Average Error: 14.7 → 0.0
Time: 5.8s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r27703449 = x;
        double r27703450 = y;
        double r27703451 = r27703449 + r27703450;
        double r27703452 = 2.0;
        double r27703453 = r27703449 * r27703452;
        double r27703454 = r27703453 * r27703450;
        double r27703455 = r27703451 / r27703454;
        return r27703455;
}
↓
double f(double x, double y) {
        double r27703456 = 0.5;
        double r27703457 = x;
        double r27703458 = r27703456 / r27703457;
        double r27703459 = y;
        double r27703460 = r27703456 / r27703459;
        double r27703461 = r27703458 + r27703460;
        return r27703461;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.7

    \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

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

  (/ (+ x y) (* (* x 2.0) y)))