Average Error: 0.0 → 0.8
Time: 3.9s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)
double f(double f, double n) {
        double r15787 = f;
        double r15788 = n;
        double r15789 = r15787 + r15788;
        double r15790 = -r15789;
        double r15791 = r15787 - r15788;
        double r15792 = r15790 / r15791;
        return r15792;
}
↓
double f(double f, double n) {
        double r15793 = f;
        double r15794 = n;
        double r15795 = r15793 + r15794;
        double r15796 = -r15795;
        double r15797 = r15793 - r15794;
        double r15798 = r15796 / r15797;
        double r15799 = log1p(r15798);
        double r15800 = expm1(r15799);
        return r15800;
}

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 expm1-log1p-u0.8

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

  4. Final simplification0.8

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))