Average Error: 0.1 → 0.1
Time: 14.9s
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 r402466 = x;
        double r402467 = y;
        double r402468 = r402466 - r402467;
        double r402469 = 2.0;
        double r402470 = r402468 / r402469;
        double r402471 = r402466 + r402470;
        return r402471;
}
↓
double f(double x, double y) {
        double r402472 = x;
        double r402473 = 2.0;
        double r402474 = r402472 / r402473;
        double r402475 = r402472 + r402474;
        double r402476 = y;
        double r402477 = r402476 / r402473;
        double r402478 = r402475 - r402477;
        return r402478;
}

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 2019195 
(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)))