Average Error: 0.0 → 0
Time: 7.9s
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 r17048233 = x;
        double r17048234 = y;
        double r17048235 = r17048234 - r17048233;
        double r17048236 = 2.0;
        double r17048237 = r17048235 / r17048236;
        double r17048238 = r17048233 + r17048237;
        return r17048238;
}
↓
double f(double x, double y) {
        double r17048239 = y;
        double r17048240 = x;
        double r17048241 = r17048239 + r17048240;
        double r17048242 = 0.5;
        double r17048243 = r17048241 * r17048242;
        return r17048243;
}

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 2019172 +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)))