Average Error: 0.1 → 0.1
Time: 7.7s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[x + \frac{x - y}{2}\]
x + \frac{x - y}{2}
↓
x + \frac{x - y}{2}
double f(double x, double y) {
        double r657875 = x;
        double r657876 = y;
        double r657877 = r657875 - r657876;
        double r657878 = 2.0;
        double r657879 = r657877 / r657878;
        double r657880 = r657875 + r657879;
        return r657880;
}
↓
double f(double x, double y) {
        double r657881 = x;
        double r657882 = y;
        double r657883 = r657881 - r657882;
        double r657884 = 2.0;
        double r657885 = r657883 / r657884;
        double r657886 = r657881 + r657885;
        return r657886;
}

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. Final simplification0.1

    \[\leadsto x + \frac{x - y}{2}\]

Reproduce

herbie shell --seed 2020064 
(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)))