Average Error: 0.0 → 0
Time: 7.8s
Precision: 64
\[x + \frac{y - x}{2.0}\]
↓
\[\left(y + x\right) \cdot 0.5\]
x + \frac{y - x}{2.0}
↓
\left(y + x\right) \cdot 0.5
double f(double x, double y) {
        double r20693195 = x;
        double r20693196 = y;
        double r20693197 = r20693196 - r20693195;
        double r20693198 = 2.0;
        double r20693199 = r20693197 / r20693198;
        double r20693200 = r20693195 + r20693199;
        return r20693200;
}
↓
double f(double x, double y) {
        double r20693201 = y;
        double r20693202 = x;
        double r20693203 = r20693201 + r20693202;
        double r20693204 = 0.5;
        double r20693205 = r20693203 * r20693204;
        return r20693205;
}

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019162 +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)))