Average Error: 0.2 → 0.2
Time: 27.1s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{y}}{3}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{y}}{3}
double f(double x, double y) {
        double r36841417 = x;
        double r36841418 = y;
        double r36841419 = 3.0;
        double r36841420 = r36841418 * r36841419;
        double r36841421 = r36841417 / r36841420;
        return r36841421;
}
↓
double f(double x, double y) {
        double r36841422 = x;
        double r36841423 = y;
        double r36841424 = r36841422 / r36841423;
        double r36841425 = 3.0;
        double r36841426 = r36841424 / r36841425;
        return r36841426;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))