms (0.5%)

prune263.0ms (1.3%)

simplify50.0ms (0.2%)

regimes801.0ms (3.9%)

bsearch325.0ms (1.6%)

simplify9.0ms (0%)

end0.0ms (0%)

sample9.9s (48.7%)

Profiling