Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[\frac{x}{y \cdot 2.0}\]
↓
\[\frac{x}{y} \cdot 0.5\]
\frac{x}{y \cdot 2.0}
↓
\frac{x}{y} \cdot 0.5
double f(double x, double y) {
        double r12641645 = x;
        double r12641646 = y;
        double r12641647 = 2.0;
        double r12641648 = r12641646 * r12641647;
        double r12641649 = r12641645 / r12641648;
        return r12641649;
}
↓
double f(double x, double y) {
        double r12641650 = x;
        double r12641651 = y;
        double r12641652 = r12641650 / r12641651;
        double r12641653 = 0.5;
        double r12641654 = r12641652 * r12641653;
        return r12641654;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x}{y \cdot 2.0}\]

  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)))