Average Error: 0.0 → 0.1
Time: 27.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right) \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}
double f(double f, double n) {
        double r927469 = f;
        double r927470 = n;
        double r927471 = r927469 + r927470;
        double r927472 = -r927471;
        double r927473 = r927469 - r927470;
        double r927474 = r927472 / r927473;
        return r927474;
}
↓
double f(double f, double n) {
        double r927475 = f;
        double r927476 = n;
        double r927477 = r927475 + r927476;
        double r927478 = -r927477;
        double r927479 = r927475 - r927476;
        double r927480 = r927478 / r927479;
        double r927481 = cbrt(r927480);
        double r927482 = r927481 * r927481;
        double r927483 = r927482 * r927481;
        return r927483;
}

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-cube-cbrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))