Average Error: 0.0 → 0.0
Time: 11.5s
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 r899239 = f;
        double r899240 = n;
        double r899241 = r899239 + r899240;
        double r899242 = -r899241;
        double r899243 = r899239 - r899240;
        double r899244 = r899242 / r899243;
        return r899244;
}
↓
double f(double f, double n) {
        double r899245 = 1.0;
        double r899246 = f;
        double r899247 = n;
        double r899248 = r899246 + r899247;
        double r899249 = r899246 - r899247;
        double r899250 = r899248 / r899249;
        double r899251 = -r899250;
        double r899252 = expm1(r899251);
        double r899253 = r899245 + r899252;
        double r899254 = log(r899253);
        return r899254;
}

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)))