Details

analyze1.5s (18.6%)

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)

sample110.0ms (1.4%)

Algorithm

1×

intervals

Results

37.0ms	71×	body	1024	invalid
29.0ms	246×	body	128	valid
10.0ms	29×	body	512	invalid
6.0ms	11×	body	256	invalid
3.0ms	5×	body	1024	valid
2.0ms	20×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify164.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune10.0ms (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

33.6b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
31.2b	(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)))
31.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite27.0ms (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:

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)))
6.0ms	(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.re)

series280.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(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)))
34.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
25.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5167	1251

prune103.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

21.3b

Counts

70 → 3

Compiler

Compiled 2910 to 774 computations (73.4% 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)))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite26.0ms (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:

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

series263.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(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)))
83.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) 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)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4953	1596
1	4953	1596

prune98.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Error

3.0b

Counts

84 → 6

Compiler

Compiled 2105 to 984 computations (53.3% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.re)
31.2b	(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)))
31.4b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
31.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite29.0ms (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:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
6.0ms	(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)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series256.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(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)))
26.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4911	1281
1	4911	1281

prune126.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Error

3.0b

Counts

76 → 6

Compiler

Compiled 3178 to 1411 computations (55.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.2b	(*.f64 (log.f64 x.re) y.re)
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`exp-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `cancel-sign-sub-inv_binary64` `exp-diff_binary64`

Counts

3 → 52

Calls

3 calls:

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

series149.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

84.0ms	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
40.0ms	(*.f64 (log.f64 x.re) y.re)
25.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	856
1	4967	856

prune47.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	60	7	67

Error

3.0b

Counts

67 → 7

Compiler

Compiled 1029 to 311 computations (69.8% saved)

regimes462.0ms (5.8%)

Accuracy

Total 5.7b remaining (62.9%)

Threshold costs 0b (0%)

Compiler

Compiled 2922 to 2115 computations (27.6% saved)

bsearch93.0ms (1.2%)

Steps

Iters	Range		Point
10	-5.771368572546493e-300	1.2644505533430413e-307	-1.63895862773914e-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	71	57
1	71	57

end0.0ms (0%)

sample3.9s (48.1%)

Algorithm

1×

intervals

Results

1.3s	2497×	body	1024	invalid
849.0ms	7618×	body	128	valid
351.0ms	987×	body	512	invalid
100.0ms	438×	body	256	invalid
82.0ms	155×	body	1024	valid
71.0ms	603×	body	128	invalid
48.0ms	137×	body	512	valid
20.0ms	86×	body	256	valid
20.0ms	26×	body	2048	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 635 to 453 computations (28.7% saved)

Details

analyze1.5s (18.6%)

sample110.0ms (1.4%)

simplify164.0ms (2%)

prune10.0ms (0.1%)

localize29.0ms (0.4%)

rewrite27.0ms (0.3%)

series280.0ms (3.5%)

simplify86.0ms (1.1%)

prune103.0ms (1.3%)

localize15.0ms (0.2%)

rewrite26.0ms (0.3%)

series263.0ms (3.3%)

simplify83.0ms (1%)

prune98.0ms (1.2%)

localize29.0ms (0.4%)

rewrite29.0ms (0.4%)

series256.0ms (3.2%)

simplify70.0ms (0.9%)

prune126.0ms (1.6%)

localize10.0ms (0.1%)

rewrite16.0ms (0.2%)

series149.0ms (1.9%)

simplify76.0ms (1%)

prune47.0ms (0.6%)

regimes462.0ms (5.8%)

bsearch93.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (48.1%)

Profiling