Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{-\frac{\frac{f + n}{f - n} \cdot \left(f + n\right)}{f - n} \cdot \frac{f + n}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{-\frac{\frac{f + n}{f - n} \cdot \left(f + n\right)}{f - n} \cdot \frac{f + n}{f - n}}
double f(double f, double n) {
        double r492925 = f;
        double r492926 = n;
        double r492927 = r492925 + r492926;
        double r492928 = -r492927;
        double r492929 = r492925 - r492926;
        double r492930 = r492928 / r492929;
        return r492930;
}
↓
double f(double f, double n) {
        double r492931 = f;
        double r492932 = n;
        double r492933 = r492931 + r492932;
        double r492934 = r492931 - r492932;
        double r492935 = r492933 / r492934;
        double r492936 = r492935 * r492933;
        double r492937 = r492936 / r492934;
        double r492938 = r492937 * r492935;
        double r492939 = -r492938;
        double r492940 = cbrt(r492939);
        return r492940;
}

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-cbrt-cube41.4

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

  4. Applied add-cbrt-cube41.5

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

  5. Applied cbrt-undiv41.5

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

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{\left(\frac{n + f}{f - n} \cdot \frac{n + f}{f - n}\right) \cdot \left(-\frac{n + f}{f - n}\right)}}\]
  7. Using strategy rm

  8. Applied associate-*r/0.0

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

  9. Final simplification0.0

    \[\leadsto \sqrt[3]{-\frac{\frac{f + n}{f - n} \cdot \left(f + n\right)}{f - n} \cdot \frac{f + n}{f - n}}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))