Average Error: 0.1 → 0.1
Time: 5.2s
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 r737252 = x;
        double r737253 = y;
        double r737254 = r737252 - r737253;
        double r737255 = 2.0;
        double r737256 = r737254 / r737255;
        double r737257 = r737252 + r737256;
        return r737257;
}
↓
double f(double x, double y) {
        double r737258 = 1.5;
        double r737259 = x;
        double r737260 = r737258 * r737259;
        double r737261 = 0.5;
        double r737262 = y;
        double r737263 = r737261 * r737262;
        double r737264 = r737260 - r737263;
        return r737264;
}

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 2020083 
(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)))