Details

analyze520.0ms (12.5%)

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
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify162.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1109` `*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
9×	`times-frac_binary64_1094`
4×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `add-log-exp_binary64_1124`
3×	`associate-/r_binary64_1034` `flip-+_binary64_1062` `flip3-+_binary64_1091` `associate-/l_binary64_1035`
2×	`associate-/l/_binary64_1037` `associate-/r/_binary64_1036` `pow1_binary64_1146`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

2 → 42

Calls

2 calls:

9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series249.0ms (6%)

Counts

2 → 6

Calls

2 calls:

182.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
66.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5028	1623

prune70.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 26.3b

Counts

49 → 9

Compiler

Compiled 1367 to 257 computations (81.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
16.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
26.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
26.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1109`
21×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
18×	`times-frac_binary64_1094` `sqrt-prod_binary64_1103`
6×	`add-cbrt-cube_binary64_1121` `associate-/r*_binary64_1034` `add-exp-log_binary64_1123` `sqrt-div_binary64_1104` `add-log-exp_binary64_1124` `pow1_binary64_1146`
5×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
3×	`associate-/l*_binary64_1035`
2×	`rem-sqrt-square_binary64_1101` `associate-/l/_binary64_1037` `associate-/r/_binary64_1036` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series395.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
69.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
48.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
48.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4993	2839
1	4993	2839

prune126.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	93	12	105

Merged error: 23.6b

Counts

105 → 12

Compiler

Compiled 3418 to 1156 computations (66.2% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
16.4b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
26.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1088`
28×	`sqrt-prod_binary64_1103`
25×	`add-sqr-sqrt_binary64_1109`
24×	`times-frac_binary64_1094`
23×	`add-cube-cbrt_binary64_1120`
10×	`unpow-prod-down_binary64_1164` `distribute-lft-out_binary64_1041`
8×	`associate-/l*_binary64_1035`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `sqrt-div_binary64_1104` `add-log-exp_binary64_1124` `pow1_binary64_1146`
5×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
3×	`associate-/r*_binary64_1034`
2×	`rem-sqrt-square_binary64_1101` `associate-/l/_binary64_1037` `associate-/r/_binary64_1036` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series325.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
69.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
44.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
43.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4954	3253
1	4954	3253

prune156.0ms (3.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	105	13	118

Merged error: 23.6b

Counts

118 → 13

Compiler

Compiled 3997 to 1813 computations (54.6% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

16.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
26.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
26.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_1088`
25×	`add-sqr-sqrt_binary64_1109` `sqrt-prod_binary64_1103`
22×	`add-cube-cbrt_binary64_1120`
18×	`times-frac_binary64_1094`
8×	`sqrt-div_binary64_1104`
7×	`pow1_binary64_1146`
6×	`add-cbrt-cube_binary64_1121` `associate-/r*_binary64_1034` `add-exp-log_binary64_1123`
5×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
4×	`unpow-prod-down_binary64_1164` `add-log-exp_binary64_1124` `distribute-lft-out_binary64_1041`
3×	`rem-sqrt-square_binary64_1101` `sqrt-pow1_binary64_1105` `associate-/l*_binary64_1035` `pow1/2_binary64_1165`
2×	`associate-/l/_binary64_1037` `associate-/r/_binary64_1036`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 92

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series373.0ms (9%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
45.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
43.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4994	2913
1	4994	2913

prune201.0ms (4.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	103	14	117

Merged error: 23.6b

Counts

117 → 14

Compiler

Compiled 4521 to 2510 computations (44.5% saved)

regimes165.0ms (4%)

Compiler: Compiled 1741 to 1220 computations (29.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	108
1	49	108

end0.0ms (0%)

sample882.0ms (21.2%)

Algorithm

1×

intervals

Results

335.0ms	8000×	body	128	valid
20.0ms	507×	body	128	invalid

Compiler

Compiled 400 to 266 computations (33.5% saved)

Details

analyze520.0ms (12.5%)

sample20.0ms (0.5%)

simplify162.0ms (3.9%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite18.0ms (0.4%)

series249.0ms (6%)

simplify44.0ms (1.1%)

prune70.0ms (1.7%)

localize12.0ms (0.3%)

rewrite33.0ms (0.8%)

series395.0ms (9.5%)

simplify73.0ms (1.7%)

prune126.0ms (3%)

localize22.0ms (0.5%)

rewrite43.0ms (1%)

series325.0ms (7.8%)

simplify113.0ms (2.7%)

prune156.0ms (3.7%)

localize24.0ms (0.6%)

rewrite45.0ms (1.1%)

series373.0ms (9%)

simplify73.0ms (1.7%)

prune201.0ms (4.8%)

regimes165.0ms (4%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample882.0ms (21.2%)

Profiling