Average Error: 29.6 → 0.5
Time: 17.9s
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 r1880718 = x;
        double r1880719 = 1.0;
        double r1880720 = r1880718 + r1880719;
        double r1880721 = cbrt(r1880720);
        double r1880722 = cbrt(r1880718);
        double r1880723 = r1880721 - r1880722;
        return r1880723;
}
↓
double f(double x) {
        double r1880724 = 1.0;
        double r1880725 = x;
        double r1880726 = cbrt(r1880725);
        double r1880727 = r1880725 + r1880724;
        double r1880728 = cbrt(r1880727);
        double r1880729 = r1880728 + r1880726;
        double r1880730 = r1880726 * r1880729;
        double r1880731 = r1880728 * r1880728;
        double r1880732 = r1880730 + r1880731;
        double r1880733 = r1880724 / r1880732;
        return r1880733;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

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

  3. Applied flip3--29.6

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

  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. 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 2019144 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))