Average Error: 15.6 → 0.0
Time: 15.8s
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 r342143 = x;
        double r342144 = y;
        double r342145 = r342143 - r342144;
        double r342146 = 2.0;
        double r342147 = r342143 * r342146;
        double r342148 = r342147 * r342144;
        double r342149 = r342145 / r342148;
        return r342149;
}
↓
double f(double x, double y) {
        double r342150 = 1.0;
        double r342151 = 2.0;
        double r342152 = r342150 / r342151;
        double r342153 = y;
        double r342154 = r342152 / r342153;
        double r342155 = x;
        double r342156 = r342155 * r342151;
        double r342157 = r342150 / r342156;
        double r342158 = r342154 - r342157;
        return r342158;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.6

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

  3. Applied div-sub15.6

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

  4. Simplified11.7

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

  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 2019323 
(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)))