Average Error: 0.1 → 0.1
Time: 11.2s
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 r822007 = x;
        double r822008 = y;
        double r822009 = r822007 - r822008;
        double r822010 = 2.0;
        double r822011 = r822009 / r822010;
        double r822012 = r822007 + r822011;
        return r822012;
}
↓
double f(double x, double y) {
        double r822013 = x;
        double r822014 = 2.0;
        double r822015 = r822013 / r822014;
        double r822016 = r822013 + r822015;
        double r822017 = y;
        double r822018 = r822017 / r822014;
        double r822019 = r822016 - r822018;
        return r822019;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +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)))