Details

analyze795.0ms (4.6%)

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)

sample24.0ms (0.1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify356.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (210.0ms)

Iter	Nodes	Cost
0	5232	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

27.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.9b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.9b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
27.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
9×	`times-frac_binary64_3494`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527`
3×	`associate-/r_binary64_3432` `associate-/l_binary64_3433`
2×	`flip3--_binary64_3492` `associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `flip--_binary64_3463` `pow1_binary64_3549`
1×	`clear-num_binary64_3487` `flip-+_binary64_3462` `diff-log_binary64_3580` `flip3-+_binary64_3491` `cancel-sign-sub-inv_binary64_3454` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-sub_binary64_3493` `div-inv_binary64_3485` `sub-neg_binary64_3481`

Counts

2 → 44

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(-.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)))

series630.0ms (3.6%)

Counts

2 → 48

Calls

2 calls:

427.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
203.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1068 to 882 computations (17.4% saved)

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4934	2277
1	4934	2277

prune267.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

3.5b

Counts

93 → 9

Compiler

Compiled 1935 to 681 computations (64.8% saved)

localize34.0ms (0.2%)

Local error

Found 8 expressions with local error:

30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
18.0b	(/.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))))
0.9b	(-.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))))
0.9b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
18.0b	(/.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))))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite83.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_3488`
28×	`sqrt-prod_binary64_3504`
25×	`add-sqr-sqrt_binary64_3510`
24×	`times-frac_binary64_3494`
23×	`add-cube-cbrt_binary64_3523`
10×	`distribute-lft-out_binary64_3439` `unpow-prod-down_binary64_3567`
8×	`associate-/r*_binary64_3432`
6×	`sqrt-div_binary64_3505` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527` `pow1_binary64_3549`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433`
2×	`flip3--_binary64_3492` `associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `pow1/2_binary64_3568` `flip--_binary64_3463` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`
1×	`clear-num_binary64_3487` `diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-sub_binary64_3493` `div-inv_binary64_3485` `sub-neg_binary64_3481`

Counts

4 → 96

Calls

8 calls:

31.0ms	(/.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))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im 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))))

series1.2s (7.1%)

Counts

4 → 94

Calls

4 calls:

647.0ms	(/.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))))
226.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
189.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
167.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3558 to 2778 computations (21.9% saved)

simplify138.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5048	4932

prune382.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	188	11	199

Error

3.5b

Counts

199 → 11

Compiler

Compiled 5852 to 2402 computations (59% saved)

localize43.0ms (0.2%)

Local error

Found 8 expressions with local error:

9.7b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))))
8.4b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.9b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
0.0b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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))))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
9.7b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite282.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

1001×	`sqrt-prod_binary64_3504`
825×	`times-frac_binary64_3494`
691×	`*-un-lft-identity_binary64_3488`
382×	`add-sqr-sqrt_binary64_3510`
379×	`add-cube-cbrt_binary64_3523`
156×	`distribute-lft-out_binary64_3439` `unpow-prod-down_binary64_3567`
58×	`sqrt-div_binary64_3505`
39×	`associate-/l*_binary64_3433`
26×	`associate-/r/_binary64_3434`
16×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
13×	`div-inv_binary64_3485`
11×	`associate-/r*_binary64_3432`
9×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
7×	`pow1_binary64_3549`
4×	`add-log-exp_binary64_3527`
3×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `rem-sqrt-square_binary64_3501`
2×	`div-sub_binary64_3493`
1×	`clear-num_binary64_3487` `associate-/l/_binary64_3435` `frac-2neg_binary64_3499`

Counts

4 → 546

Calls

8 calls:

42.0ms	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))))
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)))
0.0ms	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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))))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))

series1.2s (6.7%)

Counts

4 → 88

Calls

4 calls:

600.0ms	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))))
202.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
180.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
175.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4248 to 3324 computations (21.8% saved)

simplify584.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

634 → 634

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5122	40847

prune2.8s (16%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	634	0	634
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	634	11	645

Error

3.5b

Counts

645 → 11

Compiler

Compiled 31441 to 15143 computations (51.8% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

11.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.9b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.8b	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.3b	(*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
14.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
31.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite131.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64_3488`
49×	`add-exp-log_binary64_3526`
45×	`add-sqr-sqrt_binary64_3510`
39×	`times-frac_binary64_3494`
33×	`cbrt-prod_binary64_3519`
30×	`associate-r_binary64_3428`
24×	`add-cube-cbrt_binary64_3523`
20×	`cbrt-div_binary64_3520` `prod-exp_binary64_3537`
18×	`add-cbrt-cube_binary64_3524`
15×	`associate-l_binary64_3429` `div-exp_binary64_3539`
12×	`distribute-lft-out_binary64_3439` `unpow-prod-down_binary64_3567`
10×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434`
9×	`unswap-sqr_binary64_3456`
8×	`cbrt-unprod_binary64_3521`
7×	`cbrt-undiv_binary64_3522`
6×	`pow1_binary64_3549`
5×	`frac-times_binary64_3498`
4×	`1-exp_binary64_3532` `rec-exp_binary64_3538` `add-log-exp_binary64_3527`
3×	`associate-l/_binary64_3431` `associate-r/_binary64_3430` `pow1/3_binary64_3570`
2×	`div-inv_binary64_3485`
1×	`pow-prod-down_binary64_3559` `*-commutative_binary64_3419`

Counts

4 → 131

Calls

8 calls:

64.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.0ms	(*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series1.2s (6.7%)

Counts

4 → 60

Calls

4 calls:

442.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
265.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
243.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
214.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3102 to 2658 computations (14.3% saved)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5068	6837

prune523.0ms (3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	191	11	202

Error

3.5b

Counts

202 → 11

Compiler

Compiled 7208 to 4491 computations (37.7% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	312	1799
1	312	1799

regimes865.0ms (5%)

Accuracy

Total 11.1b remaining (68.7%)

Threshold costs 0b (0%)

Compiler

Compiled 3792 to 2776 computations (26.8% saved)

bsearch129.0ms (0.7%)

Steps

Iters	Range		Point
9	1.585010678955201e+40	6.464176775332817e+45	5.618016963658139e+45
10	1.5317612403127707e-115	3.142734090316026e-99	1.7736026235522196e-115
8	-2.271203142594088e-161	-4.727330348033218e-164	-3.5075870245798887e-162
8	-6.401469326770505e+102	-6.659753031856651e+99	-2.623594142603243e+102

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	77	159
1	77	159

end0.0ms (0%)

sample5.4s (30.8%)

Algorithm

1×

intervals

Results

490.0ms	8000×	body	128	valid
32.0ms	494×	body	128	invalid

Compiler

Compiled 3022 to 2168 computations (28.3% saved)

Pareto

0.2069895122433963

Details

analyze795.0ms (4.6%)

sample24.0ms (0.1%)

simplify356.0ms (2.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite30.0ms (0.2%)

series630.0ms (3.6%)

simplify109.0ms (0.6%)

prune267.0ms (1.5%)

localize34.0ms (0.2%)

rewrite83.0ms (0.5%)

series1.2s (7.1%)

simplify138.0ms (0.8%)

prune382.0ms (2.2%)

localize43.0ms (0.2%)

rewrite282.0ms (1.6%)

series1.2s (6.7%)

simplify584.0ms (3.4%)

prune2.8s (16%)

localize20.0ms (0.1%)

rewrite131.0ms (0.8%)

series1.2s (6.7%)

simplify179.0ms (1%)

prune523.0ms (3%)

simplify41.0ms (0.2%)

regimes865.0ms (5%)

bsearch129.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.4s (30.8%)

Profiling