Average Error: 0.0 → 0.0
Time: 35.2s
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 r1894877 = f;
        double r1894878 = n;
        double r1894879 = r1894877 + r1894878;
        double r1894880 = -r1894879;
        double r1894881 = r1894877 - r1894878;
        double r1894882 = r1894880 / r1894881;
        return r1894882;
}
↓
double f(double f, double n) {
        double r1894883 = f;
        double r1894884 = n;
        double r1894885 = r1894883 + r1894884;
        double r1894886 = r1894883 - r1894884;
        double r1894887 = r1894885 / r1894886;
        double r1894888 = r1894887 * r1894887;
        double r1894889 = -r1894887;
        double r1894890 = r1894888 * r1894889;
        double r1894891 = cbrt(r1894890);
        return r1894891;
}

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-cube40.5

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

  4. Applied add-cbrt-cube40.7

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

  5. Applied cbrt-undiv40.7

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

  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 2019158 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))