Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}
double f(double f, double n) {
        double r13745 = f;
        double r13746 = n;
        double r13747 = r13745 + r13746;
        double r13748 = -r13747;
        double r13749 = r13745 - r13746;
        double r13750 = r13748 / r13749;
        return r13750;
}
↓
double f(double f, double n) {
        double r13751 = -1.0;
        double r13752 = f;
        double r13753 = n;
        double r13754 = r13752 - r13753;
        double r13755 = r13752 + r13753;
        double r13756 = r13754 / r13755;
        double r13757 = r13751 / r13756;
        double r13758 = 3.0;
        double r13759 = pow(r13757, r13758);
        double r13760 = cbrt(r13759);
        return r13760;
}

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 neg-mul-10.0

    \[\leadsto \frac{\color{blue}{-1 \cdot \left(f + n\right)}}{f - n}\]

  4. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube42.6

    \[\leadsto \frac{-1}{\frac{f - n}{\color{blue}{\sqrt[3]{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  7. Applied add-cbrt-cube42.5

    \[\leadsto \frac{-1}{\frac{\color{blue}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}{\sqrt[3]{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}\]

  8. Applied cbrt-undiv42.5

    \[\leadsto \frac{-1}{\color{blue}{\sqrt[3]{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  9. Applied add-cbrt-cube42.5

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(-1 \cdot -1\right) \cdot -1}}}{\sqrt[3]{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}\]

  10. Applied cbrt-undiv42.5

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(-1 \cdot -1\right) \cdot -1}{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  11. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}}\]

  12. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))