Average Error: 0.0 → 0.0
Time: 18.3s
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 r13128041 = x;
        double r13128042 = y;
        double r13128043 = r13128041 + r13128042;
        double r13128044 = r13128041 / r13128043;
        return r13128044;
}
↓
double f(double x, double y) {
        double r13128045 = x;
        double r13128046 = y;
        double r13128047 = r13128046 + r13128045;
        double r13128048 = r13128045 / r13128047;
        double r13128049 = expm1(r13128048);
        double r13128050 = log1p(r13128049);
        return r13128050;
}

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)))