Details

analyze1.5s (12.6%)

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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample123.0ms (1%)

Algorithm

1×

intervals

Results

45.0ms	74×	body	1024	invalid
30.0ms	241×	body	128	valid
12.0ms	31×	body	512	invalid
4.0ms	6×	body	1024	valid
3.0ms	7×	body	512	valid
3.0ms	20×	body	128	invalid
2.0ms	8×	body	256	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify162.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune19.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

32.5b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize24.0ms (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.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)
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(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 (0.2%)

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:

9.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series575.0ms (4.7%)

Counts

4 → 49

Calls

4 calls:

297.0ms	(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)))
141.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
62.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3385 to 2219 computations (34.4% saved)

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4952	2091
1	4952	2091

prune214.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	5	107

Error

21.4b

Counts

107 → 5

Compiler

Compiled 4425 to 1161 computations (73.8% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

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 (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 (atan2.f64 x.im x.re) y.re)))
0.0b	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.2b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

8 calls:

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

series642.0ms (5.3%)

Counts

4 → 55

Calls

4 calls:

297.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
141.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
132.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2542 to 1844 computations (27.5% saved)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5338	2079

prune145.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	112	9	121

Error

3.8b

Counts

121 → 9

Compiler

Compiled 3590 to 1213 computations (66.2% saved)

localize32.0ms (0.3%)

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))
0.8b	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(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)))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

8 calls:

11.0ms	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
6.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series579.0ms (4.8%)

Counts

4 → 49

Calls

4 calls:

281.0ms	(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)))
140.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
96.0ms	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
62.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3847 to 2425 computations (37% saved)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5155	2224

prune166.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Error

3.8b

Counts

120 → 9

Compiler

Compiled 5336 to 1256 computations (76.5% saved)

localize42.0ms (0.3%)

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)))) (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 (atan2.f64 x.im x.re) y.re))))))
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))
0.8b	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
29.4b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(cos.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)))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
13×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`cbrt-prod_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×	`associate-l_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 64

Calls

8 calls:

11.0ms	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
7.0ms	(cos.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))

series594.0ms (4.9%)

Counts

4 → 49

Calls

4 calls:

276.0ms	(cos.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)))
152.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
102.0ms	(.f64 (.f64 (atan2.f64 x.im x.re) (*.f64 (cbrt.f64 y.im) (cbrt.f64 y.im))) (cbrt.f64 y.im))
65.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 4011 to 2763 computations (31.1% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5155	2254

prune208.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Error

3.8b

Counts

122 → 9

Compiler

Compiled 5404 to 2050 computations (62.1% saved)

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	404	1798
1	404	1798

regimes416.0ms (3.4%)

Accuracy

Total 6.3b remaining (67.7%)

Threshold costs 0b (0%)

Compiler

Compiled 3676 to 2532 computations (31.1% saved)

bsearch98.0ms (0.8%)

Steps

Iters	Range		Point
10	-9.990562879975715e-301	3.5972117313813e-304	-3.1333140596047e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	81
1	65	81

end0.0ms (0%)

sample6.1s (50.4%)

Algorithm

1×

intervals

Results

1.3s	2463×	body	1024	invalid
926.0ms	7617×	body	128	valid
380.0ms	1006×	body	512	invalid
107.0ms	446×	body	256	invalid
85.0ms	159×	body	1024	valid
70.0ms	561×	body	128	invalid
50.0ms	136×	body	512	valid
35.0ms	44×	body	2048	invalid
19.0ms	78×	body	256	valid
9.0ms	10×	body	2048	valid

Compiler

Compiled 2871 to 1943 computations (32.3% saved)

Pareto

0.008023196708689648

Details

analyze1.5s (12.6%)

sample123.0ms (1%)

simplify162.0ms (1.3%)

prune19.0ms (0.2%)

localize24.0ms (0.2%)

rewrite29.0ms (0.2%)

series575.0ms (4.7%)

simplify106.0ms (0.9%)

prune214.0ms (1.8%)

localize21.0ms (0.2%)

rewrite21.0ms (0.2%)

series642.0ms (5.3%)

simplify62.0ms (0.5%)

prune145.0ms (1.2%)

localize32.0ms (0.3%)

rewrite35.0ms (0.3%)

series579.0ms (4.8%)

simplify63.0ms (0.5%)

prune166.0ms (1.4%)

localize42.0ms (0.3%)

rewrite41.0ms (0.3%)

series594.0ms (4.9%)

simplify61.0ms (0.5%)

prune208.0ms (1.7%)

simplify28.0ms (0.2%)

regimes416.0ms (3.4%)

bsearch98.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (50.4%)

Profiling