Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\left(-\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right) \cdot \frac{f + n}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\left(-\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right) \cdot \frac{f + n}{f - n}}
double f(double f, double n) {
        double r493817 = f;
        double r493818 = n;
        double r493819 = r493817 + r493818;
        double r493820 = -r493819;
        double r493821 = r493817 - r493818;
        double r493822 = r493820 / r493821;
        return r493822;
}
↓
double f(double f, double n) {
        double r493823 = f;
        double r493824 = n;
        double r493825 = r493823 + r493824;
        double r493826 = r493823 - r493824;
        double r493827 = r493825 / r493826;
        double r493828 = r493827 * r493827;
        double r493829 = -r493828;
        double r493830 = r493829 * r493827;
        double r493831 = cbrt(r493830);
        return r493831;
}

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-cube40.9

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

  4. Applied add-cbrt-cube41.1

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

  5. Applied cbrt-undiv41.1

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))