Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n} \cdot \frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n} \cdot \frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n}}\right)}^{3}}
double f(double f, double n) {
        double r15147 = f;
        double r15148 = n;
        double r15149 = r15147 + r15148;
        double r15150 = -r15149;
        double r15151 = r15147 - r15148;
        double r15152 = r15150 / r15151;
        return r15152;
}
↓
double f(double f, double n) {
        double r15153 = f;
        double r15154 = n;
        double r15155 = r15153 + r15154;
        double r15156 = -r15155;
        double r15157 = r15153 - r15154;
        double r15158 = r15156 / r15157;
        double r15159 = r15158 * r15158;
        double r15160 = cbrt(r15159);
        double r15161 = cbrt(r15158);
        double r15162 = r15160 * r15161;
        double r15163 = 3.0;
        double r15164 = pow(r15162, r15163);
        double r15165 = cbrt(r15164);
        return r15165;
}

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-cube41.2

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

  4. Applied add-cbrt-cube42.0

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

  5. Applied cbrt-undiv42.0

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

  6. Simplified0.0

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

  8. Applied add-cube-cbrt0.1

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))