Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\left(\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right) \cdot \left(-\frac{f + n}{f - n}\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\left(\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 r420736 = f;
        double r420737 = n;
        double r420738 = r420736 + r420737;
        double r420739 = -r420738;
        double r420740 = r420736 - r420737;
        double r420741 = r420739 / r420740;
        return r420741;
}
↓
double f(double f, double n) {
        double r420742 = f;
        double r420743 = n;
        double r420744 = r420742 + r420743;
        double r420745 = r420742 - r420743;
        double r420746 = r420744 / r420745;
        double r420747 = r420746 * r420746;
        double r420748 = -r420746;
        double r420749 = r420747 * r420748;
        double r420750 = cbrt(r420749);
        return r420750;
}

Error

Bits error versus f

Bits error versus n

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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-cube41.2

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

  4. Applied add-cbrt-cube41.4

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

  5. Applied cbrt-undiv41.4

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))