Average Error: 15.5 → 0.0
Time: 8.8s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{1}{2} \cdot \left(\frac{1}{y} + \frac{1}{x}\right)\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{1}{2} \cdot \left(\frac{1}{y} + \frac{1}{x}\right)
double f(double x, double y) {
        double r550854 = x;
        double r550855 = y;
        double r550856 = r550854 + r550855;
        double r550857 = 2.0;
        double r550858 = r550854 * r550857;
        double r550859 = r550858 * r550855;
        double r550860 = r550856 / r550859;
        return r550860;
}
↓
double f(double x, double y) {
        double r550861 = 1.0;
        double r550862 = 2.0;
        double r550863 = r550861 / r550862;
        double r550864 = 1.0;
        double r550865 = y;
        double r550866 = r550864 / r550865;
        double r550867 = x;
        double r550868 = r550864 / r550867;
        double r550869 = r550866 + r550868;
        double r550870 = r550863 * r550869;
        return r550870;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.5

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

  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

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{1}{y} + \frac{1}{x}\right)}\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{2} \cdot \left(\frac{1}{y} + \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2) y)))