Details

analyze13.0ms

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

sample28.0ms

Algorithm

intervals

Results

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

simplify149.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

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: 20.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
20.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite18.0ms

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)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
13.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify22.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5103	655

prune57.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.5b

Counts

49 → 4

localize0.0ms

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 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.5b

Counts

4 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 y y) (.f64 x x))
20.6b	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-/r*_binary64`
7×	`add-log-exp_binary64`
5×	`neg-mul-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `distribute-neg-frac_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 94

Calls

3 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 y y) (.f64 x x))
11.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))

series145.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
5.0ms	(-.f64 (.f64 y y) (.f64 x x))
135.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4941	2092
1	4941	2092

prune77.0ms

Filtered

79 candidates to 103 candidates (-30.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	4	107

Merged error: 0.5b

Counts

107 → 4

localize11.0ms

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 x y))
19.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
19.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite45.0ms

Algorithm

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:

10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
19.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
15.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify59.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5886	2655

prune105.0ms

Filtered

114 candidates to 163 candidates (-43.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Merged error: 0.5b

Counts

167 → 4

regimes124.0ms

Accuracy

78.9% (4.5b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 21.8b

bsearch43.0ms

Steps

Iters	Range	Point
10	4.915073955433892e-170	5.148523267551369e-157	1.5574783314889873e-162
9	-9.759662152981248e-157	-5.648508456451283e-165	-1.5570222608799464e-162
9	-3.239675390048663e+155	-6.414788358883296e+148	-1.3557348503118228e+154

Iters

Range

Point

4.915073955433892e-170

5.148523267551369e-157

1.5574783314889873e-162

-9.759662152981248e-157

-5.648508456451283e-165

-1.5570222608799464e-162

-3.239675390048663e+155

-6.414788358883296e+148

-1.3557348503118228e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	31
1	63	31

end0.0ms

sample578.0ms

Algorithm

intervals

Results

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

Details

analyze13.0ms

sample28.0ms

simplify149.0ms

prune2.0ms

localize9.0ms

rewrite18.0ms

series18.0ms

simplify22.0ms

prune57.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune8.0ms

localize7.0ms

rewrite23.0ms

series145.0ms

simplify51.0ms

prune77.0ms

localize11.0ms

rewrite45.0ms

series40.0ms

simplify59.0ms

prune105.0ms

regimes124.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

sample578.0ms

Profiling