Average Error: 14.6 → 0.0
Time: 5.0s
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 r27388360 = x;
        double r27388361 = y;
        double r27388362 = r27388360 - r27388361;
        double r27388363 = 2.0;
        double r27388364 = r27388360 * r27388363;
        double r27388365 = r27388364 * r27388361;
        double r27388366 = r27388362 / r27388365;
        return r27388366;
}
↓
double f(double x, double y) {
        double r27388367 = 0.5;
        double r27388368 = y;
        double r27388369 = r27388367 / r27388368;
        double r27388370 = x;
        double r27388371 = r27388367 / r27388370;
        double r27388372 = r27388369 - r27388371;
        return r27388372;
}

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

Derivation

  1. Initial program 14.6

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

  2. Taylor expanded around 0 0.0

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

  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 2019163 
(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)))