Average Error: 14.8 → 0.0
Time: 24.1s
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 r793864 = x;
        double r793865 = y;
        double r793866 = r793864 - r793865;
        double r793867 = 2.0;
        double r793868 = r793864 * r793867;
        double r793869 = r793868 * r793865;
        double r793870 = r793866 / r793869;
        return r793870;
}
↓
double f(double x, double y) {
        double r793871 = 0.5;
        double r793872 = y;
        double r793873 = r793871 / r793872;
        double r793874 = x;
        double r793875 = r793871 / r793874;
        double r793876 = r793873 - r793875;
        return r793876;
}

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

Original14.8
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.8

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

  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 2019305 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2) y)))