Average Error: 0.0 → 0.1
Time: 19.0s
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 r2128977 = f;
        double r2128978 = n;
        double r2128979 = r2128977 + r2128978;
        double r2128980 = -r2128979;
        double r2128981 = r2128977 - r2128978;
        double r2128982 = r2128980 / r2128981;
        return r2128982;
}
↓
double f(double f, double n) {
        double r2128983 = f;
        double r2128984 = n;
        double r2128985 = r2128983 + r2128984;
        double r2128986 = -r2128985;
        double r2128987 = r2128983 - r2128984;
        double r2128988 = r2128986 / r2128987;
        double r2128989 = cbrt(r2128988);
        double r2128990 = r2128989 * r2128989;
        double r2128991 = r2128990 * r2128989;
        return r2128991;
}

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 2019173 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))