Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[\frac{x}{y + x}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)\]
\frac{x}{y + x}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y + x}\right)\right)
double f(double x, double y) {
        double r15451296 = x;
        double r15451297 = y;
        double r15451298 = r15451297 + r15451296;
        double r15451299 = r15451296 / r15451298;
        return r15451299;
}
↓
double f(double x, double y) {
        double r15451300 = x;
        double r15451301 = y;
        double r15451302 = r15451301 + r15451300;
        double r15451303 = r15451300 / r15451302;
        double r15451304 = log1p(r15451303);
        double r15451305 = expm1(r15451304);
        return r15451305;
}

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

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  (/ x (+ y x)))