Average Error: 0.0 → 0.0
Time: 17.2s
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 r31572 = f;
        double r31573 = n;
        double r31574 = r31572 + r31573;
        double r31575 = -r31574;
        double r31576 = r31572 - r31573;
        double r31577 = r31575 / r31576;
        return r31577;
}
↓
double f(double f, double n) {
        double r31578 = f;
        double r31579 = n;
        double r31580 = r31578 + r31579;
        double r31581 = -r31580;
        double r31582 = r31578 - r31579;
        double r31583 = r31581 / r31582;
        double r31584 = expm1(r31583);
        double r31585 = log1p(r31584);
        return r31585;
}

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 2019303 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))