Average Error: 0.0 → 0.0
Time: 16.6s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log_* (1 + (e^{\frac{-\left(n + f\right)}{f - n}} - 1)^*)\]
double f(double f, double n) {
        double r516899 = f;
        double r516900 = n;
        double r516901 = r516899 + r516900;
        double r516902 = -r516901;
        double r516903 = r516899 - r516900;
        double r516904 = r516902 / r516903;
        return r516904;
}
↓
double f(double f, double n) {
        double r516905 = n;
        double r516906 = f;
        double r516907 = r516905 + r516906;
        double r516908 = -r516907;
        double r516909 = r516906 - r516905;
        double r516910 = r516908 / r516909;
        double r516911 = expm1(r516910);
        double r516912 = log1p(r516911);
        return r516912;
}


\frac{-\left(f + n\right)}{f - n}
↓
\log_* (1 + (e^{\frac{-\left(n + f\right)}{f - n}} - 1)^*)

Error

Bits error versus f

Bits error versus n

Derivation

  1. Initial program 0.0

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

  3. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\log_* (1 + (e^{\frac{-\left(f + n\right)}{f - n}} - 1)^*)}\]

  4. Final simplification0.0

    \[\leadsto \log_* (1 + (e^{\frac{-\left(n + f\right)}{f - n}} - 1)^*)\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))