Details

Time bar (total: 6.8s)

sample20.0ms

Algorithm
intervals
Results
8.0ms346×body80valid

simplify30.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize8.0ms

Local error

Found 1 expressions with local error:

3.3b
(* x (+ 1.0 (* y y)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
25.0ms
(* x (+ 1.0 (* y y)))

series85.0ms

Counts
1 → 3
Calls
1 calls:
84.0ms
(* x (+ 1.0 (* y y)))

simplify1.1s

Counts
25 → 25

prune53.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.3b
(sqrt (+ 1.0 (* y y)))
3.3b
(sqrt (+ 1.0 (* y y)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
17×add-sqr-sqrt
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 83
Calls
4 calls:
29.0ms
(* x (sqrt (+ 1.0 (* y y))))
68.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
8.0ms
(sqrt (+ 1.0 (* y y)))
8.0ms
(sqrt (+ 1.0 (* y y)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* x (sqrt (+ 1.0 (* y y))))
71.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
47.0ms
(sqrt (+ 1.0 (* y y)))
57.0ms
(sqrt (+ 1.0 (* y y)))

simplify465.0ms

Counts
95 → 95

prune293.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x 1.0) (* x (* y y)))
8.4b
(* x (* y y))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt add-log-exp
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
2 → 31
Calls
2 calls:
13.0ms
(+ (* x 1.0) (* x (* y y)))
25.0ms
(* x (* y y))

series142.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(+ (* x 1.0) (* x (* y y)))
48.0ms
(* x (* y y))

simplify1.1s

Counts
37 → 37

prune80.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x 1.0) (* (* x y) y))
0.1b
(* (* x y) y)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ associate-*l* sum-log *-commutative flip-+
Counts
2 → 29
Calls
2 calls:
13.0ms
(+ (* x 1.0) (* (* x y) y))
25.0ms
(* (* x y) y)

series135.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(+ (* x 1.0) (* (* x y) y))
48.0ms
(* (* x y) y)

simplify1.6s

Counts
35 → 35

prune80.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

-9015.6% (5.4b remaining)

Error of 5.4b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify27.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
671.0ms10731×body80valid