Average Error: 10.6 → 0.3
Time: 1.9s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
\left(x \cdot 3\right) \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r746618 = x;
        double r746619 = 3.0;
        double r746620 = r746618 * r746619;
        double r746621 = r746620 * r746618;
        double r746622 = y;
        double r746623 = r746621 * r746622;
        return r746623;
}
↓
double f(double x, double y) {
        double r746624 = x;
        double r746625 = 3.0;
        double r746626 = r746624 * r746625;
        double r746627 = y;
        double r746628 = r746624 * r746627;
        double r746629 = r746626 * r746628;
        return r746629;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target0.3
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.6

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3) (* x y))

  (* (* (* x 3) x) y))