Average Error: 29.1 → 0.5
Time: 16.7s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right)}\right) \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right)}\right) \cdot \sqrt[3]{x}}
double f(double x) {
        double r2806859 = x;
        double r2806860 = 1.0;
        double r2806861 = r2806859 + r2806860;
        double r2806862 = cbrt(r2806861);
        double r2806863 = cbrt(r2806859);
        double r2806864 = r2806862 - r2806863;
        return r2806864;
}
↓
double f(double x) {
        double r2806865 = 1.0;
        double r2806866 = x;
        double r2806867 = r2806866 + r2806865;
        double r2806868 = cbrt(r2806867);
        double r2806869 = r2806868 * r2806868;
        double r2806870 = cbrt(r2806866);
        double r2806871 = r2806868 * r2806869;
        double r2806872 = cbrt(r2806871);
        double r2806873 = r2806870 + r2806872;
        double r2806874 = r2806873 * r2806870;
        double r2806875 = r2806869 + r2806874;
        double r2806876 = r2806865 / r2806875;
        return r2806876;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.1

    \[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
  2. Using strategy rm

  3. Applied flip3--29.0

    \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}}\]

  4. Simplified0.5

    \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]

  5. Simplified0.5

    \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube0.5

    \[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \sqrt[3]{x} \cdot \left(\color{blue}{\sqrt[3]{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{1 + x}}} + \sqrt[3]{x}\right)}\]

  8. Final simplification0.5

    \[\leadsto \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right)}\right) \cdot \sqrt[3]{x}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))