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 r15314 = f;
        double r15315 = n;
        double r15316 = r15314 + r15315;
        double r15317 = -r15316;
        double r15318 = r15314 - r15315;
        double r15319 = r15317 / r15318;
        return r15319;
}
↓
double f(double f, double n) {
        double r15320 = f;
        double r15321 = n;
        double r15322 = r15320 + r15321;
        double r15323 = -r15322;
        double r15324 = r15320 - r15321;
        double r15325 = r15323 / r15324;
        double r15326 = exp(r15325);
        double r15327 = log(r15326);
        return r15327;
}

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. Using strategy rm

  5. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot \log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))