Average Error: 0.0 → 0.0
Time: 59.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{-\left(\log \left(e^{\frac{f + n}{f - n}}\right) \cdot \frac{f + n}{f - n}\right) \cdot \frac{f + n}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{-\left(\log \left(e^{\frac{f + n}{f - n}}\right) \cdot \frac{f + n}{f - n}\right) \cdot \frac{f + n}{f - n}}
double f(double f, double n) {
        double r2634753 = f;
        double r2634754 = n;
        double r2634755 = r2634753 + r2634754;
        double r2634756 = -r2634755;
        double r2634757 = r2634753 - r2634754;
        double r2634758 = r2634756 / r2634757;
        return r2634758;
}
↓
double f(double f, double n) {
        double r2634759 = f;
        double r2634760 = n;
        double r2634761 = r2634759 + r2634760;
        double r2634762 = r2634759 - r2634760;
        double r2634763 = r2634761 / r2634762;
        double r2634764 = exp(r2634763);
        double r2634765 = log(r2634764);
        double r2634766 = r2634765 * r2634763;
        double r2634767 = r2634766 * r2634763;
        double r2634768 = -r2634767;
        double r2634769 = cbrt(r2634768);
        return r2634769;
}

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-cube41.7

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

  4. Applied add-cbrt-cube41.9

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

  5. Applied cbrt-undiv41.9

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

  6. Simplified0.0

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

  8. Applied add-log-exp0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))