Average Error: 14.6 → 0.0
Time: 5.5s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
double f(double x, double y) {
        double r25929767 = x;
        double r25929768 = y;
        double r25929769 = r25929767 + r25929768;
        double r25929770 = 2.0;
        double r25929771 = r25929767 * r25929770;
        double r25929772 = r25929771 * r25929768;
        double r25929773 = r25929769 / r25929772;
        return r25929773;
}
↓
double f(double x, double y) {
        double r25929774 = 0.5;
        double r25929775 = y;
        double r25929776 = r25929774 / r25929775;
        double r25929777 = x;
        double r25929778 = r25929774 / r25929777;
        double r25929779 = r25929776 + r25929778;
        return r25929779;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.6

    \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]

  2. Taylor expanded around 0 0.0

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

  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 2019163 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

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

  (/ (+ x y) (* (* x 2.0) y)))