Details

Time bar (total: 13.4s)

sample21.0ms

Algorithm
intervals
Results
11.0ms438×body80valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0913
11713
23511
34211
done4211

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
11.0ms
(* x (+ (* 2.0 y) x))
3.0ms
(+ (* y y) (* x (+ (* 2.0 y) x)))

series63.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* x (+ (* 2.0 y) x))
23.0ms
(+ (* y y) (* x (+ (* 2.0 y) x)))

simplify3.6s

Counts
41 → 41
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
073527
1228493
2998439
34872439
done5000439

prune72.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (* x (+ (* 2.0 y) x)))
0.0b
(* (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))) (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))))
8.6b
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
8.6b
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-+r+ associate-*r/ associate-*l/
1×+-commutative pow2 distribute-rgt-in distribute-lft-in pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 100
Calls
4 calls:
3.0ms
(+ (* y y) (* x (+ (* 2.0 y) x)))
21.0ms
(* (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))) (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))))
4.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
4.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (* y y) (* x (+ (* 2.0 y) x)))
23.0ms
(* (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))) (sqrt (+ (* y y) (* x (+ (* 2.0 y) x)))))
53.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
54.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))

simplify4.1s

Counts
112 → 112
Iterations

Useful iterations: 3 (577.0ms)

IterNodesCost
01062898
12282093
28821847
349381784
done50001784

prune200.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))) (sqrt (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))))
8.6b
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
9.2b
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
9.2b
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity sqrt-prod
10×cbrt-prod
9×associate-*r*
7×pow1
6×add-exp-log cbrt-div add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3 associate-*r/
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
13.0ms
(* (fabs (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))) (sqrt (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))))
4.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
2.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
2.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

series496.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (fabs (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))) (sqrt (cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))))
55.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
133.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
132.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

simplify2.1s

Counts
81 → 81
Iterations

Useful iterations: 3 (514.0ms)

IterNodesCost
01512110
13441991
210931803
344251743
done50001743

prune272.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
8.6b
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
9.2b
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
9.2b
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
4.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
4.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
2.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
2.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
53.0ms
(sqrt (+ (* y y) (* x (+ (* 2.0 y) x))))
132.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))
135.0ms
(cbrt (+ (* y y) (* x (+ (* 2.0 y) x))))

simplify955.0ms

Counts
68 → 68
Iterations

Useful iterations: 3 (242.0ms)

IterNodesCost
0801300
11811202
25841094
322511084
done50001084

prune320.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11211
done1211

end0.0ms

sample582.0ms

Algorithm
intervals
Results
371.0ms14101×body80valid