Average Error: 0.0 → 0.0
Time: 9.8s
Precision: 64
\[\frac{x}{y + x}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{y + x}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r205748 = x;
        double r205749 = y;
        double r205750 = r205749 + r205748;
        double r205751 = r205748 / r205750;
        return r205751;
}
↓
double f(double x, double y) {
        double r205752 = x;
        double r205753 = y;
        double r205754 = r205753 + r205752;
        double r205755 = r205752 / r205754;
        double r205756 = log1p(r205755);
        double r205757 = expm1(r205756);
        return r205757;
}

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

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

  3. Applied expm1-log1p-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))