Average Error: 0.0 → 0.0
Time: 37.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(1 + \mathsf{expm1}\left(-\frac{f + n}{f - n}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(1 + \mathsf{expm1}\left(-\frac{f + n}{f - n}\right)\right)
double f(double f, double n) {
        double r798094 = f;
        double r798095 = n;
        double r798096 = r798094 + r798095;
        double r798097 = -r798096;
        double r798098 = r798094 - r798095;
        double r798099 = r798097 / r798098;
        return r798099;
}
↓
double f(double f, double n) {
        double r798100 = 1.0;
        double r798101 = f;
        double r798102 = n;
        double r798103 = r798101 + r798102;
        double r798104 = r798101 - r798102;
        double r798105 = r798103 / r798104;
        double r798106 = -r798105;
        double r798107 = expm1(r798106);
        double r798108 = r798100 + r798107;
        double r798109 = log(r798108);
        return r798109;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\]
  4. Using strategy rm

  5. Applied log1p-udef0.0

    \[\leadsto \color{blue}{\log \left(1 + \mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\]

  6. Final simplification0.0

    \[\leadsto \log \left(1 + \mathsf{expm1}\left(-\frac{f + n}{f - n}\right)\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))