Average Error: 0.0 → 0.0
Time: 1.6s
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 r250529 = x;
        double r250530 = y;
        double r250531 = r250529 + r250530;
        double r250532 = r250529 / r250531;
        return r250532;
}
↓
double f(double x, double y) {
        double r250533 = x;
        double r250534 = y;
        double r250535 = r250533 + r250534;
        double r250536 = r250533 / r250535;
        double r250537 = log1p(r250536);
        double r250538 = expm1(r250537);
        return r250538;
}

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)))