Average Error: 0.0 → 0.0
Time: 17.8s
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 r439739 = f;
        double r439740 = n;
        double r439741 = r439739 + r439740;
        double r439742 = -r439741;
        double r439743 = r439739 - r439740;
        double r439744 = r439742 / r439743;
        return r439744;
}
↓
double f(double f, double n) {
        double r439745 = n;
        double r439746 = f;
        double r439747 = r439745 + r439746;
        double r439748 = -r439747;
        double r439749 = r439746 - r439745;
        double r439750 = r439748 / r439749;
        double r439751 = exp(r439750);
        double r439752 = log(r439751);
        return r439752;
}

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 2019153 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))