Average Error: 0.0 → 0.0
Time: 15.8s
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 r495612 = f;
        double r495613 = n;
        double r495614 = r495612 + r495613;
        double r495615 = -r495614;
        double r495616 = r495612 - r495613;
        double r495617 = r495615 / r495616;
        return r495617;
}
↓
double f(double f, double n) {
        double r495618 = 1.0;
        double r495619 = exp(1.0);
        double r495620 = n;
        double r495621 = f;
        double r495622 = r495620 + r495621;
        double r495623 = r495621 - r495620;
        double r495624 = r495622 / r495623;
        double r495625 = pow(r495619, r495624);
        double r495626 = r495618 / r495625;
        double r495627 = log(r495626);
        return r495627;
}

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

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

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

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

  10. Applied distribute-lft-out--0.0

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

  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 2019143 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))