Average Error: 0.0 → 0.0
Time: 17.1s
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 r622323 = f;
        double r622324 = n;
        double r622325 = r622323 + r622324;
        double r622326 = -r622325;
        double r622327 = r622323 - r622324;
        double r622328 = r622326 / r622327;
        return r622328;
}
↓
double f(double f, double n) {
        double r622329 = f;
        double r622330 = n;
        double r622331 = r622329 + r622330;
        double r622332 = r622329 - r622330;
        double r622333 = r622331 / r622332;
        double r622334 = r622333 * r622333;
        double r622335 = -r622333;
        double r622336 = r622334 * r622335;
        double r622337 = cbrt(r622336);
        return r622337;
}

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

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

  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)))