Details

analyze17.0ms

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

sample23.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify148.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune3.0ms

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: 19.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
18.9b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow1_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
13.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series20.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify24.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5103	655

prune52.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 0.3b

Counts

49 → 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 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
18.2b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
18.2b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
39×	`sqrt-prod_binary64`
12×	`associate-/r*_binary64`
9×	`associate-/l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
7×	`distribute-lft-out_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`pow1_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/.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)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
16.0ms	(/.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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6324	2427

prune108.0ms

Filtered

100 candidates to 150 candidates (-50.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	149	6	155

Merged error: 0.3b

Counts

155 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (.f64 (+.f64 x y) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))))
0.2b	(.f64 (+.f64 x y) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
18.2b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
18.2b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
48×	`add-exp-log_binary64`
40×	`associate-l_binary64`
37×	`add-cube-cbrt_binary64`
32×	`sqrt-prod_binary64`
30×	`add-cbrt-cube_binary64`
25×	`associate-r_binary64`
22×	`prod-exp_binary64`
13×	`pow1_binary64`
12×	`cbrt-unprod_binary64` `frac-times_binary64`
11×	`div-exp_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
9×	`associate-*r/_binary64`
8×	`sqrt-div_binary64`
7×	`associate-*l/_binary64`
6×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `un-div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64`

Counts

4 → 160

Calls

4 calls:

26.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (.f64 (+.f64 x y) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))))
17.0ms	(.f64 (+.f64 x y) (/.f64 1 (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

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (.f64 (+.f64 x y) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))))
16.0ms	(.f64 (+.f64 x y) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify72.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4975	2651
1	4975	2651

prune124.0ms

Filtered

112 candidates to 172 candidates (-53.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	172	6	178

Merged error: 0.3b

Counts

178 → 6

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Merged error: 0.3b

Counts

6 → 6

regimes119.0ms

Accuracy

74.1% (5.1b remaining)

Error of 5.6b against oracle of 0.5b and baseline of 20.3b

bsearch39.0ms

Steps

Iters	Range	Point
6	4.130637735382058e-205	4.8418120782494744e-204	4.755047945101056e-204
7	-1.5335732361285339e-161	-4.4451465724872585e-163	-1.5799804884119341e-162
10	-6.818987673778931e-40	-8.900687591212937e-58	-6.71233735076048e-40

Iters

Range

Point

4.130637735382058e-205

4.8418120782494744e-204

4.755047945101056e-204

-1.5335732361285339e-161

-4.4451465724872585e-163

-1.5799804884119341e-162

-6.818987673778931e-40

-8.900687591212937e-58

-6.71233735076048e-40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	42
1	39	42

end0.0ms

sample619.0ms

Algorithm

intervals

Results

308.0ms	8000×	body	80	valid
156.0ms	8000×	pre	80	true

Details

analyze17.0ms

sample23.0ms

simplify148.0ms

prune3.0ms

localize8.0ms

rewrite19.0ms

series20.0ms

simplify24.0ms

prune52.0ms

localize12.0ms

rewrite34.0ms

series46.0ms

simplify64.0ms

prune108.0ms

localize12.0ms

rewrite59.0ms

series47.0ms

simplify72.0ms

prune124.0ms

localize1.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune0.0ms

regimes119.0ms

bsearch39.0ms

simplify2.0ms

end0.0ms

sample619.0ms

Profiling