Average Error: 29.5 → 0.6
Time: 19.2s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}
double f(double x) {
        double r3971825 = x;
        double r3971826 = 1.0;
        double r3971827 = r3971825 + r3971826;
        double r3971828 = cbrt(r3971827);
        double r3971829 = cbrt(r3971825);
        double r3971830 = r3971828 - r3971829;
        return r3971830;
}
↓
double f(double x) {
        double r3971831 = 1.0;
        double r3971832 = x;
        double r3971833 = cbrt(r3971832);
        double r3971834 = cbrt(r3971833);
        double r3971835 = r3971834 * r3971834;
        double r3971836 = r3971834 * r3971835;
        double r3971837 = r3971833 * r3971836;
        double r3971838 = r3971832 + r3971831;
        double r3971839 = cbrt(r3971838);
        double r3971840 = r3971839 + r3971833;
        double r3971841 = r3971839 * r3971840;
        double r3971842 = r3971837 + r3971841;
        double r3971843 = r3971831 / r3971842;
        return r3971843;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

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

  3. Applied flip3--29.5

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

  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

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

  7. Applied add-cube-cbrt0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019125 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))