Average Error: 29.9 → 0.5
Time: 12.9s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}
double f(double x) {
        double r47198 = x;
        double r47199 = 1.0;
        double r47200 = r47198 + r47199;
        double r47201 = cbrt(r47200);
        double r47202 = cbrt(r47198);
        double r47203 = r47201 - r47202;
        return r47203;
}
↓
double f(double x) {
        double r47204 = 1.0;
        double r47205 = x;
        double r47206 = r47205 + r47204;
        double r47207 = cbrt(r47206);
        double r47208 = cbrt(r47205);
        double r47209 = r47207 + r47208;
        double r47210 = r47207 * r47209;
        double r47211 = r47208 * r47208;
        double r47212 = r47210 + r47211;
        double r47213 = r47204 / r47212;
        return r47213;
}

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 sqr-pow32.8

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

  8. Simplified32.6

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

  9. Simplified0.5

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

  10. Final simplification0.5

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

Reproduce

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