Average Error: 0.0 → 0.0
Time: 19.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\frac{-\left(n + f\right)}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{-\left(n + f\right)}{f - n}}\right)
double f(double f, double n) {
        double r455634 = f;
        double r455635 = n;
        double r455636 = r455634 + r455635;
        double r455637 = -r455636;
        double r455638 = r455634 - r455635;
        double r455639 = r455637 / r455638;
        return r455639;
}
↓
double f(double f, double n) {
        double r455640 = n;
        double r455641 = f;
        double r455642 = r455640 + r455641;
        double r455643 = -r455642;
        double r455644 = r455641 - r455640;
        double r455645 = r455643 / r455644;
        double r455646 = exp(r455645);
        double r455647 = log(r455646);
        return r455647;
}

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 add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{-\left(n + f\right)}{f - n}}\right)\]

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))