Average Error: 0.0 → 0.0
Time: 10.2s
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 r18693 = f;
        double r18694 = n;
        double r18695 = r18693 + r18694;
        double r18696 = -r18695;
        double r18697 = r18693 - r18694;
        double r18698 = r18696 / r18697;
        return r18698;
}
↓
double f(double f, double n) {
        double r18699 = f;
        double r18700 = n;
        double r18701 = r18699 + r18700;
        double r18702 = -r18701;
        double r18703 = r18699 - r18700;
        double r18704 = r18702 / r18703;
        double r18705 = exp(r18704);
        double r18706 = log(r18705);
        return r18706;
}

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

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

Reproduce

herbie shell --seed 2020042 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))