Average Error: 0.0 → 0.0
Time: 17.7s
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 r977029 = f;
        double r977030 = n;
        double r977031 = r977029 + r977030;
        double r977032 = -r977031;
        double r977033 = r977029 - r977030;
        double r977034 = r977032 / r977033;
        return r977034;
}
↓
double f(double f, double n) {
        double r977035 = n;
        double r977036 = f;
        double r977037 = r977035 + r977036;
        double r977038 = -r977037;
        double r977039 = r977036 - r977035;
        double r977040 = r977038 / r977039;
        double r977041 = exp(r977040);
        double r977042 = log(r977041);
        return r977042;
}

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 2019171 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))