Average Error: 30.2 → 0.6
Time: 18.1s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\left(\sqrt[3]{\sqrt[3]{x + 1}} \cdot \sqrt[3]{\sqrt[3]{x + 1}}\right) \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{\sqrt[3]{x + 1}}\right) + \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\left(\sqrt[3]{\sqrt[3]{x + 1}} \cdot \sqrt[3]{\sqrt[3]{x + 1}}\right) \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{\sqrt[3]{x + 1}}\right) + \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}
double f(double x) {
        double r1570764 = x;
        double r1570765 = 1.0;
        double r1570766 = r1570764 + r1570765;
        double r1570767 = cbrt(r1570766);
        double r1570768 = cbrt(r1570764);
        double r1570769 = r1570767 - r1570768;
        return r1570769;
}
↓
double f(double x) {
        double r1570770 = 1.0;
        double r1570771 = x;
        double r1570772 = r1570771 + r1570770;
        double r1570773 = cbrt(r1570772);
        double r1570774 = cbrt(r1570773);
        double r1570775 = r1570774 * r1570774;
        double r1570776 = r1570773 * r1570774;
        double r1570777 = r1570775 * r1570776;
        double r1570778 = cbrt(r1570771);
        double r1570779 = r1570773 + r1570778;
        double r1570780 = r1570779 * r1570778;
        double r1570781 = r1570777 + r1570780;
        double r1570782 = r1570770 / r1570781;
        return r1570782;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.2

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

  3. Applied flip3--30.2

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

  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-cube-cbrt0.6

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

  8. Applied associate-*l*0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2019135 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))