Average Error: 0.0 → 0.0
Time: 653.0ms
Precision: 64
\[\frac{x}{y \cdot 2}\]
↓
\[0.5 \cdot \frac{x}{y}\]
\frac{x}{y \cdot 2}
↓
0.5 \cdot \frac{x}{y}
double f(double x, double y) {
        double r317096 = x;
        double r317097 = y;
        double r317098 = 2.0;
        double r317099 = r317097 * r317098;
        double r317100 = r317096 / r317099;
        return r317100;
}
↓
double f(double x, double y) {
        double r317101 = 0.5;
        double r317102 = x;
        double r317103 = y;
        double r317104 = r317102 / r317103;
        double r317105 = r317101 * r317104;
        return r317105;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y}}\]

  3. Final simplification0.0

    \[\leadsto 0.5 \cdot \frac{x}{y}\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C"
  :precision binary64
  (/ x (* y 2)))