Average Error: 0.1 → 0.1
Time: 16.5s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[1.5 \cdot x - 0.5 \cdot y\]
x + \frac{x - y}{2}
↓
1.5 \cdot x - 0.5 \cdot y
double f(double x, double y) {
        double r412971 = x;
        double r412972 = y;
        double r412973 = r412971 - r412972;
        double r412974 = 2.0;
        double r412975 = r412973 / r412974;
        double r412976 = r412971 + r412975;
        return r412976;
}
↓
double f(double x, double y) {
        double r412977 = 1.5;
        double r412978 = x;
        double r412979 = r412977 * r412978;
        double r412980 = 0.5;
        double r412981 = y;
        double r412982 = r412980 * r412981;
        double r412983 = r412979 - r412982;
        return r412983;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{1.5 \cdot x - 0.5 \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 1.5 \cdot x - 0.5 \cdot y\]

Reproduce

herbie shell --seed 2019198 
(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)))