Details

analyze1.5s (13%)

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)

sample125.0ms (1.1%)

Algorithm

1×

intervals

Results

44.0ms	73×	body	1024	invalid
28.0ms	240×	body	128	valid
14.0ms	36×	body	512	invalid
4.0ms	16×	body	256	invalid
3.0ms	6×	body	1024	valid
3.0ms	21×	body	128	invalid
2.0ms	2×	body	2048	invalid
2.0ms	5×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify252.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4949	72
1	4949	72

prune8.0ms (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: 31.3b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(*.f64 (atan2.f64 x.im x.re) y.re)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.2b	(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)))

rewrite38.0ms (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:

11.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
9.0ms	(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)))
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.re)

series521.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(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)))
56.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
48.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4809	1251
1	4809	1251

prune113.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 17.4b

Counts

69 → 4

Compiler

Compiled 2982 to 826 computations (72.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.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)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

series493.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(-.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))
162.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
46.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4910	1650
1	4910	1650

prune97.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Merged error: 3.6b

Counts

81 → 7

Compiler

Compiled 2129 to 1050 computations (50.7% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.2b	(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)))
34.2b	(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)))
34.2b	(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)))

rewrite39.0ms (0.3%)

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×	`cos-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:

10.0ms	(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)))
7.0ms	(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)))
7.0ms	(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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series1.1s (9.2%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(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)))
337.0ms	(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)))
330.0ms	(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)))
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4898	1522
1	4898	1522

prune182.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	50	8	58

Merged error: 3.6b

Counts

58 → 8

Compiler

Compiled 4539 to 2384 computations (47.5% saved)

localize44.0ms (0.4%)

Local error

Found 4 expressions with local error:

34.2b	(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)))
34.2b	(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)))
34.2b	(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)))
34.2b	(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)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `cos-sum_binary64`

Counts

4 → 32

Calls

4 calls:

8.0ms	(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)))
8.0ms	(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)))
8.0ms	(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)))
8.0ms	(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)))

series1.3s (11.5%)

Counts

4 → 12

Calls

4 calls:

344.0ms	(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)))
329.0ms	(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)))
327.0ms	(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)))
319.0ms	(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)))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5159	1644

prune217.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	44	8	52

Merged error: 3.6b

Counts

52 → 8

Compiler

Compiled 5496 to 2850 computations (48.1% saved)

regimes511.0ms (4.4%)

Compiler: Compiled 5362 to 3570 computations (33.4% saved)

bsearch142.0ms (1.2%)

Steps

Iters	Range		Point
7	4.657199099317635e-05	0.008722533303035468	7.373182326448969e-05
7	-2.771803395673294e+30	-3.6900573604041856e+28	-3.7382618232263023e+28

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	80	96
1	80	96

end0.0ms (0%)

sample4.3s (37.8%)

Algorithm

1×

intervals

Results

1.4s	2535×	body	1024	invalid
861.0ms	7585×	body	128	valid
399.0ms	1070×	body	512	invalid
109.0ms	189×	body	1024	valid
103.0ms	415×	body	256	invalid
66.0ms	549×	body	128	invalid
44.0ms	121×	body	512	valid
36.0ms	39×	body	2048	invalid
22.0ms	91×	body	256	valid
14.0ms	14×	body	2048	valid

Compiler

Compiled 1143 to 753 computations (34.1% saved)

Details

analyze1.5s (13%)

sample125.0ms (1.1%)

simplify252.0ms (2.2%)

prune8.0ms (0.1%)

localize24.0ms (0.2%)

rewrite38.0ms (0.3%)

series521.0ms (4.5%)

simplify117.0ms (1%)

prune113.0ms (1%)

localize16.0ms (0.1%)

rewrite25.0ms (0.2%)

series493.0ms (4.3%)

simplify78.0ms (0.7%)

prune97.0ms (0.8%)

localize36.0ms (0.3%)

rewrite39.0ms (0.3%)

series1.1s (9.2%)

simplify72.0ms (0.6%)

prune182.0ms (1.6%)

localize44.0ms (0.4%)

rewrite41.0ms (0.4%)

series1.3s (11.5%)

simplify78.0ms (0.7%)

prune217.0ms (1.9%)

regimes511.0ms (4.4%)

bsearch142.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.3s (37.8%)

Profiling