Details

Time bar (total: 14.0s)

sample48.0ms

Algorithm
intervals
Results
24.0ms422×body80valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0811
1159
2249
3269
done269

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite77.0ms

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+ distribute-lft-out
Counts
2 → 25
Calls
2 calls:
15.0ms
(+ (* x 2.0) (* x x))
61.0ms
(+ (+ (* x 2.0) (* x x)) (* y y))

series117.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(+ (* x 2.0) (* x x))
42.0ms
(+ (+ (* x 2.0) (* x x)) (* y y))

simplify1.8s

Counts
31 → 31
Iterations

Useful iterations: 3 (718.0ms)

IterNodesCost
057440
1181340
2669308
32696302
done5000302

prune116.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* x (+ 2.0 x)) (pow y 2)))
0.0b
(+ (* x (+ 2.0 x)) (pow y 2))
0.0b
(+ (* x (+ 2.0 x)) (pow y 2))
0.1b
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
14×sqrt-div
13×add-cube-cbrt *-un-lft-identity
9×sqrt-pow1 flip3-+ pow1/2 flip-+
8×swap-sqr add-log-exp
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×frac-times associate-+l+ unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
30.0ms
(sqrt (+ (* x (+ 2.0 x)) (pow y 2)))
17.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
16.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
187.0ms
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (+ (* x (+ 2.0 x)) (pow y 2)))
44.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
44.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
44.0ms
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))

simplify2.3s

Counts
110 → 110
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01022423
12121733
26591573
328831470
done50001426

prune252.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x (+ 2.0 x)) (pow y 2))
0.0b
(+ (* x (+ 2.0 x)) (pow y 2))
0.1b
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))))
0.4b
(* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))))

rewrite440.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-div
83×sqrt-pow1
71×sqrt-prod
65×pow1
52×add-sqr-sqrt
43×pow1/2
39×pow-prod-up
35×flip3-+ flip-+
32×frac-times
18×add-cube-cbrt *-un-lft-identity
17×swap-sqr
16×associate-*r/
15×associate-*l*
12×pow-prod-down
11×add-exp-log pow-sqr add-cbrt-cube unswap-sqr
10×associate-*r* associate-*l/
8×add-log-exp
4×associate-+l+ prod-exp cbrt-unprod
3×sqrt-unprod
2×+-commutative distribute-rgt-in distribute-lft-in sum-log *-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 181
Calls
4 calls:
17.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
16.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
230.0ms
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))))
166.0ms
(* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
37.0ms
(+ (* x (+ 2.0 x)) (pow y 2))
52.0ms
(* (sqrt (+ (* x (+ 2.0 x)) (pow y 2))) (* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2))))))
139.0ms
(* (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))) (sqrt (sqrt (+ (* x (+ 2.0 x)) (pow y 2)))))

simplify3.6s

Counts
193 → 193
Iterations

Useful iterations: done (3.5s)

IterNodesCost
02036622
14264076
211653654
346293314
done50003283

prune442.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x (+ x 2.0)) (* y y))
0.1b
(* (* x (+ 2.0 x)) (* x (+ 2.0 x)))
1.6b
(- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4))
27.6b
(/ (- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4)) (- (* x (+ x 2.0)) (* y y)))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
25×add-sqr-sqrt
18×add-exp-log times-frac add-cbrt-cube
17×pow-prod-down
15×add-cube-cbrt *-un-lft-identity difference-of-squares
14×associate-*r/
9×distribute-rgt-in distribute-lft-in
8×prod-exp cbrt-unprod add-log-exp
6×flip3-+ associate--l+ flip-+ associate-/l*
5×unpow-prod-down sqr-pow
4×frac-times flip3-- pow-sqr pow-prod-up flip--
3×associate-/r*
2×sub-neg pow-plus diff-log associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg div-sub swap-sqr div-exp associate-*r* associate-*l* clear-num *-commutative div-inv
Counts
4 → 123
Calls
4 calls:
24.0ms
(- (* x (+ x 2.0)) (* y y))
74.0ms
(* (* x (+ 2.0 x)) (* x (+ 2.0 x)))
67.0ms
(- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4))
230.0ms
(/ (- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4)) (- (* x (+ x 2.0)) (* y y)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* x (+ x 2.0)) (* y y))
34.0ms
(* (* x (+ 2.0 x)) (* x (+ 2.0 x)))
98.0ms
(- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4))
113.0ms
(/ (- (* (* x (+ 2.0 x)) (* x (+ 2.0 x))) (pow y 4)) (- (* x (+ x 2.0)) (* y y)))

simplify1.4s

Counts
135 → 135
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02043153
15782896
223152644
done50002347

prune295.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
done1111

end0.0ms

sample1.5s

Algorithm
intervals
Results
974.0ms14320×body80valid