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

sample21.0ms

Algorithm

intervals

Results

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

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 21.2b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms

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))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series16.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify19.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5103	655

prune58.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Merged error: 0.4b

Counts

50 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
20.3b	(sqrt (+ (* x x) (* y y)))
20.3b	(sqrt (+ (* x x) (* y y)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

9.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
37.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5482	3858

prune132.0ms

Filtered

125 candidates to 195 candidates (-56.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Merged error: 0.4b

Counts

199 → 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: 0.4b

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: 0.4b

Counts

4 → 4

regimes130.0ms

Accuracy

76.8% (4.7b remaining)

Error of 5.3b against oracle of 0.5b and baseline of 20.9b

bsearch47.0ms

Steps

Iters	Range		Point
7	5.0618702058061156e-166	1.6742258267314316e-164	9.358766827125048e-165
7	6.946913436878447e-177	7.449315912227158e-175	6.786522073016132e-175
10	-7.395723035357793e-160	-5.561308432808223e-177	-1.5984312638924005e-162
8	-1.2471835756991521e+157	-3.09497069783743e+153	-1.3688387676508722e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	59
1	40	59

end0.0ms

sample586.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
152.0ms	8000×	pre	80	true

Details

analyze12.0ms

sample21.0ms

simplify116.0ms

prune12.0ms

localize8.0ms

rewrite17.0ms

series16.0ms

simplify19.0ms

prune58.0ms

localize10.0ms

rewrite61.0ms

series37.0ms

simplify40.0ms

prune132.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune2.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes130.0ms

bsearch47.0ms

simplify1.0ms

end0.0ms

sample586.0ms

Profiling