Average Error: 0.0 → 0.0
Time: 1.0m
Precision: 64
\[\frac{x}{y + x}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)\]
\frac{x}{y + x}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + y}\right)\right)
double f(double x, double y) {
        double r5599945 = x;
        double r5599946 = y;
        double r5599947 = r5599946 + r5599945;
        double r5599948 = r5599945 / r5599947;
        return r5599948;
}
↓
double f(double x, double y) {
        double r5599949 = x;
        double r5599950 = y;
        double r5599951 = r5599949 + r5599950;
        double r5599952 = r5599949 / r5599951;
        double r5599953 = log1p(r5599952);
        double r5599954 = expm1(r5599953);
        return r5599954;
}

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 expm1-log1p-u0.0

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

  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, B"
  (/ x (+ y x)))