Average Error: 0.0 → 0.0
Time: 33.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(\left(\frac{f}{f + n} \cdot \frac{n}{f + n} + \frac{n}{f + n} \cdot \frac{n}{f + n}\right) + \frac{f}{f + n} \cdot \frac{f}{f + n}\right) \cdot \frac{-1}{\left(\frac{f}{f + n} \cdot \frac{f}{f + n}\right) \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \left(\frac{n}{f + n} \cdot \frac{n}{f + n}\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\left(\left(\frac{f}{f + n} \cdot \frac{n}{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}{\left(\frac{f}{f + n} \cdot \frac{f}{f + n}\right) \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \left(\frac{n}{f + n} \cdot \frac{n}{f + n}\right)}
double f(double f, double n) {
        double r898243 = f;
        double r898244 = n;
        double r898245 = r898243 + r898244;
        double r898246 = -r898245;
        double r898247 = r898243 - r898244;
        double r898248 = r898246 / r898247;
        return r898248;
}
↓
double f(double f, double n) {
        double r898249 = f;
        double r898250 = n;
        double r898251 = r898249 + r898250;
        double r898252 = r898249 / r898251;
        double r898253 = r898250 / r898251;
        double r898254 = r898252 * r898253;
        double r898255 = r898253 * r898253;
        double r898256 = r898254 + r898255;
        double r898257 = r898252 * r898252;
        double r898258 = r898256 + r898257;
        double r898259 = -1.0;
        double r898260 = r898257 * r898252;
        double r898261 = r898253 * r898255;
        double r898262 = r898260 - r898261;
        double r898263 = r898259 / r898262;
        double r898264 = r898258 * r898263;
        return r898264;
}

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 div-sub0.0

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

  8. Applied flip3--0.0

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

  9. Applied associate-/r/0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

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