Average Error: 0.3 → 0.2
Time: 29.5s
Precision: 64
\[\frac{x}{y \cdot 3.0}\]
↓
\[\frac{\frac{x}{3.0}}{y}\]
\frac{x}{y \cdot 3.0}
↓
\frac{\frac{x}{3.0}}{y}
double f(double x, double y) {
        double r32492289 = x;
        double r32492290 = y;
        double r32492291 = 3.0;
        double r32492292 = r32492290 * r32492291;
        double r32492293 = r32492289 / r32492292;
        return r32492293;
}
↓
double f(double x, double y) {
        double r32492294 = x;
        double r32492295 = 3.0;
        double r32492296 = r32492294 / r32492295;
        double r32492297 = y;
        double r32492298 = r32492296 / r32492297;
        return r32492298;
}

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

Derivation

  1. Initial program 0.3

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

  3. Applied associate-/r*0.3

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

  5. Applied div-inv0.4

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

  6. Applied associate-/l*0.3

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

  7. Simplified0.3

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

  9. Applied associate-/r*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 +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)))