Average Error: 0.1 → 0.1
Time: 4.1s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[x + \left(\frac{x}{2} - \frac{y}{2}\right)\]
x + \frac{x - y}{2}
↓
x + \left(\frac{x}{2} - \frac{y}{2}\right)
double f(double x, double y) {
        double r618438 = x;
        double r618439 = y;
        double r618440 = r618438 - r618439;
        double r618441 = 2.0;
        double r618442 = r618440 / r618441;
        double r618443 = r618438 + r618442;
        return r618443;
}
↓
double f(double x, double y) {
        double r618444 = x;
        double r618445 = 2.0;
        double r618446 = r618444 / r618445;
        double r618447 = y;
        double r618448 = r618447 / r618445;
        double r618449 = r618446 - r618448;
        double r618450 = r618444 + r618449;
        return r618450;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2}\]
  2. Using strategy rm

  3. Applied div-sub0.1

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

  4. Applied associate-+r-0.1

    \[\leadsto \color{blue}{\left(x + \frac{x}{2}\right) - \frac{y}{2}}\]
  5. Using strategy rm

  6. Applied associate--l+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

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

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