Average Error: 10.5 → 0.3
Time: 8.1s
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 r34649812 = x;
        double r34649813 = 3.0;
        double r34649814 = r34649812 * r34649813;
        double r34649815 = r34649814 * r34649812;
        double r34649816 = y;
        double r34649817 = r34649815 * r34649816;
        return r34649817;
}
↓
double f(double x, double y) {
        double r34649818 = y;
        double r34649819 = x;
        double r34649820 = r34649818 * r34649819;
        double r34649821 = 3.0;
        double r34649822 = r34649819 * r34649821;
        double r34649823 = r34649820 * r34649822;
        return r34649823;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.3
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.5

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

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(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))