Average Error: 0.0 → 0.0
Time: 23.9s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(\frac{1}{{e}^{\left(\frac{n + f}{f - n}\right)}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(\frac{1}{{e}^{\left(\frac{n + f}{f - n}\right)}}\right)
double f(double f, double n) {
        double r674833 = f;
        double r674834 = n;
        double r674835 = r674833 + r674834;
        double r674836 = -r674835;
        double r674837 = r674833 - r674834;
        double r674838 = r674836 / r674837;
        return r674838;
}
↓
double f(double f, double n) {
        double r674839 = 1.0;
        double r674840 = exp(1.0);
        double r674841 = n;
        double r674842 = f;
        double r674843 = r674841 + r674842;
        double r674844 = r674842 - r674841;
        double r674845 = r674843 / r674844;
        double r674846 = pow(r674840, r674845);
        double r674847 = r674839 / r674846;
        double r674848 = log(r674847);
        return r674848;
}

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 distribute-frac-neg0.0

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

  6. Applied exp-neg0.0

    \[\leadsto \log \color{blue}{\left(\frac{1}{e^{\frac{f + n}{f - n}}}\right)}\]
  7. Using strategy rm

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

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

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

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

  10. Applied times-frac0.0

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

  11. Applied exp-prod0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))