Average Error: 14.5 → 0.0
Time: 8.6s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
double f(double x, double y) {
        double r27478420 = x;
        double r27478421 = y;
        double r27478422 = r27478420 + r27478421;
        double r27478423 = 2.0;
        double r27478424 = r27478420 * r27478423;
        double r27478425 = r27478424 * r27478421;
        double r27478426 = r27478422 / r27478425;
        return r27478426;
}
↓
double f(double x, double y) {
        double r27478427 = 0.5;
        double r27478428 = y;
        double r27478429 = r27478427 / r27478428;
        double r27478430 = x;
        double r27478431 = r27478427 / r27478430;
        double r27478432 = r27478429 + r27478431;
        return r27478432;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.5

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

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(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)))