Average Error: 0.0 → 0.0
Time: 635.0ms
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 r219034 = x;
        double r219035 = y;
        double r219036 = 2.0;
        double r219037 = r219035 * r219036;
        double r219038 = r219034 / r219037;
        return r219038;
}
↓
double f(double x, double y) {
        double r219039 = 0.5;
        double r219040 = x;
        double r219041 = y;
        double r219042 = r219040 / r219041;
        double r219043 = r219039 * r219042;
        return r219043;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

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