Average Error: 30.0 → 0.5
Time: 35.8s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}
double f(double x) {
        double r2876618 = x;
        double r2876619 = 1.0;
        double r2876620 = r2876618 + r2876619;
        double r2876621 = cbrt(r2876620);
        double r2876622 = cbrt(r2876618);
        double r2876623 = r2876621 - r2876622;
        return r2876623;
}
↓
double f(double x) {
        double r2876624 = 1.0;
        double r2876625 = x;
        double r2876626 = cbrt(r2876625);
        double r2876627 = r2876626 * r2876626;
        double r2876628 = r2876625 + r2876624;
        double r2876629 = cbrt(r2876628);
        double r2876630 = r2876629 + r2876626;
        double r2876631 = r2876629 * r2876630;
        double r2876632 = r2876627 + r2876631;
        double r2876633 = r2876624 / r2876632;
        return r2876633;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.0

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

  3. Applied flip3--29.9

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

  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

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1.0)) (cbrt x)))