Details

analyze1.4s (14.9%)

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)

sample118.0ms (1.2%)

Algorithm

1×

intervals

Results

39.0ms	78×	body	1024	invalid
31.0ms	243×	body	128	valid
13.0ms	37×	body	512	invalid
5.0ms	18×	body	256	invalid
3.0ms	6×	body	1024	valid
3.0ms	22×	body	128	invalid
2.0ms	7×	body	512	valid
2.0ms	2×	body	2048	invalid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify163.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	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

Error

33.1b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.9b	(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)))

rewrite28.0ms (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:

8.0ms	(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)))
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)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series569.0ms (6%)

Counts

4 → 53

Calls

4 calls:

252.0ms	(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)))
136.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
107.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3528 to 2321 computations (34.2% saved)

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4945	2077
1	4945	2077

prune154.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Error

20.7b

Counts

110 → 6

Compiler

Compiled 4624 to 1246 computations (73.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.7b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
29.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite18.0ms (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` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 58

Calls

4 calls:

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)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
1.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series399.0ms (4.2%)

Counts

4 → 48

Calls

4 calls:

135.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
128.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
67.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2214 to 1566 computations (29.3% saved)

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5015	1573

prune112.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	103	9	112

Error

3.4b

Counts

112 → 9

Compiler

Compiled 3297 to 854 computations (74.1% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

29.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.9b	(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)))
34.9b	(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)))
34.9b	(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)))

rewrite32.0ms (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:

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

series961.0ms (10.1%)

Counts

4 → 54

Calls

4 calls:

266.0ms	(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)))
264.0ms	(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)))
258.0ms	(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)))
172.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 7908 to 5223 computations (34% saved)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5200	2604

prune324.0ms (3.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Error

3.3b

Counts

102 → 9

Compiler

Compiled 7722 to 3903 computations (49.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (log.f64 x.im) y.re)
0.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.7b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
9×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`log-pow_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(*.f64 (log.f64 x.im) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
1.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series395.0ms (4.1%)

Counts

4 → 35

Calls

4 calls:

134.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
130.0ms	(*.f64 (log.f64 x.im) y.re)
66.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
64.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1294 to 946 computations (26.9% saved)

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4839	1167
1	4839	1167

prune71.0ms (0.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	97	9	106

Error

3.3b

Counts

106 → 9

Compiler

Compiled 2040 to 313 computations (84.7% saved)

regimes414.0ms (4.3%)

Accuracy

Total 6.0b remaining (62.5%)

Threshold costs 0b (0%)

Compiler

Compiled 3912 to 2635 computations (32.6% saved)

bsearch132.0ms (1.4%)

Steps

Iters	Range		Point
8	0.42676375621528584	118.17033086044722	0.9814661405475972
6	-6.431309576284371e-242	-4.502762892178998e-243	-4.5722153193652987e-243

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	82	138
1	82	138

end0.0ms (0%)

sample3.8s (39.6%)

Algorithm

1×

intervals

Results

1.2s	2446×	body	1024	invalid
822.0ms	7563×	body	128	valid
326.0ms	980×	body	512	invalid
96.0ms	188×	body	1024	valid
93.0ms	415×	body	256	invalid
61.0ms	548×	body	128	invalid
50.0ms	150×	body	512	valid
35.0ms	47×	body	2048	invalid
20.0ms	89×	body	256	valid
8.0ms	10×	body	2048	valid

Compiler

Compiled 874 to 571 computations (34.7% saved)

Details

analyze1.4s (14.9%)

sample118.0ms (1.2%)

simplify163.0ms (1.7%)

prune8.0ms (0.1%)

localize30.0ms (0.3%)

rewrite28.0ms (0.3%)

series569.0ms (6%)

simplify101.0ms (1.1%)

prune154.0ms (1.6%)

localize18.0ms (0.2%)

rewrite18.0ms (0.2%)

series399.0ms (4.2%)

simplify51.0ms (0.5%)

prune112.0ms (1.2%)

localize35.0ms (0.4%)

rewrite32.0ms (0.3%)

series961.0ms (10.1%)

simplify71.0ms (0.7%)

prune324.0ms (3.4%)

localize12.0ms (0.1%)

rewrite17.0ms (0.2%)

series395.0ms (4.1%)

simplify100.0ms (1%)

prune71.0ms (0.7%)

regimes414.0ms (4.3%)

bsearch132.0ms (1.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.8s (39.6%)

Profiling