Details

analyze849.0ms (5.8%)

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)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune4.0ms (0%)

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

Error

23.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

23.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.0b	(/.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 (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
9×	`times-frac_binary64_766`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`flip3-+_binary64_763` `associate-/r_binary64_704` `flip-+_binary64_734` `associate-/l_binary64_705`
2×	`associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow1_binary64_821`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

2 → 42

Calls

4 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))
0.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series681.0ms (4.6%)

Counts

2 → 48

Calls

2 calls:

467.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
213.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 1044 to 858 computations (17.8% saved)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5131	2283

prune238.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Error

4.7b

Counts

91 → 8

Compiler

Compiled 1880 to 677 computations (64% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

14.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_760`
30×	`sqrt-prod_binary64_776`
25×	`add-sqr-sqrt_binary64_782`
24×	`times-frac_binary64_766`
23×	`add-cube-cbrt_binary64_795`
12×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
8×	`associate-/r*_binary64_704`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
3×	`associate-/l*_binary64_705`
2×	`rem-sqrt-square_binary64_773` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 96

Calls

8 calls:

14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series1.2s (8.1%)

Counts

4 → 93

Calls

4 calls:

614.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
220.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
175.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
173.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3792 to 3216 computations (15.2% saved)

simplify135.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5031	4836

prune480.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	189	8	197

Error

4.7b

Counts

197 → 8

Compiler

Compiled 6102 to 3670 computations (39.9% saved)

localize26.0ms (0.2%)

Local error

Found 6 expressions with local error:

22.4b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
0.7b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.7b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
22.4b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite101.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_766`
135×	`*-un-lft-identity_binary64_760`
71×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
32×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
24×	`associate-/r*_binary64_704`
16×	`add-exp-log_binary64_798`
11×	`associate-/r/_binary64_706`
10×	`add-cbrt-cube_binary64_796`
8×	`associate-/l*_binary64_705` `div-exp_binary64_811`
7×	`flip3-+_binary64_763` `flip-+_binary64_734`
6×	`div-inv_binary64_757`
5×	`add-log-exp_binary64_799`
4×	`cbrt-undiv_binary64_794` `pow1_binary64_821`
2×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
1×	`inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `pow-flip_binary64_834`

Counts

3 → 158

Calls

6 calls:

30.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
25.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
7.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))

series1.1s (7.4%)

Counts

3 → 78

Calls

3 calls:

451.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

415.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

223.0ms

(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

Compiler

Compiled 2502 to 2106 computations (15.8% saved)

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5170	8728

prune377.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	233	3	236
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	235	9	244

Error

2.6b

Counts

244 → 9

Compiler

Compiled 6043 to 2915 computations (51.8% saved)

localize33.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
14.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite106.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-div_binary64_777`
21×	`*-un-lft-identity_binary64_760`
15×	`sqrt-prod_binary64_776`
12×	`add-sqr-sqrt_binary64_782`
10×	`flip3-+_binary64_763` `flip-+_binary64_734`
9×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
8×	`associate-/r/_binary64_706`
7×	`pow1_binary64_821`
6×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `frac-times_binary64_770`
3×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `associate-/l*_binary64_705` `pow1/2_binary64_840` `times-frac_binary64_766`
2×	`cbrt-undiv_binary64_794` `associate-l/_binary64_703` `associate-/l/_binary64_707` `associate-r/_binary64_702` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `prod-exp_binary64_809` `associate-/r*_binary64_704` `div-inv_binary64_757` `cbrt-unprod_binary64_793` `clear-num_binary64_759`

Counts

4 → 82

Calls

8 calls:

33.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
13.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series1.2s (8.3%)

Counts

4 → 87

Calls

4 calls:

600.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
224.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
199.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
193.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4470 to 3726 computations (16.6% saved)

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4978	3917
1	4978	3917

prune532.0ms (3.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	169	9	178

Error

2.6b

Counts

178 → 9

Compiler

Compiled 6558 to 4285 computations (34.7% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	337	1952
1	337	1952

regimes878.0ms (6%)

Accuracy

Total 15.5b remaining (86.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4172 to 3116 computations (25.3% saved)

bsearch43.0ms (0.3%)

Steps

Iters	Range		Point
8	2.5979637607691394e+52	4.097030592216735e+55	4.0463340212107907e+55
9	-5.810018931600796e+144	-2.000326219039384e+136	-3.6836303645104744e+137

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	70
1	37	70

end0.0ms (0%)

sample6.0s (40.9%)

Algorithm

1×

intervals

Results

559.0ms	8000×	body	128	valid
34.0ms	463×	body	128	invalid

Compiler

Compiled 3213 to 2383 computations (25.8% saved)

Pareto

0.2834237228222638

Details

analyze849.0ms (5.8%)

sample22.0ms (0.2%)

simplify126.0ms (0.9%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite17.0ms (0.1%)

series681.0ms (4.6%)

simplify83.0ms (0.6%)

prune238.0ms (1.6%)

localize17.0ms (0.1%)

rewrite46.0ms (0.3%)

series1.2s (8.1%)

simplify135.0ms (0.9%)

prune480.0ms (3.3%)

localize26.0ms (0.2%)

rewrite101.0ms (0.7%)

series1.1s (7.4%)

simplify174.0ms (1.2%)

prune377.0ms (2.6%)

localize33.0ms (0.2%)

rewrite106.0ms (0.7%)

series1.2s (8.3%)

simplify138.0ms (0.9%)

prune532.0ms (3.6%)

simplify44.0ms (0.3%)

regimes878.0ms (6%)

bsearch43.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (40.9%)

Profiling