Details

analyze2.7s (16.7%)

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)

sample182.0ms (1.1%)

Algorithm

1×

intervals

Results

60.0ms	59×	body	1024	invalid
54.0ms	244×	body	128	valid
16.0ms	23×	body	512	invalid
5.0ms	5×	body	1024	valid
5.0ms	22×	body	128	invalid
5.0ms	10×	body	256	invalid
2.0ms	1×	body	2048	valid
2.0ms	4×	body	256	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify302.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune15.0ms (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: 29.3b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize48.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.7b	(*.f64 (atan2.f64 x.im x.re) y.re)
26.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.7b	(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)))

rewrite57.0ms (0.4%)

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:

16.0ms	(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)))
9.0ms	(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)))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series531.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(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)))
47.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
46.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify154.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5167	1251

prune201.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Merged error: 17.0b

Counts

69 → 5

Compiler

Compiled 2981 to 825 computations (72.3% saved)

localize32.0ms (0.2%)

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))
0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
26.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite48.0ms (0.3%)

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` `cancel-sign-sub-inv_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 66

Calls

4 calls:

11.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
9.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(-.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))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series466.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(-.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))
140.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
50.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4958	1662
1	4958	1662

prune190.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	9	83

Merged error: 3.3b

Counts

83 → 9

Compiler

Compiled 2189 to 1081 computations (50.6% saved)

localize66.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.7b	(*.f64 (atan2.f64 x.im x.re) y.re)
26.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.2b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
33.7b	(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)))

rewrite59.0ms (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:

16.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
13.0ms	(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	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series442.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(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	(*.f64 (atan2.f64 x.im x.re) y.re)
38.0ms	(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)))

simplify134.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4911	1281
1	4911	1281

prune240.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 3.3b

Counts

79 → 9

Compiler

Compiled 3222 to 1425 computations (55.8% saved)

localize66.0ms (0.4%)

Local error

Found 4 expressions with local error:

26.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.7b	(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)))
33.7b	(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)))
33.7b	(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)))

rewrite63.0ms (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×	`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:

13.0ms	(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)))
13.0ms	(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)))
13.0ms	(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	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series1.0s (6.4%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(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)))
311.0ms	(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)))
38.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify140.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4990	1522
1	4990	1522

prune314.0ms (1.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	51	9	60

Merged error: 3.3b

Counts

60 → 9

Compiler

Compiled 4249 to 2180 computations (48.7% saved)

regimes744.0ms (4.6%)

Compiler: Compiled 3392 to 2350 computations (30.7% saved)

bsearch792.0ms (4.9%)

Steps

Iters	Range		Point
10	1.220338033316471e+68	2.812177458163507e+79	1.2402240252271068e+68
9	7.904071702402736e-160	5.494307707565754e-155	6.478699131241855e-157
12	-2.3035672796801733e-298	1.01704339783044e-275	-5.1084976626782e-311
10	-3.894530153713234e-186	-4.539596605562279e-200	-7.429944111692088e-189
8	-2.729319344950773e+85	-9.362988138218616e+82	-1.1018666543681226e+83

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	101	203
1	101	203

end0.0ms (0%)

sample7.0s (43.3%)

Algorithm

1×

intervals

Results

2.2s	2346×	body	1024	invalid
1.5s	7587×	body	128	valid
636.0ms	981×	body	512	invalid
189.0ms	445×	body	256	invalid
157.0ms	160×	body	1024	valid
122.0ms	548×	body	128	invalid
109.0ms	164×	body	512	valid
70.0ms	48×	body	2048	invalid
34.0ms	80×	body	256	valid
14.0ms	9×	body	2048	valid

Compiler

Compiled 804 to 524 computations (34.8% saved)

Details

analyze2.7s (16.7%)

sample182.0ms (1.1%)

simplify302.0ms (1.9%)

prune15.0ms (0.1%)

localize48.0ms (0.3%)

rewrite57.0ms (0.4%)

series531.0ms (3.3%)

simplify154.0ms (1%)

prune201.0ms (1.2%)

localize32.0ms (0.2%)

rewrite48.0ms (0.3%)

series466.0ms (2.9%)

simplify123.0ms (0.8%)

prune190.0ms (1.2%)

localize66.0ms (0.4%)

rewrite59.0ms (0.4%)

series442.0ms (2.7%)

simplify134.0ms (0.8%)

prune240.0ms (1.5%)

localize66.0ms (0.4%)

rewrite63.0ms (0.4%)

series1.0s (6.4%)

simplify140.0ms (0.9%)

prune314.0ms (1.9%)

regimes744.0ms (4.6%)

bsearch792.0ms (4.9%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample7.0s (43.3%)

Profiling