Details

sample62.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 81.262212%

Space saved by search: 81.262212%

Guaranteed chance to sample good point: 99.987793%

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1343	7
7	5001	7

prune5.0ms

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: 17.8b

Counts

2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
17.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
20.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series16.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune61.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Merged error: 0.5b

Counts

49 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
17.1b	(sqrt (+ (* x x) (* y y)))
17.1b	(sqrt (+ (* x x) (* y y)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
90×	`times-frac`
55×	`add-cube-cbrt`
54×	`sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 175

Calls

4 calls:

31.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
8.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
5.0ms	(sqrt (+ (* x x) (* y y)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
15.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
6.0ms	(sqrt (+ (* x x) (* y y)))
6.0ms	(sqrt (+ (* x x) (* y y)))

simplify69.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	579	2358
1	2429	2169
2	5001	2080

prune121.0ms

Filtered

118 candidates to 187 candidates (-58.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	187	4	191

Merged error: 0.5b

Counts

191 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Merged error: 0.5b

Counts

4 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Merged error: 0.5b

Counts

4 → 4

regimes135.0ms

Accuracy

76.1% (4.8b remaining)

Error of 5.3b against oracle of 0.5b and baseline of 20.8b

bsearch96.0ms

Steps

Iters	Range	Point
8	9.225300238822177e-165	1.9499815645811423e-161	1.9116594609265736e-161
10	-3.6192374959309305e-153	-2.22378472391342e-167	-2.6242548116494392e-160
8	-9.572001587333725e+156	-6.618629093142626e+152	-1.3258250458662918e+154

Iters

Range

Point

9.225300238822177e-165

1.9499815645811423e-161

1.9116594609265736e-161

-3.6192374959309305e-153

-2.22378472391342e-167

-2.6242548116494392e-160

-9.572001587333725e+156

-6.618629093142626e+152

-1.3258250458662918e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample712.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 81.262212%

Space saved by search: 81.262212%

Guaranteed chance to sample good point: 99.987793%

Results

308.0ms	8000×	body	80	valid
151.0ms	8000×	pre	80	true

Details

sample62.0ms

simplify67.0ms

prune5.0ms

localize16.0ms

rewrite26.0ms

series16.0ms

simplify42.0ms

prune61.0ms

localize11.0ms

rewrite55.0ms

series38.0ms

simplify69.0ms

prune121.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune2.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes135.0ms

bsearch96.0ms

simplify1.0ms

end0.0ms

sample712.0ms

Profiling