Average Error: 0.1 → 0.1
Time: 18.0s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[\left(x + \frac{x}{2}\right) - \frac{y}{2}\]
x + \frac{x - y}{2}
↓
\left(x + \frac{x}{2}\right) - \frac{y}{2}
double f(double x, double y) {
        double r528833 = x;
        double r528834 = y;
        double r528835 = r528833 - r528834;
        double r528836 = 2.0;
        double r528837 = r528835 / r528836;
        double r528838 = r528833 + r528837;
        return r528838;
}
↓
double f(double x, double y) {
        double r528839 = x;
        double r528840 = 2.0;
        double r528841 = r528839 / r528840;
        double r528842 = r528839 + r528841;
        double r528843 = y;
        double r528844 = r528843 / r528840;
        double r528845 = r528842 - r528844;
        return r528845;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"

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

  (+ x (/ (- x y) 2.0)))