Average Error: 0.0 → 0
Time: 7.4s
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 r272276 = x;
        double r272277 = y;
        double r272278 = r272277 - r272276;
        double r272279 = 2.0;
        double r272280 = r272278 / r272279;
        double r272281 = r272276 + r272280;
        return r272281;
}
↓
double f(double x, double y) {
        double r272282 = y;
        double r272283 = 2.0;
        double r272284 = r272282 / r272283;
        double r272285 = x;
        double r272286 = r272285 / r272283;
        double r272287 = r272286 - r272285;
        double r272288 = r272284 - r272287;
        return r272288;
}

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 2019179 +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)))