Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[\frac{x}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r10147578 = x;
        double r10147579 = y;
        double r10147580 = r10147578 + r10147579;
        double r10147581 = r10147578 / r10147580;
        return r10147581;
}
↓
double f(double x, double y) {
        double r10147582 = x;
        double r10147583 = y;
        double r10147584 = r10147583 + r10147582;
        double r10147585 = r10147582 / r10147584;
        double r10147586 = expm1(r10147585);
        double r10147587 = log1p(r10147586);
        return r10147587;
}

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 log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  (/ x (+ x y)))