Average Error: 15.4 → 0.0
Time: 754.0ms
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r494992 = x;
        double r494993 = y;
        double r494994 = r494992 - r494993;
        double r494995 = 2.0;
        double r494996 = r494992 * r494995;
        double r494997 = r494996 * r494993;
        double r494998 = r494994 / r494997;
        return r494998;
}
↓
double f(double x, double y) {
        double r494999 = 1.0;
        double r495000 = 2.0;
        double r495001 = y;
        double r495002 = r495000 * r495001;
        double r495003 = r494999 / r495002;
        double r495004 = x;
        double r495005 = r495004 * r495000;
        double r495006 = r494999 / r495005;
        double r495007 = r495003 - r495006;
        return r495007;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.4
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.4

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

  3. Applied div-sub15.4

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

  4. Simplified11.4

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(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)))