Average Error: 14.5 → 0.0
Time: 9.3s
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 r25262901 = x;
        double r25262902 = y;
        double r25262903 = r25262901 + r25262902;
        double r25262904 = 2.0;
        double r25262905 = r25262901 * r25262904;
        double r25262906 = r25262905 * r25262902;
        double r25262907 = r25262903 / r25262906;
        return r25262907;
}
↓
double f(double x, double y) {
        double r25262908 = 0.5;
        double r25262909 = y;
        double r25262910 = r25262908 / r25262909;
        double r25262911 = x;
        double r25262912 = r25262908 / r25262911;
        double r25262913 = r25262910 + r25262912;
        return r25262913;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.5

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

  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 2019162 
(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)))