Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[\frac{x}{x + y}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{x + y}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r13645149 = x;
        double r13645150 = y;
        double r13645151 = r13645149 + r13645150;
        double r13645152 = r13645149 / r13645151;
        return r13645152;
}
↓
double f(double x, double y) {
        double r13645153 = x;
        double r13645154 = y;
        double r13645155 = r13645154 + r13645153;
        double r13645156 = r13645153 / r13645155;
        double r13645157 = log1p(r13645156);
        double r13645158 = expm1(r13645157);
        return r13645158;
}

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

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  (/ x (+ x y)))