Average Error: 14.6 → 0.0
Time: 7.2s
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 r22633901 = x;
        double r22633902 = y;
        double r22633903 = r22633901 - r22633902;
        double r22633904 = 2.0;
        double r22633905 = r22633901 * r22633904;
        double r22633906 = r22633905 * r22633902;
        double r22633907 = r22633903 / r22633906;
        return r22633907;
}
↓
double f(double x, double y) {
        double r22633908 = 0.5;
        double r22633909 = y;
        double r22633910 = r22633908 / r22633909;
        double r22633911 = x;
        double r22633912 = r22633908 / r22633911;
        double r22633913 = r22633910 - r22633912;
        return r22633913;
}

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 +o rules:numerics
(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)))