Details

analyze1.5s (12.5%)

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)

sample135.0ms (1.1%)

Algorithm

1×

intervals

Results

51.0ms	85×	body	1024	invalid
29.0ms	238×	body	128	valid
13.0ms	33×	body	512	invalid
5.0ms	15×	body	256	invalid
4.0ms	7×	body	1024	valid
2.0ms	3×	body	2048	invalid
2.0ms	16×	body	128	invalid
2.0ms	4×	body	512	valid
2.0ms	6×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify161.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune19.0ms (0.2%)

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

36.8b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

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 (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))
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(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)))

rewrite30.0ms (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:

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)))
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))

series559.0ms (4.6%)

Counts

4 → 51

Calls

4 calls:

255.0ms	(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)))
137.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
93.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3422 to 2245 computations (34.4% saved)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4945	2028
1	4945	2028

prune212.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Error

22.1b

Counts

108 → 5

Compiler

Compiled 4480 to 1181 computations (73.6% 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))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.3b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
32.3b	(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)
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 (atan2.f64 x.im x.re) y.re))
0.0ms	(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))

series672.0ms (5.5%)

Counts

4 → 54

Calls

4 calls:

338.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
132.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
131.0ms	(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 2540 to 1844 computations (27.4% saved)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5039	2019

prune141.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

4.4b

Counts

120 → 8

Compiler

Compiled 3513 to 1189 computations (66.2% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
0.0b	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.im)) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(-.f64 (.f64 (log.f64 (neg.f64 x.im)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.im)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (.f64 (atan2.f64 x.im x.re) y.re)))
0.1b	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
0.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.3b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
9×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`log-pow_binary64`

Counts

4 → 62

Calls

8 calls:

4.0ms	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
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 (exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.im)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (.f64 (atan2.f64 x.im x.re) y.re)))

series423.0ms (3.5%)

Counts

4 → 34

Calls

4 calls:

171.0ms	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
124.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
64.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
64.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1312 to 977 computations (25.5% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5148	1176

prune84.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

4.4b

Counts

104 → 8

Compiler

Compiled 2348 to 463 computations (80.3% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
0.0b	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 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 (log.f64 (neg.f64 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 (exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 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)))))) (cos.f64 (.f64 (atan2.f64 x.im x.re) y.re)))
4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
19.3b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

8 calls:

2.0ms	(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))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
0.0ms	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 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)))))) (cos.f64 (.f64 (atan2.f64 x.im x.re) y.re)))

series607.0ms (5%)

Counts

4 → 28

Calls

4 calls:

167.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
161.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
153.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
125.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

Compiler

Compiled 1707 to 1028 computations (39.8% saved)

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4910	768
1	4910	768

prune69.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Error

4.4b

Counts

76 → 8

Compiler

Compiled 2220 to 253 computations (88.6% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	357	1421
1	357	1421

regimes384.0ms (3.2%)

Compiler: Compiled 2908 to 2016 computations (30.7% saved)

bsearch219.0ms (1.8%)

Steps

Iters	Range		Point
10	-2.0900747234974714e-303	2.790433275347491e-300	4.3354624121682e-310
8	-2.2018441581627254e-65	-9.670250962732699e-70	-1.0023614876036504e-65
6	-2493285051684366.5	-319741171256093.3	-326275111805596.6

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes328.0ms (2.7%)

Compiler: Compiled 2192 to 1560 computations (28.8% saved)

bsearch233.0ms (1.9%)

Steps

Iters	Range		Point
10	-2.0900747234974714e-303	2.790433275347491e-300	4.3354624121682e-310
8	-2.2018441581627254e-65	-9.670250962732699e-70	-9.834281750438918e-70
6	-2493285051684366.5	-319741171256093.3	-925944660526301.8

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes263.0ms (2.2%)

Compiler: Compiled 1600 to 1152 computations (28% saved)

bsearch214.0ms (1.8%)

Steps

Iters	Range		Point
10	-2.0900747234974714e-303	2.790433275347491e-300	4.3354624121682e-310
8	-2.2018441581627254e-65	-9.670250962732699e-70	-1.0162343325851357e-69
6	-2493285051684366.5	-319741171256093.3	-339342992904603.25

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes154.0ms (1.3%)

Compiler: Compiled 284 to 296 computations (-4.2% saved)

bsearch196.0ms (1.6%)

Steps

Iters	Range		Point
10	-2.0900747234974714e-303	2.790433275347491e-300	4.3354624121682e-310
8	-2.2018441581627254e-65	-9.670250962732699e-70	-1.8575264693177687e-69
6	-2493285051684366.5	-319741171256093.3	-339342992904603.25

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes127.0ms (1%)

Compiler: Compiled 140 to 192 computations (-37.1% saved)

bsearch264.0ms (2.2%)

Steps

Iters	Range		Point
10	2.3372972800024355e-05	32438381851594.934	0.0011869954206574697
9	4.155612138687374e-29	1.1739286950373954e-23	4.2003005748055775e-29
9	2.664181243983387e-69	8.780853057274785e-64	3.5192623145897594e-65
9	-1.190299236294038e-08	-9.496995252881928e-17	-1.7214144504141627e-15

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes150.0ms (1.2%)

Accuracy

Total 6.3b remaining (66.7%)

Threshold costs 0b (0%)

Compiler

Compiled 68 to 136 computations (-100% saved)

bsearch245.0ms (2%)

Steps

Iters	Range		Point
10	2.3372972800024355e-05	32438381851594.934	8.825529323851523e-05
5	1.268664387818345e-40	4.445456705749919e-40	1.2949051645648911e-40
9	3.1591285939219716e-60	5.629644129336155e-53	5.531442779259403e-53
10	-144906351.1093351	-0.010704970374718521	-0.010833561531639842

Compiler

Compiled 465 to 218 computations (53.1% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	249	899
1	249	899

end0.0ms (0%)

sample4.2s (34.9%)

Algorithm

1×

intervals

Results

1.3s	2387×	body	1024	invalid
909.0ms	7580×	body	128	valid
364.0ms	979×	body	512	invalid
105.0ms	189×	body	1024	valid
103.0ms	415×	body	256	invalid
69.0ms	556×	body	128	invalid
53.0ms	138×	body	512	valid
27.0ms	34×	body	2048	invalid
20.0ms	81×	body	256	valid
10.0ms	12×	body	2048	valid

Compiler

Compiled 1227 to 734 computations (40.2% saved)

Pareto

0.8924915478245478

Details

analyze1.5s (12.5%)

sample135.0ms (1.1%)

simplify161.0ms (1.3%)

prune19.0ms (0.2%)

localize25.0ms (0.2%)

rewrite30.0ms (0.2%)

series559.0ms (4.6%)

simplify105.0ms (0.9%)

prune212.0ms (1.7%)

localize21.0ms (0.2%)

rewrite21.0ms (0.2%)

series672.0ms (5.5%)

simplify63.0ms (0.5%)

prune141.0ms (1.2%)

localize17.0ms (0.1%)

rewrite19.0ms (0.2%)

series423.0ms (3.5%)

simplify88.0ms (0.7%)

prune84.0ms (0.7%)

localize22.0ms (0.2%)

rewrite9.0ms (0.1%)

series607.0ms (5%)

simplify73.0ms (0.6%)

prune69.0ms (0.6%)

simplify23.0ms (0.2%)

regimes384.0ms (3.2%)

bsearch219.0ms (1.8%)

regimes328.0ms (2.7%)

bsearch233.0ms (1.9%)

regimes263.0ms (2.2%)

bsearch214.0ms (1.8%)

regimes154.0ms (1.3%)

bsearch196.0ms (1.6%)

regimes127.0ms (1%)

bsearch264.0ms (2.2%)

regimes150.0ms (1.2%)

bsearch245.0ms (2%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample4.2s (34.9%)

Profiling