Average Error: 0.0 → 0.0
Time: 16.7s
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 r552033 = f;
        double r552034 = n;
        double r552035 = r552033 + r552034;
        double r552036 = -r552035;
        double r552037 = r552033 - r552034;
        double r552038 = r552036 / r552037;
        return r552038;
}
↓
double f(double f, double n) {
        double r552039 = f;
        double r552040 = n;
        double r552041 = r552039 + r552040;
        double r552042 = r552039 - r552040;
        double r552043 = r552041 / r552042;
        double r552044 = r552043 * r552041;
        double r552045 = r552044 / r552042;
        double r552046 = r552045 * r552043;
        double r552047 = -r552046;
        double r552048 = cbrt(r552047);
        return r552048;
}

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

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

  8. Applied associate-*r/0.0

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

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