Average Error: 9.9 → 0.2
Time: 12.6s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[\left(y \cdot x\right) \cdot \left(x \cdot 3\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
\left(y \cdot x\right) \cdot \left(x \cdot 3\right)
double f(double x, double y) {
        double r37497732 = x;
        double r37497733 = 3.0;
        double r37497734 = r37497732 * r37497733;
        double r37497735 = r37497734 * r37497732;
        double r37497736 = y;
        double r37497737 = r37497735 * r37497736;
        return r37497737;
}
↓
double f(double x, double y) {
        double r37497738 = y;
        double r37497739 = x;
        double r37497740 = r37497738 * r37497739;
        double r37497741 = 3.0;
        double r37497742 = r37497739 * r37497741;
        double r37497743 = r37497740 * r37497742;
        return r37497743;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.9
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 9.9

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

  3. Applied associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* (* x 3.0) (* x y))

  (* (* (* x 3.0) x) y))