Average Error: 0.0 → 0
Time: 6.0s
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 r333509 = x;
        double r333510 = y;
        double r333511 = r333510 - r333509;
        double r333512 = 2.0;
        double r333513 = r333511 / r333512;
        double r333514 = r333509 + r333513;
        return r333514;
}
↓
double f(double x, double y) {
        double r333515 = y;
        double r333516 = 2.0;
        double r333517 = r333515 / r333516;
        double r333518 = x;
        double r333519 = r333518 / r333516;
        double r333520 = r333519 - r333518;
        double r333521 = r333517 - r333520;
        return r333521;
}

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 2019195 
(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)))