Average Error: 0.0 → 0.0
Time: 58.3s
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 r3875846 = f;
        double r3875847 = n;
        double r3875848 = r3875846 + r3875847;
        double r3875849 = -r3875848;
        double r3875850 = r3875846 - r3875847;
        double r3875851 = r3875849 / r3875850;
        return r3875851;
}
↓
double f(double f, double n) {
        double r3875852 = 1.0;
        double r3875853 = exp(1.0);
        double r3875854 = n;
        double r3875855 = f;
        double r3875856 = r3875854 + r3875855;
        double r3875857 = r3875855 - r3875854;
        double r3875858 = r3875856 / r3875857;
        double r3875859 = pow(r3875853, r3875858);
        double r3875860 = r3875852 / r3875859;
        double r3875861 = log(r3875860);
        return r3875861;
}

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 neg-sub00.0

    \[\leadsto \log \left(e^{\frac{\color{blue}{0 - \left(f + n\right)}}{f - n}}\right)\]

  6. Applied div-sub0.0

    \[\leadsto \log \left(e^{\color{blue}{\frac{0}{f - n} - \frac{f + n}{f - n}}}\right)\]

  7. Applied exp-diff0.0

    \[\leadsto \log \color{blue}{\left(\frac{e^{\frac{0}{f - n}}}{e^{\frac{f + n}{f - n}}}\right)}\]

  8. Simplified0.0

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

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

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

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

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

  12. Applied times-frac0.0

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

  13. Applied exp-prod0.0

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

  14. Simplified0.0

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

  15. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))