Details

analyze1.4s (16.6%)

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)

sample114.0ms (1.3%)

Algorithm

1×

intervals

Results

41.0ms	69×	body	1024	invalid
32.0ms	239×	body	128	valid
9.0ms	25×	body	512	invalid
5.0ms	9×	body	1024	valid
2.0ms	18×	body	128	invalid
2.0ms	5×	body	512	valid
2.0ms	7×	body	256	invalid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify242.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4949	72
1	4949	72

prune14.0ms (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

Merged error: 31.0b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(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 (0.4%)

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

4 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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
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)

series537.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

380.0ms	(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)))
55.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
51.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
51.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4807	1251
1	4807	1251

prune119.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 18.9b

Counts

69 → 6

Compiler

Compiled 3088 to 887 computations (71.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 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))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite27.0ms (0.3%)

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×	`add-log-exp_binary64` `associate-r_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` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 65

Calls

4 calls:

8.0ms	(.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 (.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))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series482.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(-.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))
148.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
46.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4910	1650
1	4910	1650

prune105.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 3.9b

Counts

83 → 8

Compiler

Compiled 2222 to 1099 computations (50.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.6b	(cbrt.f64 (atan2.f64 x.im x.re))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(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)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

7.0ms	(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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series503.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(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)))
75.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
41.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
39.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5020	1143

prune108.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	61	8	69

Merged error: 3.9b

Counts

69 → 8

Compiler

Compiled 3480 to 889 computations (74.5% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(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)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_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-r_binary64` `associate-l_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×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

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)))
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)

series471.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

337.0ms	(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)))
55.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
41.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
38.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5139	1281

prune123.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 3.9b

Counts

78 → 9

Compiler

Compiled 3102 to 1387 computations (55.3% saved)

regimes183.0ms (2.1%)

Compiler: Compiled 1408 to 976 computations (30.7% saved)

bsearch78.0ms (0.9%)

Steps

Iters	Range		Point
8	-2.7048063731127513e-306	6.969975571578694e-308	2.48163431909736e-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	63	53
1	63	53

end0.0ms (0%)

sample3.7s (42.2%)

Algorithm

1×

intervals

Results

1.3s	2445×	body	1024	invalid
843.0ms	7595×	body	128	valid
346.0ms	959×	body	512	invalid
98.0ms	431×	body	256	invalid
97.0ms	172×	body	1024	valid
69.0ms	589×	body	128	invalid
45.0ms	129×	body	512	valid
23.0ms	26×	body	2048	invalid
22.0ms	92×	body	256	valid
12.0ms	12×	body	2048	valid

Compiler

Compiled 415 to 278 computations (33% saved)

Details

analyze1.4s (16.6%)

sample114.0ms (1.3%)

simplify242.0ms (2.8%)

prune14.0ms (0.2%)

localize23.0ms (0.3%)

rewrite30.0ms (0.4%)

series537.0ms (6.2%)

simplify99.0ms (1.1%)

prune119.0ms (1.4%)

localize15.0ms (0.2%)

rewrite27.0ms (0.3%)

series482.0ms (5.6%)

simplify76.0ms (0.9%)

prune105.0ms (1.2%)

localize26.0ms (0.3%)

rewrite25.0ms (0.3%)

series503.0ms (5.8%)

simplify62.0ms (0.7%)

prune108.0ms (1.2%)

localize30.0ms (0.3%)

rewrite36.0ms (0.4%)

series471.0ms (5.4%)

simplify45.0ms (0.5%)

prune123.0ms (1.4%)

regimes183.0ms (2.1%)

bsearch78.0ms (0.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.7s (42.2%)

Profiling