Details

analyze1.4s (15.8%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample123.0ms (1.3%)

Algorithm

1×

intervals

Results

44.0ms	82×	body	1024	invalid
35.0ms	244×	body	128	valid
11.0ms	30×	body	512	invalid
4.0ms	4×	body	2048	invalid
3.0ms	6×	body	1024	valid
3.0ms	22×	body	128	invalid
1.0ms	6×	body	256	invalid
1.0ms	3×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify163.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (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

36.1b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.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 (0.3%)

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(sin.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)))
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)

series299.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(sin.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)))
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4884	1270
1	4884	1270

prune126.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Error

20.0b

Counts

70 → 8

Compiler

Compiled 3170 to 932 computations (70.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.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)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

8.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
7.0ms	(sin.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)))

series329.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(sin.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)))
87.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 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)))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4897	1383
1	4897	1383

prune122.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Error

20.0b

Counts

77 → 8

Compiler

Compiled 3703 to 1059 computations (71.4% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

6.4b	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.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)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

7.0ms	(sin.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	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
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)))

series390.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(sin.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)))
148.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
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)))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4888	1237
1	4888	1237

prune157.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Error

20.0b

Counts

67 → 8

Compiler

Compiled 4472 to 1899 computations (57.5% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

6.4b	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.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)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

7.0ms	(sin.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)))
5.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series381.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(sin.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)))
140.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) (pow.f64 (cbrt.f64 y.im) 2)))
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)))

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4888	1237
1	4888	1237

prune200.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Error

20.0b

Counts

67 → 7

Compiler

Compiled 5412 to 2405 computations (55.6% saved)

regimes478.0ms (5.2%)

Accuracy

Total 2.8b remaining (12.3%)

Threshold costs 0b (0%)

Compiler

Compiled 5217 to 3205 computations (38.6% saved)

bsearch115.0ms (1.3%)

Steps

Iters	Range		Point
10	-8.088438286647767e-300	5.542257536724659e-307	-5.69725882226024e-309

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	130
1	86	130

end0.0ms (0%)

sample4.2s (45.8%)

Algorithm

1×

intervals

Results

1.3s	2539×	body	1024	invalid
858.0ms	7584×	body	128	valid
344.0ms	939×	body	512	invalid
163.0ms	188×	body	2048	invalid
94.0ms	176×	body	1024	valid
80.0ms	335×	body	256	invalid
61.0ms	497×	body	128	invalid
52.0ms	144×	body	512	valid
20.0ms	85×	body	256	valid
9.0ms	11×	body	2048	valid

Compiler

Compiled 1131 to 681 computations (39.8% saved)

Details

analyze1.4s (15.8%)

sample123.0ms (1.3%)

simplify163.0ms (1.8%)

prune9.0ms (0.1%)

localize22.0ms (0.2%)

rewrite30.0ms (0.3%)

series299.0ms (3.3%)

simplify105.0ms (1.1%)

prune126.0ms (1.4%)

localize25.0ms (0.3%)

rewrite34.0ms (0.4%)

series329.0ms (3.6%)

simplify71.0ms (0.8%)

prune122.0ms (1.3%)

localize34.0ms (0.4%)

rewrite29.0ms (0.3%)

series390.0ms (4.3%)

simplify100.0ms (1.1%)

prune157.0ms (1.7%)

localize36.0ms (0.4%)

rewrite34.0ms (0.4%)

series381.0ms (4.2%)

simplify102.0ms (1.1%)

prune200.0ms (2.2%)

regimes478.0ms (5.2%)

bsearch115.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.2s (45.8%)

Profiling