Average Error: 0.0 → 0.0
Time: 57.6s
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 r12395523 = x;
        double r12395524 = y;
        double r12395525 = r12395523 + r12395524;
        double r12395526 = r12395523 / r12395525;
        return r12395526;
}
↓
double f(double x, double y) {
        double r12395527 = x;
        double r12395528 = y;
        double r12395529 = r12395527 + r12395528;
        double r12395530 = r12395527 / r12395529;
        double r12395531 = log1p(r12395530);
        double r12395532 = expm1(r12395531);
        return r12395532;
}

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 2019200 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  (/ x (+ x y)))