Average Error: 0.0 → 0
Time: 3.3s
Precision: 64
\[x + \frac{y - x}{2.0}\]
↓
\[\left(x + y\right) \cdot 0.5\]
x + \frac{y - x}{2.0}
↓
\left(x + y\right) \cdot 0.5
double f(double x, double y) {
        double r19128706 = x;
        double r19128707 = y;
        double r19128708 = r19128707 - r19128706;
        double r19128709 = 2.0;
        double r19128710 = r19128708 / r19128709;
        double r19128711 = r19128706 + r19128710;
        return r19128711;
}
↓
double f(double x, double y) {
        double r19128712 = x;
        double r19128713 = y;
        double r19128714 = r19128712 + r19128713;
        double r19128715 = 0.5;
        double r19128716 = r19128714 * r19128715;
        return r19128716;
}

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

    \[x + \frac{y - x}{2.0}\]

  2. Taylor expanded around 0 0

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

  3. Simplified0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019163 +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)))