Details

analyze2.7s (15%)

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)

sample201.0ms (1.1%)

Algorithm

1×

intervals

Results

70.0ms	70×	body	1024	invalid
53.0ms	244×	body	128	valid
25.0ms	27×	body	512	invalid
5.0ms	5×	body	1024	valid
4.0ms	8×	body	256	invalid
4.0ms	2×	body	2048	invalid
3.0ms	5×	body	512	valid
3.0ms	14×	body	128	invalid
1.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify258.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune14.0ms (0.1%)

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: 28.0b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize57.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.9b	(*.f64 (atan2.f64 x.im x.re) y.re)
24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(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)))

rewrite54.0ms (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:

15.0ms	(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)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series505.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

387.0ms	(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)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
39.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
36.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify181.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4874	1270
1	4874	1270

prune226.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 16.7b

Counts

69 → 9

Compiler

Compiled 3222 to 962 computations (70.1% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.7b	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)))))

rewrite51.0ms (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:

16.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series668.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

436.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)))))
149.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4871	1173
1	4871	1173

prune192.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 16.7b

Counts

68 → 9

Compiler

Compiled 3546 to 913 computations (74.3% saved)

localize69.0ms (0.4%)

Local error

Found 4 expressions with local error:

24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sin.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)))
31.1b	(sin.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)))
31.1b	(sin.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)))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

16.0ms	(sin.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)))
13.0ms	(sin.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)))
13.0ms	(sin.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)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series1.1s (5.9%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(sin.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)))
331.0ms	(sin.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)))
325.0ms	(sin.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)))
51.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5056	1579

prune335.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	51	9	60

Merged error: 16.7b

Counts

60 → 9

Compiler

Compiled 4545 to 2355 computations (48.2% saved)

localize63.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.8b	(cbrt.f64 (pow.f64 (sin.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))) 3))
24.8b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
24.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sin.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)))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cube-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `sin-sum_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 61

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
12.0ms	(sin.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)))
9.0ms	(cbrt.f64 (pow.f64 (sin.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))) 3))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series769.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(cbrt.f64 (pow.f64 (sin.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))) 3))
323.0ms	(sin.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)))
42.0ms	(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)))

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5157	2116

prune236.0ms (1.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	71	11	82

Merged error: 16.7b

Counts

82 → 11

Compiler

Compiled 3323 to 1447 computations (56.5% saved)

regimes1.2s (6.5%)

Compiler: Compiled 6427 to 4215 computations (34.4% saved)

bsearch453.0ms (2.5%)

Steps

Iters	Range	Point
10	-2.3035672796801733e-298	2.2681328871212016e-307	2.03323265387355e-310
7	-4.112949967345281e-264	-1.1636684244090466e-265	-3.681246395840957e-264
9	-2.7033259684250657e+100	-1.915997100528093e+95	-1.938303095832879e+95

Iters

Range

Point

-2.3035672796801733e-298

2.2681328871212016e-307

2.03323265387355e-310

-4.112949967345281e-264

-1.1636684244090466e-265

-3.681246395840957e-264

-2.7033259684250657e+100

-1.915997100528093e+95

-1.938303095832879e+95

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	87	279
1	87	279

end0.0ms (0%)

sample8.1s (45.3%)

Algorithm

1×

intervals

Results

2.4s	2491×	body	1024	invalid
1.6s	7579×	body	128	valid
595.0ms	913×	body	512	invalid
256.0ms	161×	body	2048	invalid
161.0ms	170×	body	1024	valid
157.0ms	350×	body	256	invalid
108.0ms	507×	body	128	invalid
103.0ms	157×	body	512	valid
34.0ms	80×	body	256	valid
21.0ms	14×	body	2048	valid

Compiler

Compiled 1448 to 892 computations (38.4% saved)

Details

analyze2.7s (15%)

sample201.0ms (1.1%)

simplify258.0ms (1.4%)

prune14.0ms (0.1%)

localize57.0ms (0.3%)

rewrite54.0ms (0.3%)

series505.0ms (2.8%)

simplify181.0ms (1%)

prune226.0ms (1.3%)

localize53.0ms (0.3%)

rewrite51.0ms (0.3%)

series668.0ms (3.7%)

simplify122.0ms (0.7%)

prune192.0ms (1.1%)

localize69.0ms (0.4%)

rewrite65.0ms (0.4%)

series1.1s (5.9%)

simplify137.0ms (0.8%)

prune335.0ms (1.9%)

localize63.0ms (0.4%)

rewrite59.0ms (0.3%)

series769.0ms (4.3%)

simplify137.0ms (0.8%)

prune236.0ms (1.3%)

regimes1.2s (6.5%)

bsearch453.0ms (2.5%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample8.1s (45.3%)

Profiling