Details

analyze19.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample13.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	248×	body	128	valid
0.0ms	4×	body	2048	valid
0.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify110.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	159	12
1	159	12

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64_4852` `add-log-exp_binary64_4891`
1×	`add-exp-log_binary64_4890` `+-commutative_binary64_4782` `flip-+_binary64_4826` `add-cube-cbrt_binary64_4887` `distribute-lft-out_binary64_4803` `add-cbrt-cube_binary64_4888` `add-sqr-sqrt_binary64_4874` `pow1_binary64_4913` `flip3-+_binary64_4855` `sum-log_binary64_4943`

Counts

1 → 12

Calls

1 calls:

6.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series22.0ms (1.1%)

Counts

1 → 3

Calls

1 calls:

22.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify69.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5354	255

prune15.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Compiler

Compiled 257 to 135 computations (47.5% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.4b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))

rewrite47.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_4852` `sqrt-prod_binary64_4868`
30×	`add-sqr-sqrt_binary64_4874`
21×	`pow1_binary64_4913`
16×	`sqrt-div_binary64_4869`
14×	`add-cube-cbrt_binary64_4887`
11×	`swap-sqr_binary64_4819`
10×	`pow1/2_binary64_4932` `sqrt-pow1_binary64_4870`
9×	`flip-+_binary64_4826` `distribute-lft-out_binary64_4803` `flip3-+_binary64_4855`
7×	`associate-l_binary64_4793` `associate-r_binary64_4792`
6×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888` `add-log-exp_binary64_4891`
5×	`pow-prod-up_binary64_4922`
4×	`unswap-sqr_binary64_4820` `frac-times_binary64_4862` `rem-sqrt-square_binary64_4865`
3×	`pow-sqr_binary64_4825` `pow-prod-down_binary64_4923`
2×	`associate-r/_binary64_4794` `associate-l/_binary64_4795`
1×	`sqrt-unprod_binary64_4872` `+-commutative_binary64_4782` `cbrt-unprod_binary64_4885` `pow-plus_binary64_4915` `prod-exp_binary64_4901` `rem-square-sqrt_binary64_4864` `pow2_binary64_4933` `sqr-abs_binary64_4867` `sum-log_binary64_4943` `*-commutative_binary64_4783`

Counts

4 → 107

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
6.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
6.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
6.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

series175.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
62.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
23.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
20.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify96.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4941	2487
1	4941	2487

prune119.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Error

0.0b

Counts

123 → 4

Compiler

Compiled 2780 to 1410 computations (49.3% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
0.0b	(*.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))
10.6b	(-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x)))
27.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

rewrite54.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64_4874`
54×	`*-un-lft-identity_binary64_4852`
48×	`times-frac_binary64_4858`
36×	`add-cube-cbrt_binary64_4887`
26×	`cancel-sign-sub-inv_binary64_4818`
19×	`associate-l_binary64_4793`
14×	`difference-of-squares_binary64_4821`
11×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
9×	`distribute-lft-out--_binary64_4804`
8×	`associate--r+_binary64_4788` `distribute-lft-in_binary64_4801` `add-log-exp_binary64_4891` `distribute-rgt-in_binary64_4802`
6×	`flip3--_binary64_4856` `sub-neg_binary64_4845` `associate-/r*_binary64_4796` `pow1_binary64_4913` `flip--_binary64_4827`
5×	`associate-r_binary64_4792`
3×	`div-inv_binary64_4849` `associate-/l*_binary64_4797`
2×	`unswap-sqr_binary64_4820` `frac-times_binary64_4862` `cbrt-unprod_binary64_4885` `associate-*r/_binary64_4794` `associate-/l/_binary64_4799` `prod-exp_binary64_4901` `associate-/r/_binary64_4798` `diff-log_binary64_4944` `cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
1×	`div-sub_binary64_4857` `clear-num_binary64_4851` `associate-l/_binary64_4795` `pow-prod-down_binary64_4923` `frac-2neg_binary64_4863` `-commutative_binary64_4783`

Counts

4 → 143

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
13.0ms	(*.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))
7.0ms	(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
5.0ms	(-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x)))

series145.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
29.0ms	(-.f64 (.f64 x x) (.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x)))
22.0ms	(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
19.0ms	(*.f64 (/.f64 (-.f64 y x) 4) (-.f64 y x))

simplify70.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4997	4297
1	4997	4297

prune179.0ms (8.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	155	4	159

Error

0.0b

Counts

159 → 4

Compiler

Compiled 4923 to 2083 computations (57.7% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
0.1b	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3)
37.8b	(cbrt.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3))

rewrite25.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_4852`
14×	`cbrt-prod_binary64_4883`
9×	`add-cube-cbrt_binary64_4887` `add-sqr-sqrt_binary64_4874`
8×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
5×	`distribute-lft-out_binary64_4803` `add-log-exp_binary64_4891`
4×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888` `pow1_binary64_4913` `cube-div_binary64_4881`
3×	`flip-+_binary64_4826` `pow-unpow_binary64_4929` `flip3-+_binary64_4855`
2×	`cube-mult_binary64_4882` `cbrt-div_binary64_4884` `unpow3_binary64_4918` `sqr-pow_binary64_4824`
1×	`+-commutative_binary64_4782` `pow-pow_binary64_4924` `rem-cube-cbrt_binary64_4875` `pow1/3_binary64_4934` `pow-to-exp_binary64_4921` `pow-exp_binary64_4920` `rem-cbrt-cube_binary64_4876` `sum-log_binary64_4943`

Counts

3 → 64

Calls

3 calls:

7.0ms	(cbrt.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3))
7.0ms	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3)
6.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series97.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3)
24.0ms	(cbrt.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)) 3))
19.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify75.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4987	1447
1	4987	1447

prune62.0ms (3.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	73	4	77

Error

0.0b

Counts

77 → 4

Compiler

Compiled 1233 to 669 computations (45.7% saved)

regimes55.0ms (2.7%)

Accuracy

Total 0.0b remaining (50.7%)

Threshold costs 0.0b (50.7%)

Compiler

Compiled 389 to 295 computations (24.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms (0%)

sample528.0ms (26.1%)

Algorithm

1×

intervals

Results

200.0ms	7704×	body	128	valid
11.0ms	118×	body	1024	valid
9.0ms	78×	body	2048	valid
4.0ms	59×	body	512	valid
2.0ms	41×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 140 to 108 computations (22.9% saved)

Details

analyze19.0ms (0.9%)

sample13.0ms (0.7%)

simplify110.0ms (5.4%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

rewrite7.0ms (0.3%)

series22.0ms (1.1%)

simplify69.0ms (3.4%)

prune15.0ms (0.7%)

localize8.0ms (0.4%)

rewrite47.0ms (2.3%)

series175.0ms (8.7%)

simplify96.0ms (4.7%)

prune119.0ms (5.9%)

localize11.0ms (0.6%)

rewrite54.0ms (2.7%)

series145.0ms (7.2%)

simplify70.0ms (3.5%)

prune179.0ms (8.8%)

localize8.0ms (0.4%)

rewrite25.0ms (1.2%)

series97.0ms (4.8%)

simplify75.0ms (3.7%)

prune62.0ms (3.1%)

regimes55.0ms (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample528.0ms (26.1%)

Profiling