Average Error: 15.5 → 0.0
Time: 8.2s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r26970364 = x;
        double r26970365 = y;
        double r26970366 = r26970364 - r26970365;
        double r26970367 = 2.0;
        double r26970368 = r26970364 * r26970367;
        double r26970369 = r26970368 * r26970365;
        double r26970370 = r26970366 / r26970369;
        return r26970370;
}
↓
double f(double x, double y) {
        double r26970371 = 0.5;
        double r26970372 = y;
        double r26970373 = r26970371 / r26970372;
        double r26970374 = x;
        double r26970375 = r26970371 / r26970374;
        double r26970376 = r26970373 - r26970375;
        return r26970376;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.5

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}\]

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} - \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))