Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\frac{x}{y + x}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{y + x}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r217787 = x;
        double r217788 = y;
        double r217789 = r217788 + r217787;
        double r217790 = r217787 / r217789;
        return r217790;
}
↓
double f(double x, double y) {
        double r217791 = x;
        double r217792 = y;
        double r217793 = r217792 + r217791;
        double r217794 = r217791 / r217793;
        double r217795 = expm1(r217794);
        double r217796 = log1p(r217795);
        return r217796;
}

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 log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))