Average Error: 0.0 → 0
Time: 3.4s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[\left(y + x\right) \cdot 0.5\]
x + \frac{y - x}{2}
↓
\left(y + x\right) \cdot 0.5
double f(double x, double y) {
        double r17332770 = x;
        double r17332771 = y;
        double r17332772 = r17332771 - r17332770;
        double r17332773 = 2.0;
        double r17332774 = r17332772 / r17332773;
        double r17332775 = r17332770 + r17332774;
        return r17332775;
}
↓
double f(double x, double y) {
        double r17332776 = y;
        double r17332777 = x;
        double r17332778 = r17332776 + r17332777;
        double r17332779 = 0.5;
        double r17332780 = r17332778 * r17332779;
        return r17332780;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[0.5 \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[x + \frac{y - x}{2}\]

  2. Taylor expanded around 0 0

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

  3. Simplified0

    \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)}\]

  4. Final simplification0

    \[\leadsto \left(y + x\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"

  :herbie-target
  (* 0.5 (+ x y))

  (+ x (/ (- y x) 2.0)))