Average Error: 0.0 → 0.0
Time: 3.9s
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 r15930 = f;
        double r15931 = n;
        double r15932 = r15930 + r15931;
        double r15933 = -r15932;
        double r15934 = r15930 - r15931;
        double r15935 = r15933 / r15934;
        return r15935;
}
↓
double f(double f, double n) {
        double r15936 = f;
        double r15937 = n;
        double r15938 = r15936 + r15937;
        double r15939 = -r15938;
        double r15940 = r15936 - r15937;
        double r15941 = r15939 / r15940;
        double r15942 = exp(r15941);
        double r15943 = log(r15942);
        return r15943;
}

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 2020035 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))