Average Error: 0.1 → 0.1
Time: 44.1s
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 r34011585 = x;
        double r34011586 = y;
        double r34011587 = r34011585 - r34011586;
        double r34011588 = 2.0;
        double r34011589 = r34011587 / r34011588;
        double r34011590 = r34011585 + r34011589;
        return r34011590;
}
↓
double f(double x, double y) {
        double r34011591 = 1.5;
        double r34011592 = x;
        double r34011593 = r34011591 * r34011592;
        double r34011594 = 0.5;
        double r34011595 = y;
        double r34011596 = r34011594 * r34011595;
        double r34011597 = r34011593 - r34011596;
        return r34011597;
}

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 2019168 
(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)))