Average Error: 15.0 → 0.0
Time: 2.9s
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 r703285 = x;
        double r703286 = y;
        double r703287 = r703285 - r703286;
        double r703288 = 2.0;
        double r703289 = r703285 * r703288;
        double r703290 = r703289 * r703286;
        double r703291 = r703287 / r703290;
        return r703291;
}
↓
double f(double x, double y) {
        double r703292 = 1.0;
        double r703293 = 2.0;
        double r703294 = r703292 / r703293;
        double r703295 = y;
        double r703296 = r703294 / r703295;
        double r703297 = x;
        double r703298 = r703297 * r703293;
        double r703299 = r703292 / r703298;
        double r703300 = r703296 - r703299;
        return r703300;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 15.0

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

  3. Applied div-sub15.0

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

  4. Simplified11.1

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

  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 2020045 +o rules:numerics
(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)))