Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}
double f(double f, double n) {
        double r16692 = f;
        double r16693 = n;
        double r16694 = r16692 + r16693;
        double r16695 = -r16694;
        double r16696 = r16692 - r16693;
        double r16697 = r16695 / r16696;
        return r16697;
}
↓
double f(double f, double n) {
        double r16698 = f;
        double r16699 = n;
        double r16700 = r16698 + r16699;
        double r16701 = -r16700;
        double r16702 = r16698 - r16699;
        double r16703 = r16701 / r16702;
        double r16704 = 3.0;
        double r16705 = pow(r16703, r16704);
        double r16706 = cbrt(r16705);
        return r16706;
}

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-cube41.6

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

  4. Applied add-cbrt-cube42.4

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

  5. Applied cbrt-undiv42.4

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))