Average Error: 14.6 → 0.0
Time: 5.2s
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 r21295833 = x;
        double r21295834 = y;
        double r21295835 = r21295833 + r21295834;
        double r21295836 = 2.0;
        double r21295837 = r21295833 * r21295836;
        double r21295838 = r21295837 * r21295834;
        double r21295839 = r21295835 / r21295838;
        return r21295839;
}
↓
double f(double x, double y) {
        double r21295840 = 0.5;
        double r21295841 = x;
        double r21295842 = r21295840 / r21295841;
        double r21295843 = y;
        double r21295844 = r21295840 / r21295843;
        double r21295845 = r21295842 + r21295844;
        return r21295845;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.6

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

  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 2019163 +o rules:numerics
(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)))