Average Error: 0.0 → 0.0
Time: 8.2s
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 r347918 = x;
        double r347919 = y;
        double r347920 = r347918 + r347919;
        double r347921 = r347918 / r347920;
        return r347921;
}
↓
double f(double x, double y) {
        double r347922 = x;
        double r347923 = y;
        double r347924 = r347922 + r347923;
        double r347925 = r347922 / r347924;
        double r347926 = log1p(r347925);
        double r347927 = expm1(r347926);
        return r347927;
}

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 2020046 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))