Average Error: 15.6 → 0.0
Time: 4.5s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{\frac{1}{y}}{2} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{\frac{1}{y}}{2} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r815041 = x;
        double r815042 = y;
        double r815043 = r815041 - r815042;
        double r815044 = 2.0;
        double r815045 = r815041 * r815044;
        double r815046 = r815045 * r815042;
        double r815047 = r815043 / r815046;
        return r815047;
}
↓
double f(double x, double y) {
        double r815048 = 1.0;
        double r815049 = y;
        double r815050 = r815048 / r815049;
        double r815051 = 2.0;
        double r815052 = r815050 / r815051;
        double r815053 = x;
        double r815054 = r815053 * r815051;
        double r815055 = r815048 / r815054;
        double r815056 = r815052 - r815055;
        return r815056;
}

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. Simplified11.9

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))