Average Error: 0.3 → 0.2
Time: 15.6s
Precision: 64
\[\frac{x}{y \cdot 3.0}\]
↓
\[\frac{\frac{x}{y}}{3.0}\]
\frac{x}{y \cdot 3.0}
↓
\frac{\frac{x}{y}}{3.0}
double f(double x, double y) {
        double r27493002 = x;
        double r27493003 = y;
        double r27493004 = 3.0;
        double r27493005 = r27493003 * r27493004;
        double r27493006 = r27493002 / r27493005;
        return r27493006;
}
↓
double f(double x, double y) {
        double r27493007 = x;
        double r27493008 = y;
        double r27493009 = r27493007 / r27493008;
        double r27493010 = 3.0;
        double r27493011 = r27493009 / r27493010;
        return r27493011;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.3
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{3.0}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3.0}\]
  2. Using strategy rm

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

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot 3.0}\]

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3.0}}\]
  5. Using strategy rm

  6. Applied associate-*r/0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{y} \cdot x}{3.0}}\]

  7. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{3.0}\]

  8. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y}}{3.0}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))