Details

analyze1.5s (14.3%)

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)

sample129.0ms (1.2%)

Algorithm

1×

intervals

Results

53.0ms	80×	body	1024	invalid
29.0ms	237×	body	128	valid
10.0ms	27×	body	512	invalid
4.0ms	4×	body	2048	invalid
4.0ms	10×	body	512	valid
3.0ms	6×	body	1024	valid
2.0ms	10×	body	256	invalid
2.0ms	13×	body	128	invalid
1.0ms	1×	body	2048	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify250.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4949	72
1	4949	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: 34.3b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.4b	(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)

series535.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(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)))
54.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
50.0ms	(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)))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4837	1270
1	4837	1270

prune126.0ms (1.2%)

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: 20.2b

Counts

69 → 9

Compiler

Compiled 3196 to 969 computations (69.7% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

29.3b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.3b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.4b	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.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)))

rewrite75.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`sqrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`sin-sum_binary64`

Counts

4 → 57

Calls

4 calls:

40.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.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 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series508.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

377.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.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)))
49.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
40.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5027	1297

prune191.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Merged error: 20.1b

Counts

78 → 9

Compiler

Compiled 4427 to 2387 computations (46.1% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

29.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.4b	(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)))
31.4b	(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)))
31.4b	(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)))

rewrite37.0ms (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:

9.0ms	(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)))
7.0ms	(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)))
7.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series1.1s (10.3%)

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)))
345.0ms	(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)))
332.0ms	(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)))
47.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5043	1579

prune183.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	50	10	60

Merged error: 20.1b

Counts

60 → 10

Compiler

Compiled 4615 to 2412 computations (47.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
18.4b	(sin.f64 (+.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 x.re))))
29.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series367.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(sin.f64 (+.f64 (.f64 (atan2.f64 x.im x.re) y.re) (.f64 y.im (log.f64 x.re))))
55.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
52.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
47.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4920	1120
1	4920	1120

prune84.0ms (0.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	68	13	81

Merged error: 13.9b

Counts

81 → 13

Compiler

Compiled 2433 to 457 computations (81.2% saved)

regimes276.0ms (2.7%)

Compiler: Compiled 2204 to 1528 computations (30.7% saved)

bsearch291.0ms (2.8%)

Steps

Iters	Range		Point
10	15821337948131.822	4.2902547215702305e+24	35323782267678.79
7	8.510819758434254e-65	4.71210344297255e-63	2.7034704071498713e-64
10	-3.067921034983855e-296	1.2608510414788044e-302	-3.27709251007574e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	107	241
1	107	241

end0.0ms (0%)

sample4.2s (40.9%)

Algorithm

1×

intervals

Results

1.5s	2512×	body	1024	invalid
888.0ms	7562×	body	128	valid
361.0ms	941×	body	512	invalid
200.0ms	164×	body	2048	invalid
108.0ms	188×	body	1024	valid
84.0ms	325×	body	256	invalid
63.0ms	502×	body	128	invalid
55.0ms	148×	body	512	valid
20.0ms	83×	body	256	valid
19.0ms	19×	body	2048	valid

Compiler

Compiled 712 to 465 computations (34.7% saved)

Details

analyze1.5s (14.3%)

sample129.0ms (1.2%)

simplify250.0ms (2.4%)

prune14.0ms (0.1%)

localize24.0ms (0.2%)

rewrite30.0ms (0.3%)

series535.0ms (5.2%)

simplify99.0ms (1%)

prune126.0ms (1.2%)

localize37.0ms (0.4%)

rewrite75.0ms (0.7%)

series508.0ms (4.9%)

simplify72.0ms (0.7%)

prune191.0ms (1.8%)

localize36.0ms (0.3%)

rewrite37.0ms (0.4%)

series1.1s (10.3%)

simplify73.0ms (0.7%)

prune183.0ms (1.8%)

localize23.0ms (0.2%)

rewrite24.0ms (0.2%)

series367.0ms (3.5%)

simplify78.0ms (0.8%)

prune84.0ms (0.8%)

regimes276.0ms (2.7%)

bsearch291.0ms (2.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.2s (40.9%)

Profiling