Average Error: 14.9 → 0.0
Time: 28.3s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r23946873 = x;
        double r23946874 = y;
        double r23946875 = r23946873 - r23946874;
        double r23946876 = 2.0;
        double r23946877 = r23946873 * r23946876;
        double r23946878 = r23946877 * r23946874;
        double r23946879 = r23946875 / r23946878;
        return r23946879;
}
↓
double f(double x, double y) {
        double r23946880 = 0.5;
        double r23946881 = y;
        double r23946882 = r23946880 / r23946881;
        double r23946883 = x;
        double r23946884 = r23946880 / r23946883;
        double r23946885 = r23946882 - r23946884;
        return r23946885;
}

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

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.9

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} - \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))