Details

Time bar (total: 1.9s)

sample31.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 81.262212%

Space saved by search: 81.262212%

Guaranteed chance to sample good point: 0%

Results
11.0ms256×pre80true
10.0ms256×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1487
21047
31967
43597
56867
613437
750017

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.6b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
18.3b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
associate-/l/
add-exp-log add-cbrt-cube
flip3-+ flip-+
add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
flip3-- times-frac associate-/r* flip--
pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
+-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)))

series17.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (* x x) (* y y))
11.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0308388
11848330
25001322

prune70.0ms

Filtered
39 candidates to 48 candidates (-23.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New45348
Fresh000
Picked101
Done000
Total46349

Merged error: 0.5b

Counts
49 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (pow y 2))
0.2b
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
17.7b
(/ (+ x y) (+ (pow x 2) (pow y 2)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
41×times-frac
32×add-sqr-sqrt
31×distribute-lft-out
26×associate-*r*
25×add-cube-cbrt
20×unpow-prod-down
10×add-exp-log add-cbrt-cube
pow1 associate-*l* associate-/r* add-log-exp
flip3-+ associate-/r/ flip-+ associate-/l*
cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 109
Calls
3 calls:
8.0ms
(+ (pow x 2) (pow y 2))
21.0ms
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
14.0ms
(/ (+ x y) (+ (pow x 2) (pow y 2)))

series25.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (pow x 2) (pow y 2))
11.0ms
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
8.0ms
(/ (+ x y) (+ (pow x 2) (pow y 2)))

simplify59.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0390902
11953823
25002822

prune165.0ms

Filtered
69 candidates to 118 candidates (-71.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1171118
Fresh022
Picked011
Done000
Total1174121

Merged error: 0.5b

Counts
121 → 4

localize1.0ms

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)

IterNodesCost
000

prune6.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New000
Fresh022
Picked011
Done011
Total044

Merged error: 0.5b

Counts
4 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x y))
0.1b
(* (- x y) (* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))))
2.5b
(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2))))
4.4b
(/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
134×*-un-lft-identity
74×times-frac
65×add-sqr-sqrt
57×sqrt-prod
46×add-cube-cbrt
43×distribute-lft-out
42×associate-*r*
30×unpow-prod-down
20×add-exp-log sqrt-div add-cbrt-cube
18×frac-times
12×pow1 flip3-+ associate-*l* flip-+
10×associate-*l/
associate-*r/
prod-exp cbrt-unprod associate-/l*
flip3-- flip-- unswap-sqr
associate-/r*
pow-prod-down associate-/r/ add-log-exp
cbrt-undiv div-exp
*-commutative div-inv associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num distribute-lft-out-- difference-of-squares
Counts
4 → 190
Calls
4 calls:
3.0ms
(sqrt (+ x y))
23.0ms
(* (- x y) (* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))))
27.0ms
(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2))))
15.0ms
(/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))

series52.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ x y))
17.0ms
(* (- x y) (* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))))
17.0ms
(* (sqrt (+ x y)) (/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2))))
12.0ms
(/ (sqrt (+ x y)) (+ (pow x 2) (pow y 2)))

simplify92.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06032075
129121823
250011783

prune254.0ms

Filtered
115 candidates to 202 candidates (-75.7%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2020202
Fresh011
Picked011
Done022
Total2024206

Merged error: 0.5b

Counts
206 → 4

regimes104.0ms

Accuracy

73.8% (5.2b remaining)

Error of 5.7b against oracle of 0.5b and baseline of 20.3b

bsearch38.0ms

Steps
ItersRangePoint
6
9.081409731783568e-147
6.510853931669902e-146
1.804732805562769e-146
8
-1.4739504802020988e-159
-2.9750816689068754e-162
-1.4540419235939954e-159
4
-1.2884646919133893e-25
-6.579346138184302e-26
-1.2570093409768951e-25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914

end0.0ms

sample665.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 81.262212%

Space saved by search: 81.262212%

Guaranteed chance to sample good point: 0%

Results
308.0ms8000×body80valid
160.0ms8000×pre80true

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