Average Error: 0.0 → 0
Time: 1.6s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[0.5 \cdot \left(x + y\right)\]
x + \frac{y - x}{2}
↓
0.5 \cdot \left(x + y\right)
double f(double x, double y) {
        double r679086 = x;
        double r679087 = y;
        double r679088 = r679087 - r679086;
        double r679089 = 2.0;
        double r679090 = r679088 / r679089;
        double r679091 = r679086 + r679090;
        return r679091;
}
↓
double f(double x, double y) {
        double r679092 = 0.5;
        double r679093 = x;
        double r679094 = y;
        double r679095 = r679093 + r679094;
        double r679096 = r679092 * r679095;
        return r679096;
}

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64

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

  (+ x (/ (- y x) 2)))