Average Error: 0.0 → 0.0
Time: 17.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\log \left(e^{\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}}\right) \cdot \left(-\frac{f + n}{f - n}\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\log \left(e^{\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}}\right) \cdot \left(-\frac{f + n}{f - n}\right)}
double f(double f, double n) {
        double r513783 = f;
        double r513784 = n;
        double r513785 = r513783 + r513784;
        double r513786 = -r513785;
        double r513787 = r513783 - r513784;
        double r513788 = r513786 / r513787;
        return r513788;
}
↓
double f(double f, double n) {
        double r513789 = f;
        double r513790 = n;
        double r513791 = r513789 + r513790;
        double r513792 = r513789 - r513790;
        double r513793 = r513791 / r513792;
        double r513794 = r513793 * r513793;
        double r513795 = exp(r513794);
        double r513796 = log(r513795);
        double r513797 = -r513793;
        double r513798 = r513796 * r513797;
        double r513799 = cbrt(r513798);
        return r513799;
}

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-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-undiv41.6

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

  6. Simplified0.0

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

  8. Applied add-log-exp0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))