Average Error: 29.7 → 0.6
Time: 19.2s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}
double f(double x) {
        double r2265172 = x;
        double r2265173 = 1.0;
        double r2265174 = r2265172 + r2265173;
        double r2265175 = cbrt(r2265174);
        double r2265176 = cbrt(r2265172);
        double r2265177 = r2265175 - r2265176;
        return r2265177;
}
↓
double f(double x) {
        double r2265178 = 1.0;
        double r2265179 = x;
        double r2265180 = cbrt(r2265179);
        double r2265181 = cbrt(r2265180);
        double r2265182 = r2265181 * r2265181;
        double r2265183 = r2265181 * r2265182;
        double r2265184 = r2265180 * r2265183;
        double r2265185 = r2265179 + r2265178;
        double r2265186 = cbrt(r2265185);
        double r2265187 = r2265186 + r2265180;
        double r2265188 = r2265186 * r2265187;
        double r2265189 = r2265184 + r2265188;
        double r2265190 = r2265178 / r2265189;
        return r2265190;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.7

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

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

  7. Applied add-cube-cbrt0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))