Average Error: 0.0 → 0.0
Time: 18.5s
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 r29527 = f;
        double r29528 = n;
        double r29529 = r29527 + r29528;
        double r29530 = -r29529;
        double r29531 = r29527 - r29528;
        double r29532 = r29530 / r29531;
        return r29532;
}
↓
double f(double f, double n) {
        double r29533 = f;
        double r29534 = n;
        double r29535 = r29533 + r29534;
        double r29536 = -r29535;
        double r29537 = r29533 - r29534;
        double r29538 = r29536 / r29537;
        double r29539 = expm1(r29538);
        double r29540 = log1p(r29539);
        return r29540;
}

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)))