Average Error: 15.6 → 0.0
Time: 9.4s
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 r1131996 = x;
        double r1131997 = y;
        double r1131998 = r1131996 - r1131997;
        double r1131999 = 2.0;
        double r1132000 = r1131996 * r1131999;
        double r1132001 = r1132000 * r1131997;
        double r1132002 = r1131998 / r1132001;
        return r1132002;
}
↓
double f(double x, double y) {
        double r1132003 = 1.0;
        double r1132004 = 2.0;
        double r1132005 = r1132003 / r1132004;
        double r1132006 = y;
        double r1132007 = r1132005 / r1132006;
        double r1132008 = x;
        double r1132009 = r1132008 * r1132004;
        double r1132010 = r1132003 / r1132009;
        double r1132011 = r1132007 - r1132010;
        return r1132011;
}

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

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

  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 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)))