Details

Time bar (total: 14.2s)

sample47.0ms

Algorithm
intervals
Results
25.0ms472×body80valid

simplify60.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0913
11713
23711
34511
done4511

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
0.0b
(+ (* x x) (* (* x 2.0) y))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×sum-log
2×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
1×associate-+l+
Counts
2 → 24
Calls
2 calls:
42.0ms
(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
18.0ms
(+ (* x x) (* (* x 2.0) y))

series112.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
71.0ms
(+ (* x x) (* (* x 2.0) y))

simplify2.7s

Counts
30 → 30
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
058525
1190459
2773381
33577373
done5000373

prune103.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (+ (* x 2.0) y))
0.0b
(* (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))) (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
6.7b
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
6.7b
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×sqrt-prod
23×pow1
16×add-cube-cbrt *-un-lft-identity sqrt-div
10×sqrt-pow1 pow1/2
9×flip3-+ associate-*r* associate-*l* flip-+
8×add-exp-log swap-sqr add-cbrt-cube
5×pow-prod-up unswap-sqr
4×frac-times associate-*r/ pow-prod-down add-log-exp
3×pow-sqr
2×rem-sqrt-square associate-*l/ prod-exp *-commutative cbrt-unprod
1×pow2 distribute-rgt-in distribute-lft-in pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 109
Calls
4 calls:
45.0ms
(* y (+ (* x 2.0) y))
142.0ms
(* (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))) (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
30.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
31.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* y (+ (* x 2.0) y))
44.0ms
(* (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))) (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
93.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
92.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

simplify3.3s

Counts
121 → 121
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01302877
13022068
29651880
343461777
done50001743

prune325.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
0.9b
(pow (cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))) 5)
6.7b
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
6.7b
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity sqrt-prod
9×unpow-prod-down
7×pow1
6×sqrt-div
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow flip3-+ flip-+
2×rem-sqrt-square cbrt-div pow-pow sqrt-pow1 pow1/2 pow1/3
1×pow-to-exp pow-exp sqr-pow
Counts
4 → 70
Calls
4 calls:
16.0ms
(cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
27.0ms
(pow (cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))) 5)
19.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
26.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x))))
274.0ms
(pow (cbrt (sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))) 5)
64.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))
71.0ms
(sqrt (+ (* y (+ (* x 2.0) y)) (* x x)))

simplify1.5s

Counts
82 → 82
Iterations

Useful iterations: 3 (551.0ms)

IterNodesCost
01311683
13061539
27691413
323381382
done50001382

prune314.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (- (* x 2.0) y))
0.2b
(* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x)))
2.9b
(- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4))
33.4b
(/ (- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4)) (+ (* x x) (* y (- (* x 2.0) y))))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
29×add-sqr-sqrt
20×add-exp-log add-cbrt-cube
18×times-frac pow-prod-down
17×add-cube-cbrt *-un-lft-identity
16×associate-*r/
15×difference-of-squares
10×distribute-rgt-in distribute-lft-in
9×prod-exp cbrt-unprod
7×flip3-+ flip-+
6×associate-/l* add-log-exp
5×unpow-prod-down sqr-pow
4×frac-times associate-*r* associate-*l* associate--l+ pow-sqr pow-prod-up
3×sub-neg flip3-- associate-/r* flip--
2×pow-plus associate-*l/ associate-/r/ *-commutative associate-/l/
1×cbrt-undiv pow2 frac-2neg diff-log div-sub swap-sqr div-exp clear-num div-inv unswap-sqr
Counts
4 → 133
Calls
4 calls:
29.0ms
(* y (- (* x 2.0) y))
74.0ms
(* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x)))
88.0ms
(- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4))
204.0ms
(/ (- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4)) (+ (* x x) (* y (- (* x 2.0) y))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* y (- (* x 2.0) y))
42.0ms
(* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x)))
109.0ms
(- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4))
76.0ms
(/ (- (* (* x (+ (* 2.0 y) x)) (* x (+ (* 2.0 y) x))) (pow y 4)) (+ (* x x) (* y (- (* x 2.0) y))))

simplify1.5s

Counts
145 → 145
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02393932
16553691
224653325
done50023284

prune470.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes83.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11313
done1313

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s14235×body80valid