Average Error: 0.0 → 0.0
Time: 15.9s
Precision: 64
\[\frac{x}{y \cdot 2}\]
↓
\[\frac{x}{y} \cdot 0.5\]
\frac{x}{y \cdot 2}
↓
\frac{x}{y} \cdot 0.5
double f(double x, double y) {
        double r6563093 = x;
        double r6563094 = y;
        double r6563095 = 2.0;
        double r6563096 = r6563094 * r6563095;
        double r6563097 = r6563093 / r6563096;
        return r6563097;
}
↓
double f(double x, double y) {
        double r6563098 = x;
        double r6563099 = y;
        double r6563100 = r6563098 / r6563099;
        double r6563101 = 0.5;
        double r6563102 = r6563100 * r6563101;
        return r6563102;
}

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

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C"
  (/ x (* y 2.0)))