Average Error: 15.1 → 0.0
Time: 22.0s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r372682 = x;
        double r372683 = y;
        double r372684 = r372682 - r372683;
        double r372685 = 2.0;
        double r372686 = r372682 * r372685;
        double r372687 = r372686 * r372683;
        double r372688 = r372684 / r372687;
        return r372688;
}
↓
double f(double x, double y) {
        double r372689 = 0.5;
        double r372690 = y;
        double r372691 = r372689 / r372690;
        double r372692 = x;
        double r372693 = r372689 / r372692;
        double r372694 = r372691 - r372693;
        return r372694;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.1

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

  2. Simplified8.3

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +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)))