Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\frac{x}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right)\]
\frac{x}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right)
double f(double x, double y) {
        double r238100 = x;
        double r238101 = y;
        double r238102 = r238100 + r238101;
        double r238103 = r238100 / r238102;
        return r238103;
}
↓
double f(double x, double y) {
        double r238104 = x;
        double r238105 = y;
        double r238106 = r238104 + r238105;
        double r238107 = r238104 / r238106;
        double r238108 = expm1(r238107);
        double r238109 = log1p(r238108);
        return r238109;
}

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

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))