Average Error: 0.0 → 0.0
Time: 4.3s
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 r19613 = f;
        double r19614 = n;
        double r19615 = r19613 + r19614;
        double r19616 = -r19615;
        double r19617 = r19613 - r19614;
        double r19618 = r19616 / r19617;
        return r19618;
}
↓
double f(double f, double n) {
        double r19619 = f;
        double r19620 = n;
        double r19621 = r19619 + r19620;
        double r19622 = -r19621;
        double r19623 = r19619 - r19620;
        double r19624 = r19622 / r19623;
        double r19625 = 3.0;
        double r19626 = pow(r19624, r19625);
        double r19627 = cbrt(r19626);
        return r19627;
}

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-cube42.1

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

  4. Applied add-cbrt-cube43.0

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

  5. Applied cbrt-undiv43.0

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

  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 2020018 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))