Average Error: 0.0 → 0.0
Time: 17.0s
Precision: 64
\[\frac{x}{x + y}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)\]
\frac{x}{x + y}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)
double f(double x, double y) {
        double r176823 = x;
        double r176824 = y;
        double r176825 = r176823 + r176824;
        double r176826 = r176823 / r176825;
        return r176826;
}
↓
double f(double x, double y) {
        double r176827 = x;
        double r176828 = y;
        double r176829 = r176827 + r176828;
        double r176830 = r176827 / r176829;
        double r176831 = log1p(r176830);
        double r176832 = expm1(r176831);
        return r176832;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x}{x + y}\]
  2. Using strategy rm

  3. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))