Average Error: 0.0 → 0.0
Time: 10.7s
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 r431246 = f;
        double r431247 = n;
        double r431248 = r431246 + r431247;
        double r431249 = -r431248;
        double r431250 = r431246 - r431247;
        double r431251 = r431249 / r431250;
        return r431251;
}
↓
double f(double f, double n) {
        double r431252 = n;
        double r431253 = f;
        double r431254 = r431252 + r431253;
        double r431255 = -r431254;
        double r431256 = r431253 - r431252;
        double r431257 = r431255 / r431256;
        double r431258 = exp(r431257);
        double r431259 = log(r431258);
        return r431259;
}

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 2019154 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))