Details

analyze12.0ms

Algorithm

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

sample20.0ms

Algorithm

intervals

Results

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

simplify141.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune2.0ms

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: 22.0b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

21.7b

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

rewrite14.0ms

Algorithm

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)))

series12.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify23.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5037	530

prune29.0ms

Filtered

29 candidates to 34 candidates (-17.2%)

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: 0.5b

Counts

35 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
21.7b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
42×	`cbrt-prod_binary64`
36×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`difference-of-squares_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/l*_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 156

Calls

4 calls:

4.0ms	(-.f64 (.f64 x x) (.f64 y y))
13.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(-.f64 (.f64 x x) (.f64 y y))
14.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
11.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

simplify41.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5141	3499

prune58.0ms

Filtered

96 candidates to 168 candidates (-75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	168	5	173

Merged error: 0.5b

Counts

173 → 5

localize12.0ms

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)))))
21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite61.0ms

Algorithm

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:

10.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
35.0ms	(.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)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
12.0ms	(.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)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify39.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5365	3657

prune58.0ms

Filtered

118 candidates to 187 candidates (-58.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Merged error: 0.5b

Counts

192 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4905	656
1	4905	656

prune35.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	72	5	77

Merged error: 0.5b

Counts

77 → 5

regimes79.0ms

Accuracy

75.7% (4.9b remaining)

Error of 5.4b against oracle of 0.5b and baseline of 20.5b

bsearch37.0ms

Steps

Iters	Range	Point
9	4.763976081445814e-183	3.564488819899749e-175	3.499968286662803e-175
7	-7.106694359012905e-162	-4.9495550466928255e-164	-1.601462366399571e-162
9	-1.6971016249681123e+159	-1.2388388534000808e+151	-1.3482160583740896e+154

Iters

Range

Point

4.763976081445814e-183

3.564488819899749e-175

3.499968286662803e-175

-7.106694359012905e-162

-4.9495550466928255e-164

-1.601462366399571e-162

-1.6971016249681123e+159

-1.2388388534000808e+151

-1.3482160583740896e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	57
1	49	57

end0.0ms

sample581.0ms

Algorithm

intervals

Results

294.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

analyze12.0ms

sample20.0ms

simplify141.0ms

prune2.0ms

localize8.0ms

rewrite14.0ms

series12.0ms

simplify23.0ms

prune29.0ms

localize9.0ms

rewrite43.0ms

series41.0ms

simplify41.0ms

prune58.0ms

localize12.0ms

rewrite61.0ms

series41.0ms

simplify39.0ms

prune58.0ms

localize16.0ms

rewrite19.0ms

series25.0ms

simplify54.0ms

prune35.0ms

regimes79.0ms

bsearch37.0ms

simplify2.0ms

end0.0ms

sample581.0ms

Profiling