Details

analyze18.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

sample22.0ms (1.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify145.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune5.0ms (0.3%)

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: 18.8b

Counts

2 → 1

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

18.6b

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`-un-lft-identity_binary64` `associate-/r_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `flip--_binary64`
2×	`cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

1 → 31

Calls

1 calls:

13.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

series13.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

13.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

simplify20.0ms (1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5037	530

prune58.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 0.2b

Counts

35 → 5

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
18.6b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite38.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64` `exp-prod_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
19×	`log-pow_binary64`
11×	`difference-of-squares_binary64`
7×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
5×	`pow1_binary64`
4×	`associate-/l*_binary64`
3×	`flip3-+_binary64` `associate-/r*_binary64` `log-prod_binary64` `div-sub_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `exp-diff_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 106

Calls

4 calls:

10.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
10.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
9.0ms	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
5.0ms	(-.f64 (.f64 x x) (.f64 y y))

series46.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
12.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
12.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
8.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify59.0ms (3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4968	1906
1	4968	1906

prune115.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Merged error: 0.2b

Counts

123 → 5

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
18.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
18.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite66.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
55×	`add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
36×	`associate-l_binary64`
30×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`distribute-lft-out_binary64`
10×	`sqrt-div_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 175

Calls

4 calls:

37.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
10.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series44.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
13.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify40.0ms (2%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5365	3657

prune166.0ms (8.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Merged error: 0.2b

Counts

192 → 5

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
18.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
18.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite47.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`
36×	`associate-l_binary64`
13×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `sqrt-div_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-/r/_binary64`
3×	`unswap-sqr_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

22.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series47.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
15.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify58.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5881	2655

prune143.0ms (7.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	163	5	168

Merged error: 0.2b

Counts

168 → 5

regimes119.0ms (6.1%)

Accuracy

Total 4.8b remaining (90.6%)

Threshold costs 0b (0%)

bsearch42.0ms (2.1%)

Steps

Iters	Range	Point
9	4.489922899979828e-165	1.4700532434388884e-159	1.5914560295974384e-162
9	-2.0025949026897407e-162	-7.7078244958492525e-171	-1.5477292189177258e-162
8	-2.4190552886522042e+154	-8.450831678082356e+149	-1.3746297857855241e+154

Iters

Range

Point

4.489922899979828e-165

1.4700532434388884e-159

1.5914560295974384e-162

-2.0025949026897407e-162

-7.7078244958492525e-171

-1.5477292189177258e-162

-2.4190552886522042e+154

-8.450831678082356e+149

-1.3746297857855241e+154

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	32
1	41	32

end0.0ms (0%)

sample608.0ms (30.8%)

Algorithm

1×

intervals

Results

306.0ms	8000×	body	80	valid
160.0ms	8000×	pre	80	true

Details

analyze18.0ms (0.9%)

sample22.0ms (1.1%)

simplify145.0ms (7.3%)

prune5.0ms (0.3%)

localize8.0ms (0.4%)

rewrite14.0ms (0.7%)

series13.0ms (0.7%)

simplify20.0ms (1%)

prune58.0ms (2.9%)

localize10.0ms (0.5%)

rewrite38.0ms (1.9%)

series46.0ms (2.3%)

simplify59.0ms (3%)

prune115.0ms (5.8%)

localize10.0ms (0.5%)

rewrite66.0ms (3.3%)

series44.0ms (2.2%)

simplify40.0ms (2%)

prune166.0ms (8.4%)

localize10.0ms (0.5%)

rewrite47.0ms (2.4%)

series47.0ms (2.4%)

simplify58.0ms (2.9%)

prune143.0ms (7.2%)

regimes119.0ms (6.1%)

bsearch42.0ms (2.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample608.0ms (30.8%)

Profiling