Average Error: 0.0 → 0.0
Time: 22.2s
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 r677648 = f;
        double r677649 = n;
        double r677650 = r677648 + r677649;
        double r677651 = -r677650;
        double r677652 = r677648 - r677649;
        double r677653 = r677651 / r677652;
        return r677653;
}
↓
double f(double f, double n) {
        double r677654 = n;
        double r677655 = f;
        double r677656 = r677654 + r677655;
        double r677657 = -r677656;
        double r677658 = r677655 - r677654;
        double r677659 = r677657 / r677658;
        double r677660 = exp(r677659);
        double r677661 = log(r677660);
        return r677661;
}

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 2019135 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))