Average Error: 0.0 → 0.0
Time: 11.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)
double f(double f, double n) {
        double r29743 = f;
        double r29744 = n;
        double r29745 = r29743 + r29744;
        double r29746 = -r29745;
        double r29747 = r29743 - r29744;
        double r29748 = r29746 / r29747;
        return r29748;
}
↓
double f(double f, double n) {
        double r29749 = f;
        double r29750 = n;
        double r29751 = r29749 + r29750;
        double r29752 = -r29751;
        double r29753 = r29749 - r29750;
        double r29754 = r29752 / r29753;
        double r29755 = exp(r29754);
        double r29756 = log(r29755);
        return r29756;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))