Details

analyze1.5s (17.5%)

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)

sample123.0ms (1.5%)

Algorithm

1×

intervals

Results

48.0ms	82×	body	1024	invalid
29.0ms	243×	body	128	valid
13.0ms	37×	body	512	invalid
3.0ms	8×	body	512	valid
3.0ms	26×	body	128	invalid
3.0ms	12×	body	256	invalid
2.0ms	4×	body	1024	valid
2.0ms	2×	body	2048	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify210.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

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

Merged error: 32.0b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(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)))

rewrite28.0ms (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` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_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)

series278.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(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)))
25.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify117.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4863	1251
1	4863	1251

prune112.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 16.2b

Counts

70 → 5

Compiler

Compiled 3006 to 826 computations (72.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 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)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.2b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 69

Calls

4 calls:

6.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
5.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series254.0ms (3%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(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)))
71.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	1596
1	4953	1596

prune103.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 3.3b

Counts

86 → 8

Compiler

Compiled 2178 to 1029 computations (52.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.8b	(cbrt.f64 (atan2.f64 x.im x.re))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(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)))

rewrite23.0ms (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)))
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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series272.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(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)))
43.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4870	1143
1	4870	1143

prune102.0ms (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: 3.3b

Counts

69 → 8

Compiler

Compiled 3394 to 833 computations (75.5% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

4.8b	(cbrt.f64 (atan2.f64 x.im x.re))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.2b	(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)))

rewrite24.0ms (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)))
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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series274.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(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)))
44.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4870	1143
1	4870	1143

prune102.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	60	9	69

Merged error: 3.3b

Counts

69 → 9

Compiler

Compiled 3985 to 720 computations (81.9% saved)

regimes416.0ms (4.9%)

Compiler: Compiled 3837 to 2500 computations (34.8% saved)

bsearch240.0ms (2.8%)

Steps

Iters	Range	Point
9	-2.6378467169733085e-303	9.88395856728751e-308	-3.36918648162485e-310
8	-2.2810350029924174e-150	-2.5726787852147576e-153	-3.0746072600574835e-153
7	-3.110177977605169e-50	-1.6038460653286676e-51	-2.64822747959788e-50

Iters

Range

Point

-2.6378467169733085e-303

9.88395856728751e-308

-3.36918648162485e-310

-2.2810350029924174e-150

-2.5726787852147576e-153

-3.0746072600574835e-153

-3.110177977605169e-50

-1.6038460653286676e-51

-2.64822747959788e-50

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	153
1	90	153

end0.0ms (0%)

sample3.9s (45.7%)

Algorithm

1×

intervals

Results

1.2s	2410×	body	1024	invalid
876.0ms	7627×	body	128	valid
326.0ms	920×	body	512	invalid
106.0ms	444×	body	256	invalid
72.0ms	576×	body	128	invalid
72.0ms	139×	body	1024	valid
53.0ms	150×	body	512	valid
27.0ms	32×	body	2048	invalid
18.0ms	75×	body	256	valid
7.0ms	9×	body	2048	valid

Compiler

Compiled 867 to 547 computations (36.9% saved)

Details

analyze1.5s (17.5%)

sample123.0ms (1.5%)

simplify210.0ms (2.5%)

prune8.0ms (0.1%)

localize29.0ms (0.3%)

rewrite28.0ms (0.3%)

series278.0ms (3.3%)

simplify117.0ms (1.4%)

prune112.0ms (1.3%)

localize15.0ms (0.2%)

rewrite27.0ms (0.3%)

series254.0ms (3%)

simplify82.0ms (1%)

prune103.0ms (1.2%)

localize25.0ms (0.3%)

rewrite23.0ms (0.3%)

series272.0ms (3.2%)

simplify97.0ms (1.1%)

prune102.0ms (1.2%)

localize32.0ms (0.4%)

rewrite24.0ms (0.3%)

series274.0ms (3.3%)

simplify96.0ms (1.1%)

prune102.0ms (1.2%)

regimes416.0ms (4.9%)

bsearch240.0ms (2.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.9s (45.7%)

Profiling