Average Error: 0.1 → 0.1
Time: 4.3s
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 r801024 = x;
        double r801025 = y;
        double r801026 = r801024 - r801025;
        double r801027 = 2.0;
        double r801028 = r801026 / r801027;
        double r801029 = r801024 + r801028;
        return r801029;
}
↓
double f(double x, double y) {
        double r801030 = x;
        double r801031 = 2.0;
        double r801032 = r801030 / r801031;
        double r801033 = r801030 + r801032;
        double r801034 = y;
        double r801035 = r801034 / r801031;
        double r801036 = r801033 - r801035;
        return r801036;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 +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)))