Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)
double f(double f, double n) {
        double r32625 = f;
        double r32626 = n;
        double r32627 = r32625 + r32626;
        double r32628 = -r32627;
        double r32629 = r32625 - r32626;
        double r32630 = r32628 / r32629;
        return r32630;
}
↓
double f(double f, double n) {
        double r32631 = f;
        double r32632 = n;
        double r32633 = r32631 + r32632;
        double r32634 = -r32633;
        double r32635 = r32631 - r32632;
        double r32636 = r32634 / r32635;
        double r32637 = expm1(r32636);
        double r32638 = log1p(r32637);
        return r32638;
}

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. Simplified0.0

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

  4. Applied log1p-expm1-u0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))