Average Error: 0.0 → 0.0
Time: 32.8s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(\left(\frac{n}{f + n} \cdot \frac{f}{f + n} + \frac{n}{f + n} \cdot \frac{n}{f + n}\right) + \frac{f}{f + n} \cdot \frac{f}{f + n}\right) \cdot \frac{-1}{\frac{f}{f + n} \cdot \left(\frac{f}{f + n} \cdot \frac{f}{f + n}\right) - \frac{n}{f + n} \cdot \left(\frac{n}{f + n} \cdot \frac{n}{f + n}\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\left(\left(\frac{n}{f + n} \cdot \frac{f}{f + n} + \frac{n}{f + n} \cdot \frac{n}{f + n}\right) + \frac{f}{f + n} \cdot \frac{f}{f + n}\right) \cdot \frac{-1}{\frac{f}{f + n} \cdot \left(\frac{f}{f + n} \cdot \frac{f}{f + n}\right) - \frac{n}{f + n} \cdot \left(\frac{n}{f + n} \cdot \frac{n}{f + n}\right)}
double f(double f, double n) {
        double r807259 = f;
        double r807260 = n;
        double r807261 = r807259 + r807260;
        double r807262 = -r807261;
        double r807263 = r807259 - r807260;
        double r807264 = r807262 / r807263;
        return r807264;
}
↓
double f(double f, double n) {
        double r807265 = n;
        double r807266 = f;
        double r807267 = r807266 + r807265;
        double r807268 = r807265 / r807267;
        double r807269 = r807266 / r807267;
        double r807270 = r807268 * r807269;
        double r807271 = r807268 * r807268;
        double r807272 = r807270 + r807271;
        double r807273 = r807269 * r807269;
        double r807274 = r807272 + r807273;
        double r807275 = -1.0;
        double r807276 = r807269 * r807273;
        double r807277 = r807268 * r807271;
        double r807278 = r807276 - r807277;
        double r807279 = r807275 / r807278;
        double r807280 = r807274 * r807279;
        return r807280;
}

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 neg-mul-10.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  5. Using strategy rm

  6. Applied add-log-exp0.0

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

  8. Applied div-sub0.0

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

  9. Applied exp-diff0.0

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

  10. Applied log-div0.0

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

  11. Simplified0.0

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

  12. Simplified0.0

    \[\leadsto \frac{-1}{\frac{f}{n + f} - \color{blue}{\frac{n}{n + f}}}\]
  13. Using strategy rm

  14. Applied flip3--0.0

    \[\leadsto \frac{-1}{\color{blue}{\frac{{\left(\frac{f}{n + f}\right)}^{3} - {\left(\frac{n}{n + f}\right)}^{3}}{\frac{f}{n + f} \cdot \frac{f}{n + f} + \left(\frac{n}{n + f} \cdot \frac{n}{n + f} + \frac{f}{n + f} \cdot \frac{n}{n + f}\right)}}}\]

  15. Applied associate-/r/0.0

    \[\leadsto \color{blue}{\frac{-1}{{\left(\frac{f}{n + f}\right)}^{3} - {\left(\frac{n}{n + f}\right)}^{3}} \cdot \left(\frac{f}{n + f} \cdot \frac{f}{n + f} + \left(\frac{n}{n + f} \cdot \frac{n}{n + f} + \frac{f}{n + f} \cdot \frac{n}{n + f}\right)\right)}\]

  16. Simplified0.0

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

  17. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))