Average Error: 14.9 → 0.0
Time: 12.4s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r384894 = x;
        double r384895 = y;
        double r384896 = r384894 + r384895;
        double r384897 = 2.0;
        double r384898 = r384894 * r384897;
        double r384899 = r384898 * r384895;
        double r384900 = r384896 / r384899;
        return r384900;
}
↓
double f(double x, double y) {
        double r384901 = 0.5;
        double r384902 = x;
        double r384903 = r384901 / r384902;
        double r384904 = y;
        double r384905 = r384901 / r384904;
        double r384906 = r384903 + r384905;
        return r384906;
}

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
\[\frac{0.5}{x} + \frac{0.5}{y}\]

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))