Average Error: 0.0 → 0.0
Time: 19.2s
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 r29516 = f;
        double r29517 = n;
        double r29518 = r29516 + r29517;
        double r29519 = -r29518;
        double r29520 = r29516 - r29517;
        double r29521 = r29519 / r29520;
        return r29521;
}
↓
double f(double f, double n) {
        double r29522 = f;
        double r29523 = n;
        double r29524 = r29522 + r29523;
        double r29525 = -r29524;
        double r29526 = r29522 - r29523;
        double r29527 = r29525 / r29526;
        double r29528 = expm1(r29527);
        double r29529 = log1p(r29528);
        return r29529;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))