Average Error: 14.9 → 0.0
Time: 40.6s
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 r17321686 = x;
        double r17321687 = y;
        double r17321688 = r17321686 - r17321687;
        double r17321689 = 2.0;
        double r17321690 = r17321686 * r17321689;
        double r17321691 = r17321690 * r17321687;
        double r17321692 = r17321688 / r17321691;
        return r17321692;
}
↓
double f(double x, double y) {
        double r17321693 = 0.5;
        double r17321694 = y;
        double r17321695 = r17321693 / r17321694;
        double r17321696 = x;
        double r17321697 = r17321693 / r17321696;
        double r17321698 = r17321695 - r17321697;
        return r17321698;
}

Error

Bits error versus x

Bits error versus y

Try it out

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 +o rules:numerics
(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)))