Average Error: 0.0 → 0.0
Time: 10.8s
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 r10723369 = x;
        double r10723370 = y;
        double r10723371 = r10723369 + r10723370;
        double r10723372 = r10723369 / r10723371;
        return r10723372;
}
↓
double f(double x, double y) {
        double r10723373 = x;
        double r10723374 = y;
        double r10723375 = r10723374 + r10723373;
        double r10723376 = r10723373 / r10723375;
        double r10723377 = log1p(r10723376);
        double r10723378 = expm1(r10723377);
        return r10723378;
}

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)))