Average Error: 0.0 → 0.0
Time: 882.0ms
Precision: 64
\[\frac{x}{y \cdot 2}\]
↓
\[\frac{\frac{x}{y}}{2}\]
\frac{x}{y \cdot 2}
↓
\frac{\frac{x}{y}}{2}
double f(double x, double y) {
        double r138825 = x;
        double r138826 = y;
        double r138827 = 2.0;
        double r138828 = r138826 * r138827;
        double r138829 = r138825 / r138828;
        return r138829;
}
↓
double f(double x, double y) {
        double r138830 = x;
        double r138831 = y;
        double r138832 = r138830 / r138831;
        double r138833 = 2.0;
        double r138834 = r138832 / r138833;
        return r138834;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied associate-/r*0.0

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2}}\]

  4. Final simplification0.0

    \[\leadsto \frac{\frac{x}{y}}{2}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C"
  :precision binary64
  (/ x (* y 2)))