Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[\frac{x}{x + y}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)\]
\frac{x}{x + y}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)
double f(double x, double y) {
        double r203309 = x;
        double r203310 = y;
        double r203311 = r203309 + r203310;
        double r203312 = r203309 / r203311;
        return r203312;
}
↓
double f(double x, double y) {
        double r203313 = x;
        double r203314 = y;
        double r203315 = r203313 + r203314;
        double r203316 = r203313 / r203315;
        double r203317 = log1p(r203316);
        double r203318 = expm1(r203317);
        return r203318;
}

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

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))