Average Error: 0.2 → 0.2
Time: 9.1s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{x}{3 \cdot y}\]
\frac{x}{y \cdot 3}
↓
\frac{x}{3 \cdot y}
double f(double x, double y) {
        double r478780 = x;
        double r478781 = y;
        double r478782 = 3.0;
        double r478783 = r478781 * r478782;
        double r478784 = r478780 / r478783;
        return r478784;
}
↓
double f(double x, double y) {
        double r478785 = x;
        double r478786 = 3.0;
        double r478787 = y;
        double r478788 = r478786 * r478787;
        double r478789 = r478785 / r478788;
        return r478789;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.3
Herbie0.2
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.2

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot 3}\]

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.3

    \[\leadsto \color{blue}{\left(1 \cdot \frac{1}{y}\right)} \cdot \frac{x}{3}\]

  7. Applied associate-*l*0.3

    \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{y} \cdot \frac{x}{3}\right)}\]

  8. Simplified0.2

    \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{3}}{y}}\]
  9. Using strategy rm

  10. Applied div-inv0.3

    \[\leadsto 1 \cdot \frac{\color{blue}{x \cdot \frac{1}{3}}}{y}\]

  11. Applied associate-/l*0.3

    \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{y}{\frac{1}{3}}}}\]

  12. Simplified0.2

    \[\leadsto 1 \cdot \frac{x}{\color{blue}{3 \cdot y}}\]

  13. Final simplification0.2

    \[\leadsto \frac{x}{3 \cdot y}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))