Details

analyze658.0ms (15.2%)

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	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune5.0ms (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: 26.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

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))

series251.0ms (5.8%)

Counts

2 → 6

Calls

2 calls:

178.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
74.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5028	1623

prune62.0ms (1.4%)

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: 25.7b

Counts

49 → 9

Compiler

Compiled 1379 to 266 computations (80.7% 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))
15.6b	(/.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))))
30.5b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.5b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 84

Calls

4 calls:

14.0ms	(/.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	(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)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series411.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(/.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))))
77.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
46.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4993	2839
1	4993	2839

prune128.0ms (3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 23.9b

Counts

105 → 11

Compiler

Compiled 3385 to 1122 computations (66.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.8b	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
30.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.5b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite58.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
28×	`times-frac_binary64`
25×	`sqrt-prod_binary64`
22×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64` `unpow-prod-down_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
5×	`unswap-sqr_binary64`
3×	`associate-l_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

29.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
9.0ms	(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)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series396.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
69.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
44.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
40.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5268	2872

prune159.0ms (3.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	113	11	124

Merged error: 23.9b

Counts

124 → 11

Compiler

Compiled 3971 to 1828 computations (54% saved)

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.8b	(/.f64 (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
30.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.5b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite57.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`sqrt-prod_binary64`
55×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
11×	`associate-/r*_binary64`
10×	`sqrt-div_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 112

Calls

4 calls:

18.0ms	(/.f64 (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(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)))

series515.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
50.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
44.0ms	(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)))

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5069	4067

prune252.0ms (5.8%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	124	11	135

Merged error: 23.9b

Counts

135 → 11

Compiler

Compiled 5784 to 3054 computations (47.2% saved)

regimes131.0ms (3%)

Compiler: Compiled 1414 to 861 computations (39.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	20	50

end0.0ms (0%)

sample804.0ms (18.6%)

Algorithm

1×

intervals

Results

344.0ms	8000×	body	128	valid
22.0ms	478×	body	128	invalid

Compiler

Compiled 297 to 180 computations (39.4% saved)

Details

analyze658.0ms (15.2%)

sample20.0ms (0.5%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite17.0ms (0.4%)

series251.0ms (5.8%)

simplify44.0ms (1%)

prune62.0ms (1.4%)

localize12.0ms (0.3%)

rewrite36.0ms (0.8%)

series411.0ms (9.5%)

simplify74.0ms (1.7%)

prune128.0ms (3%)

localize19.0ms (0.4%)

rewrite58.0ms (1.4%)

series396.0ms (9.2%)

simplify78.0ms (1.8%)

prune159.0ms (3.7%)

localize26.0ms (0.6%)

rewrite57.0ms (1.3%)

series515.0ms (11.9%)

simplify84.0ms (2%)

prune252.0ms (5.8%)

regimes131.0ms (3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample804.0ms (18.6%)

Profiling