Average Error: 0.0 → 0.0
Time: 17.8s
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 r11576675 = x;
        double r11576676 = y;
        double r11576677 = r11576676 + r11576675;
        double r11576678 = r11576675 / r11576677;
        return r11576678;
}
↓
double f(double x, double y) {
        double r11576679 = x;
        double r11576680 = y;
        double r11576681 = r11576680 + r11576679;
        double r11576682 = r11576679 / r11576681;
        double r11576683 = expm1(r11576682);
        double r11576684 = log1p(r11576683);
        return r11576684;
}

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 2019168 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  (/ x (+ y x)))