Average Error: 0.0 → 0
Time: 5.2s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[\frac{y}{2} - \left(\frac{x}{2} - x\right)\]
x + \frac{y - x}{2}
↓
\frac{y}{2} - \left(\frac{x}{2} - x\right)
double f(double x, double y) {
        double r227007 = x;
        double r227008 = y;
        double r227009 = r227008 - r227007;
        double r227010 = 2.0;
        double r227011 = r227009 / r227010;
        double r227012 = r227007 + r227011;
        return r227012;
}
↓
double f(double x, double y) {
        double r227013 = y;
        double r227014 = 2.0;
        double r227015 = r227013 / r227014;
        double r227016 = x;
        double r227017 = r227016 / r227014;
        double r227018 = r227017 - r227016;
        double r227019 = r227015 - r227018;
        return r227019;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{y - x}{2} + x}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \color{blue}{\left(\frac{y}{2} - \frac{x}{2}\right)} + x\]

  5. Applied associate-+l-0

    \[\leadsto \color{blue}{\frac{y}{2} - \left(\frac{x}{2} - x\right)}\]

  6. Final simplification0

    \[\leadsto \frac{y}{2} - \left(\frac{x}{2} - x\right)\]

Reproduce

herbie shell --seed 2019196 
(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)))