Average Error: 29.7 → 0.5
Time: 19.1s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right)}\right) \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right)}\right) \cdot \sqrt[3]{x}}
double f(double x) {
        double r1528221 = x;
        double r1528222 = 1.0;
        double r1528223 = r1528221 + r1528222;
        double r1528224 = cbrt(r1528223);
        double r1528225 = cbrt(r1528221);
        double r1528226 = r1528224 - r1528225;
        return r1528226;
}
↓
double f(double x) {
        double r1528227 = 1.0;
        double r1528228 = x;
        double r1528229 = r1528228 + r1528227;
        double r1528230 = cbrt(r1528229);
        double r1528231 = r1528230 * r1528230;
        double r1528232 = cbrt(r1528228);
        double r1528233 = r1528230 * r1528231;
        double r1528234 = cbrt(r1528233);
        double r1528235 = r1528232 + r1528234;
        double r1528236 = r1528235 * r1528232;
        double r1528237 = r1528231 + r1528236;
        double r1528238 = r1528227 / r1528237;
        return r1528238;
}

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

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

  7. Applied add-cbrt-cube0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))