Average Error: 0.3 → 0.2
Time: 1.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y}
double f(double x, double y) {
        double r851887 = x;
        double r851888 = y;
        double r851889 = 3.0;
        double r851890 = r851888 * r851889;
        double r851891 = r851887 / r851890;
        return r851891;
}
↓
double f(double x, double y) {
        double r851892 = x;
        double r851893 = 3.0;
        double r851894 = r851892 / r851893;
        double r851895 = y;
        double r851896 = r851894 / r851895;
        return r851896;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.3

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

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

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))