Details

analyze1.4s (11.8%)

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)

sample122.0ms (1%)

Algorithm

1×

intervals

Results

46.0ms	80×	body	1024	invalid
27.0ms	242×	body	128	valid
12.0ms	35×	body	512	invalid
4.0ms	7×	body	1024	valid
3.0ms	12×	body	256	invalid
2.0ms	3×	body	2048	invalid
2.0ms	17×	body	128	invalid
1.0ms	3×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify160.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

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

33.7b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.9b	(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)))

rewrite103.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

33.7b

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×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 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)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series712.0ms (5.8%)

Error

21.5b

Counts

4 → 54

Calls

4 calls:

327.0ms	(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)))
147.0ms	(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 5790 to 2933 computations (49.3% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5090	2235

prune159.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Error

21.5b

Counts

112 → 8

Compiler

Compiled 4796 to 1314 computations (72.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(*.f64 y.re (atan2.f64 x.im x.re))
1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
18.9b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite73.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

21.5b

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 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series432.0ms (3.5%)

Error

3.2b

Counts

4 → 45

Calls

4 calls:

131.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
117.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
71.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3270 to 1723 computations (47.3% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	1447

prune117.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Error

3.2b

Counts

111 → 10

Compiler

Compiled 3259 to 855 computations (73.8% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

29.5b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
34.9b	(cos.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)))))))
34.9b	(cos.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)))))))
34.9b	(cos.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)))))))

rewrite174.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cos-sum_binary64`
2×	`sqrt-div_binary64` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 41

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
7.0ms	(cos.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	(cos.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)))))))
6.0ms	(cos.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)))))))

Compiler

Compiled 3740 to 1859 computations (50.3% saved)

series1.3s (11%)

Error

3.1b

Counts

4 → 57

Calls

4 calls:

372.0ms	(cos.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)))))))
357.0ms	(cos.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)))))))
350.0ms	(cos.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)))))))
113.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 13163 to 7526 computations (42.8% saved)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5042	3108

prune329.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	97	11	108

Error

3.1b

Counts

108 → 11

Compiler

Compiled 8402 to 3882 computations (53.8% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.5b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.9b	(cos.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)))))))

rewrite135.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_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-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
6.0ms	(cos.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)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2850 to 1225 computations (57% saved)

series698.0ms (5.7%)

Error

3.1b

Counts

4 → 53

Calls

4 calls:

290.0ms	(cos.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)))))))
149.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
94.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
83.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6037 to 3705 computations (38.6% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5063	2192

prune187.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	8	9
Picked	1	0	1
Done	1	0	1
Total	112	10	122

Error

3.1b

Counts

122 → 10

Compiler

Compiled 4817 to 2093 computations (56.5% saved)

regimes903.0ms (7.4%)

Accuracy

Total 5.8b remaining (63.3%)

Threshold costs 0b (0%)

Compiler

Compiled 8437 to 5325 computations (36.9% saved)

bsearch225.0ms (1.8%)

Steps

Iters	Range	Point
10	-3.8466135451263836e-302	7.634085012861782e-305	-2.6381424290801e-310
8	-2.97254989460645e-206	-4.920538051693623e-211	-1.558725057380641e-207
7	-2.0344027908684668e+83	-5.200238348771135e+81	-5.278865873276349e+81

Iters

Range

Point

-3.8466135451263836e-302

7.634085012861782e-305

-2.6381424290801e-310

-2.97254989460645e-206

-4.920538051693623e-211

-1.558725057380641e-207

-2.0344027908684668e+83

-5.200238348771135e+81

-5.278865873276349e+81

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	195
1	90	195

end0.0ms (0%)

sample4.5s (36.8%)

Algorithm

1×

intervals

Results

1.2s	2432×	body	1024	invalid
813.0ms	7593×	body	128	valid
344.0ms	963×	body	512	invalid
97.0ms	437×	body	256	invalid
95.0ms	184×	body	1024	valid
67.0ms	551×	body	128	invalid
47.0ms	129×	body	512	valid
24.0ms	32×	body	2048	invalid
17.0ms	77×	body	256	valid
14.0ms	17×	body	2048	valid

Compiler

Compiled 1808 to 1115 computations (38.3% saved)

Details

analyze1.4s (11.8%)

sample122.0ms (1%)

simplify160.0ms (1.3%)

prune8.0ms (0.1%)

localize31.0ms (0.3%)

rewrite103.0ms (0.8%)

series712.0ms (5.8%)

simplify75.0ms (0.6%)

prune159.0ms (1.3%)

localize17.0ms (0.1%)

rewrite73.0ms (0.6%)

series432.0ms (3.5%)

simplify65.0ms (0.5%)

prune117.0ms (1%)

localize39.0ms (0.3%)

rewrite174.0ms (1.4%)

series1.3s (11%)

simplify74.0ms (0.6%)

prune329.0ms (2.7%)

localize32.0ms (0.3%)

rewrite135.0ms (1.1%)

series698.0ms (5.7%)

simplify72.0ms (0.6%)

prune187.0ms (1.5%)

regimes903.0ms (7.4%)

bsearch225.0ms (1.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.5s (36.8%)

Profiling