Average Error: 29.9 → 0.5
Time: 10.8s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \left|\sqrt[3]{x}\right| \cdot \left|\sqrt[3]{x}\right|}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \left|\sqrt[3]{x}\right| \cdot \left|\sqrt[3]{x}\right|}
double f(double x) {
        double r58798 = x;
        double r58799 = 1.0;
        double r58800 = r58798 + r58799;
        double r58801 = cbrt(r58800);
        double r58802 = cbrt(r58798);
        double r58803 = r58801 - r58802;
        return r58803;
}
↓
double f(double x) {
        double r58804 = 1.0;
        double r58805 = x;
        double r58806 = r58805 + r58804;
        double r58807 = cbrt(r58806);
        double r58808 = cbrt(r58805);
        double r58809 = r58807 + r58808;
        double r58810 = r58807 * r58809;
        double r58811 = fabs(r58808);
        double r58812 = r58811 * r58811;
        double r58813 = r58810 + r58812;
        double r58814 = r58804 / r58813;
        return r58814;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.9

    \[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
  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

    \[\leadsto \frac{\color{blue}{0 + 1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]

  5. Simplified32.8

    \[\leadsto \frac{0 + 1}{\color{blue}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + {x}^{\frac{2}{3}}}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt32.8

    \[\leadsto \frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \color{blue}{\sqrt{{x}^{\frac{2}{3}}} \cdot \sqrt{{x}^{\frac{2}{3}}}}}\]

  8. Simplified32.6

    \[\leadsto \frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \color{blue}{\left|\sqrt[3]{x}\right|} \cdot \sqrt{{x}^{\frac{2}{3}}}}\]

  9. Simplified0.5

    \[\leadsto \frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \left|\sqrt[3]{x}\right| \cdot \color{blue}{\left|\sqrt[3]{x}\right|}}\]

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1)) (cbrt x)))