Average Error: 0.0 → 0.0
Time: 17.9s
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 r23590 = f;
        double r23591 = n;
        double r23592 = r23590 + r23591;
        double r23593 = -r23592;
        double r23594 = r23590 - r23591;
        double r23595 = r23593 / r23594;
        return r23595;
}
↓
double f(double f, double n) {
        double r23596 = f;
        double r23597 = n;
        double r23598 = r23596 + r23597;
        double r23599 = -r23598;
        double r23600 = r23596 - r23597;
        double r23601 = r23599 / r23600;
        double r23602 = 3.0;
        double r23603 = pow(r23601, r23602);
        double r23604 = cbrt(r23603);
        return r23604;
}

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)))