Average Error: 29.4 → 0.5
Time: 15.5s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}
double f(double x) {
        double r2331819 = x;
        double r2331820 = 1.0;
        double r2331821 = r2331819 + r2331820;
        double r2331822 = cbrt(r2331821);
        double r2331823 = cbrt(r2331819);
        double r2331824 = r2331822 - r2331823;
        return r2331824;
}
↓
double f(double x) {
        double r2331825 = 1.0;
        double r2331826 = x;
        double r2331827 = cbrt(r2331826);
        double r2331828 = r2331826 + r2331825;
        double r2331829 = cbrt(r2331828);
        double r2331830 = r2331829 + r2331827;
        double r2331831 = r2331827 * r2331830;
        double r2331832 = r2331829 * r2331829;
        double r2331833 = r2331831 + r2331832;
        double r2331834 = r2331825 / r2331833;
        return r2331834;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.4

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

  3. Applied flip3--29.3

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

  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

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1.0)) (cbrt x)))