Average Error: 0.0 → 0.0
Time: 17.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}
double f(double f, double n) {
        double r23597 = f;
        double r23598 = n;
        double r23599 = r23597 + r23598;
        double r23600 = -r23599;
        double r23601 = r23597 - r23598;
        double r23602 = r23600 / r23601;
        return r23602;
}
↓
double f(double f, double n) {
        double r23603 = f;
        double r23604 = n;
        double r23605 = r23603 + r23604;
        double r23606 = -r23605;
        double r23607 = r23603 - r23604;
        double r23608 = r23606 / r23607;
        double r23609 = 3.0;
        double r23610 = pow(r23608, r23609);
        double r23611 = cbrt(r23610);
        return r23611;
}

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-cube41.5

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

  4. Applied add-cbrt-cube42.3

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

  5. Applied cbrt-undiv42.3

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))