Average Error: 0.0 → 0.1
Time: 11.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}
double f(double f, double n) {
        double r17924 = f;
        double r17925 = n;
        double r17926 = r17924 + r17925;
        double r17927 = -r17926;
        double r17928 = r17924 - r17925;
        double r17929 = r17927 / r17928;
        return r17929;
}
↓
double f(double f, double n) {
        double r17930 = f;
        double r17931 = n;
        double r17932 = r17930 + r17931;
        double r17933 = -r17932;
        double r17934 = r17930 - r17931;
        double r17935 = r17933 / r17934;
        double r17936 = cbrt(r17935);
        double r17937 = r17936 * r17936;
        double r17938 = r17937 * r17936;
        return r17938;
}

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-cube-cbrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))