Average Error: 14.8 → 0.0
Time: 19.6s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{\frac{1}{2}}{y} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{\frac{1}{2}}{y} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r482601 = x;
        double r482602 = y;
        double r482603 = r482601 - r482602;
        double r482604 = 2.0;
        double r482605 = r482601 * r482604;
        double r482606 = r482605 * r482602;
        double r482607 = r482603 / r482606;
        return r482607;
}
↓
double f(double x, double y) {
        double r482608 = 1.0;
        double r482609 = 2.0;
        double r482610 = r482608 / r482609;
        double r482611 = y;
        double r482612 = r482610 / r482611;
        double r482613 = x;
        double r482614 = r482613 * r482609;
        double r482615 = r482608 / r482614;
        double r482616 = r482612 - r482615;
        return r482616;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.8

    \[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
  2. Using strategy rm

  3. Applied div-sub14.8

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

  4. Simplified11.2

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

  5. Simplified0.0

    \[\leadsto \frac{\frac{1}{2}}{y} - \color{blue}{\frac{1}{x \cdot 2}}\]

  6. Final simplification0.0

    \[\leadsto \frac{\frac{1}{2}}{y} - \frac{1}{x \cdot 2}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2) y)))