Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left({e}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left({e}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)
double f(double f, double n) {
        double r27104 = f;
        double r27105 = n;
        double r27106 = r27104 + r27105;
        double r27107 = -r27106;
        double r27108 = r27104 - r27105;
        double r27109 = r27107 / r27108;
        return r27109;
}
↓
double f(double f, double n) {
        double r27110 = exp(1.0);
        double r27111 = f;
        double r27112 = n;
        double r27113 = r27111 + r27112;
        double r27114 = -r27113;
        double r27115 = r27111 - r27112;
        double r27116 = r27114 / r27115;
        double r27117 = pow(r27110, r27116);
        double r27118 = log(r27117);
        return r27118;
}

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

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

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

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

  7. Applied times-frac0.0

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

  8. Applied exp-prod0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

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