Average Error: 0.0 → 0.0
Time: 11.5s
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 r30065 = f;
        double r30066 = n;
        double r30067 = r30065 + r30066;
        double r30068 = -r30067;
        double r30069 = r30065 - r30066;
        double r30070 = r30068 / r30069;
        return r30070;
}
↓
double f(double f, double n) {
        double r30071 = f;
        double r30072 = n;
        double r30073 = r30071 + r30072;
        double r30074 = r30071 - r30072;
        double r30075 = r30073 / r30074;
        double r30076 = -r30075;
        double r30077 = exp(r30076);
        double r30078 = log(r30077);
        return r30078;
}

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)))