Average Error: 0.0 → 0.1
Time: 5.9s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}
double f(double f, double n) {
        double r24741 = f;
        double r24742 = n;
        double r24743 = r24741 + r24742;
        double r24744 = -r24743;
        double r24745 = r24741 - r24742;
        double r24746 = r24744 / r24745;
        return r24746;
}
↓
double f(double f, double n) {
        double r24747 = f;
        double r24748 = n;
        double r24749 = r24747 + r24748;
        double r24750 = -r24749;
        double r24751 = r24747 - r24748;
        double r24752 = r24750 / r24751;
        double r24753 = cbrt(r24752);
        double r24754 = 3.0;
        double r24755 = pow(r24752, r24754);
        double r24756 = cbrt(r24755);
        double r24757 = cbrt(r24756);
        double r24758 = r24753 * r24757;
        double r24759 = r24758 * r24753;
        return r24759;
}

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. Using strategy rm

  5. Applied add-cbrt-cube41.6

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

  6. Applied add-cbrt-cube42.6

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

  7. Applied cbrt-undiv42.6

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))