Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{-\frac{f + n}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{-\frac{f + n}{f - n}}\right)
double f(double f, double n) {
        double r31326 = f;
        double r31327 = n;
        double r31328 = r31326 + r31327;
        double r31329 = -r31328;
        double r31330 = r31326 - r31327;
        double r31331 = r31329 / r31330;
        return r31331;
}
↓
double f(double f, double n) {
        double r31332 = f;
        double r31333 = n;
        double r31334 = r31332 + r31333;
        double r31335 = r31332 - r31333;
        double r31336 = r31334 / r31335;
        double r31337 = -r31336;
        double r31338 = exp(r31337);
        double r31339 = log(r31338);
        return r31339;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{-\left(n + f\right)}{f - n}}\]
  3. Using strategy rm

  4. Applied add-log-exp0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

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