Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{-1}{{\left(\frac{f - n}{f + n}\right)}^{3}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\frac{-1}{{\left(\frac{f - n}{f + n}\right)}^{3}}}
double f(double f, double n) {
        double r18652 = f;
        double r18653 = n;
        double r18654 = r18652 + r18653;
        double r18655 = -r18654;
        double r18656 = r18652 - r18653;
        double r18657 = r18655 / r18656;
        return r18657;
}
↓
double f(double f, double n) {
        double r18658 = -1.0;
        double r18659 = f;
        double r18660 = n;
        double r18661 = r18659 - r18660;
        double r18662 = r18659 + r18660;
        double r18663 = r18661 / r18662;
        double r18664 = 3.0;
        double r18665 = pow(r18663, r18664);
        double r18666 = r18658 / r18665;
        double r18667 = cbrt(r18666);
        return r18667;
}

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-cube41.7

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

  5. Applied cbrt-undiv41.7

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

  6. Simplified0.0

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

  8. Applied neg-mul-10.0

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

  9. Applied associate-/l*0.0

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

  11. Applied cube-div0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))