Average Error: 10.9 → 0.2
Time: 6.7s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[\left(x \cdot 3\right) \cdot \left(y \cdot x\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
\left(x \cdot 3\right) \cdot \left(y \cdot x\right)
double f(double x, double y) {
        double r602813 = x;
        double r602814 = 3.0;
        double r602815 = r602813 * r602814;
        double r602816 = r602815 * r602813;
        double r602817 = y;
        double r602818 = r602816 * r602817;
        return r602818;
}
↓
double f(double x, double y) {
        double r602819 = x;
        double r602820 = 3.0;
        double r602821 = r602819 * r602820;
        double r602822 = y;
        double r602823 = r602822 * r602819;
        double r602824 = r602821 * r602823;
        return r602824;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.9

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(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))