Details

analyze532.0ms (5.3%)

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)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify225.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5232	30

prune3.0ms (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

30.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.0b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
30.0b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
9×	`times-frac_binary64_743`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `add-exp-log_binary64_775`
3×	`associate-/l_binary64_682` `associate-/r_binary64_681`
2×	`associate-/r/_binary64_683` `pow1_binary64_798` `flip3--_binary64_741` `flip--_binary64_712` `associate-/l/_binary64_684`
1×	`diff-log_binary64_829` `flip3-+_binary64_740` `frac-2neg_binary64_748` `div-sub_binary64_742` `clear-num_binary64_736` `sub-neg_binary64_730` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `flip-+_binary64_711` `div-exp_binary64_788` `cancel-sign-sub-inv_binary64_703`

Counts

2 → 44

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series474.0ms (4.8%)

Counts

2 → 48

Calls

2 calls:

320.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
154.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1068 to 882 computations (17.4% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4934	2277
1	4934	2277

prune163.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Error

7.3b

Counts

93 → 7

Compiler

Compiled 1841 to 613 computations (66.7% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

34.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
17.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0b	(/.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
17.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
34.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
34.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_737`
28×	`sqrt-prod_binary64_753`
25×	`add-sqr-sqrt_binary64_759`
24×	`times-frac_binary64_743`
23×	`add-cube-cbrt_binary64_772`
10×	`unpow-prod-down_binary64_816` `distribute-lft-out_binary64_688`
8×	`associate-/r*_binary64_681`
6×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `add-exp-log_binary64_775` `pow1_binary64_798` `sqrt-div_binary64_754`
3×	`flip3-+_binary64_740` `associate-/l*_binary64_682` `flip-+_binary64_711`
2×	`associate-/r/_binary64_683` `pow1/2_binary64_817` `rem-sqrt-square_binary64_750` `flip3--_binary64_741` `flip--_binary64_712` `sqrt-pow1_binary64_755` `associate-/l/_binary64_684`
1×	`diff-log_binary64_829` `frac-2neg_binary64_748` `div-sub_binary64_742` `clear-num_binary64_736` `sub-neg_binary64_730` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `cancel-sign-sub-inv_binary64_703`

Counts

4 → 96

Calls

8 calls:

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

series866.0ms (8.7%)

Counts

4 → 89

Calls

4 calls:

433.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
164.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
141.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
128.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3518 to 2748 computations (21.9% saved)

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5011	4697

prune236.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	182	10	192

Error

7.3b

Counts

192 → 10

Compiler

Compiled 5612 to 2275 computations (59.5% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

29.6b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.9b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.9b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.6b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_737`
32×	`times-frac_binary64_743`
30×	`add-sqr-sqrt_binary64_759`
23×	`add-cube-cbrt_binary64_772`
21×	`associate-r_binary64_677`
16×	`add-exp-log_binary64_775`
14×	`unpow-prod-down_binary64_816` `distribute-lft-out_binary64_688`
10×	`add-cbrt-cube_binary64_773`
6×	`pow1_binary64_798`
5×	`add-log-exp_binary64_776` `associate-/r*_binary64_681`
4×	`associate-/r/_binary64_683` `prod-exp_binary64_786` `div-exp_binary64_788`
3×	`unswap-sqr_binary64_705` `associate-/l_binary64_682` `flip3--_binary64_741` `flip--_binary64_712` `associate-l*_binary64_678`
2×	`frac-times_binary64_747` `flip3-+_binary64_740` `cbrt-unprod_binary64_770` `associate-*l/_binary64_680` `1-exp_binary64_781` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `flip-+_binary64_711` `rec-exp_binary64_787`
1×	`diff-log_binary64_829` `frac-2neg_binary64_748` `clear-num_binary64_736` `sub-neg_binary64_730` `inv-pow_binary64_822` `pow-flip_binary64_811` `cancel-sign-sub-inv_binary64_703` `pow-prod-down_binary64_808` `-commutative_binary64_668` `un-div-inv_binary64_735` `associate-r/_binary64_679`

Counts

3 → 101

Calls

6 calls:

20.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
10.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series526.0ms (5.3%)

Counts

3 → 54

Calls

3 calls:

323.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
161.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
42.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 1344 to 1206 computations (10.3% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5444	3365

prune164.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	154	11	165

Error

7.3b

Counts

165 → 11

Compiler

Compiled 3335 to 1770 computations (46.9% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im))))
18.2b	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
18.2b	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
18.2b	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
20.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_737`
36×	`associate-r_binary64_677`
32×	`times-frac_binary64_743`
30×	`cbrt-div_binary64_769`
29×	`add-sqr-sqrt_binary64_759`
25×	`cbrt-prod_binary64_768`
24×	`add-cube-cbrt_binary64_772`
16×	`frac-times_binary64_747` `add-exp-log_binary64_775`
15×	`flip3--_binary64_741` `flip--_binary64_712`
12×	`associate-*l/_binary64_680` `unpow-prod-down_binary64_816` `distribute-lft-out_binary64_688`
10×	`add-cbrt-cube_binary64_773`
9×	`pow1_binary64_798`
6×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786`
5×	`associate-*r/_binary64_679`
4×	`add-log-exp_binary64_776`
3×	`pow1/3_binary64_819` `unswap-sqr_binary64_705` `pow-prod-down_binary64_808`
2×	`associate-/r/_binary64_683` `cbrt-undiv_binary64_771` `div-exp_binary64_788`
1×	`flip3-+_binary64_740` `div-inv_binary64_734` `flip-+_binary64_711` `associate-l_binary64_678` `*-commutative_binary64_668`

Counts

4 → 114

Calls

8 calls:

37.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
0.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im))))

series1.4s (14%)

Counts

4 → 90

Calls

4 calls:

401.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
333.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
329.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
329.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))

Compiler

Compiled 6473 to 4553 computations (29.7% saved)

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	8266
1	4969	8266

prune303.0ms (3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	204	11	215

Error

7.3b

Counts

215 → 11

Compiler

Compiled 8191 to 2791 computations (65.9% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	349	1753
1	349	1753

regimes747.0ms (7.5%)

Accuracy

Total 9.3b remaining (65.8%)

Threshold costs 0b (0%)

Compiler

Compiled 3688 to 2620 computations (29% saved)

bsearch61.0ms (0.6%)

Steps

Iters	Range		Point
6	7.228788391165348e+124	4.351321275675043e+125	1.400268501927579e+125
6	7.488680352529629e-129	5.514159515309266e-128	1.5711842677325443e-128
5	-5.0616238871190186e-141	-1.7462236958216747e-141	-2.5652367524611406e-141
5	-1.1698921252641593e+93	-3.950917608142549e+92	-1.1437132202364462e+93

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	84	161
1	84	161

end0.0ms (0%)

sample3.6s (36%)

Algorithm

1×

intervals

Results

359.0ms	8000×	body	128	valid
20.0ms	482×	body	128	invalid

Compiler

Compiled 2946 to 2049 computations (30.4% saved)

Pareto

0.13450273783531452

Details

analyze532.0ms (5.3%)

sample26.0ms (0.3%)

simplify225.0ms (2.3%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite21.0ms (0.2%)

series474.0ms (4.8%)

simplify80.0ms (0.8%)

prune163.0ms (1.6%)

localize16.0ms (0.2%)

rewrite41.0ms (0.4%)

series866.0ms (8.7%)

simplify107.0ms (1.1%)

prune236.0ms (2.4%)

localize12.0ms (0.1%)

rewrite44.0ms (0.4%)

series526.0ms (5.3%)

simplify91.0ms (0.9%)

prune164.0ms (1.6%)

localize15.0ms (0.2%)

rewrite67.0ms (0.7%)

series1.4s (14%)

simplify126.0ms (1.3%)

prune303.0ms (3%)

simplify24.0ms (0.2%)

regimes747.0ms (7.5%)

bsearch61.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (36%)

Profiling