Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[\frac{x}{y + x}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{y + x}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r341281 = x;
        double r341282 = y;
        double r341283 = r341282 + r341281;
        double r341284 = r341281 / r341283;
        return r341284;
}
↓
double f(double x, double y) {
        double r341285 = x;
        double r341286 = y;
        double r341287 = r341286 + r341285;
        double r341288 = r341285 / r341287;
        double r341289 = log1p(r341288);
        double r341290 = expm1(r341289);
        return r341290;
}

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

    \[\frac{x}{y + x}\]
  2. Using strategy rm

  3. Applied expm1-log1p-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))