Average Error: 30.1 → 0.6
Time: 1.3m
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\left(\left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x}} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{1 + x} + \sqrt[3]{x} \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\left(\left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x}} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{1 + x} + \sqrt[3]{x} \cdot \sqrt[3]{x}}
double f(double x) {
        double r2630438 = x;
        double r2630439 = 1.0;
        double r2630440 = r2630438 + r2630439;
        double r2630441 = cbrt(r2630440);
        double r2630442 = cbrt(r2630438);
        double r2630443 = r2630441 - r2630442;
        return r2630443;
}
↓
double f(double x) {
        double r2630444 = 1.0;
        double r2630445 = x;
        double r2630446 = cbrt(r2630445);
        double r2630447 = cbrt(r2630446);
        double r2630448 = r2630447 * r2630447;
        double r2630449 = r2630448 * r2630447;
        double r2630450 = r2630444 + r2630445;
        double r2630451 = cbrt(r2630450);
        double r2630452 = r2630449 + r2630451;
        double r2630453 = r2630452 * r2630451;
        double r2630454 = r2630446 * r2630446;
        double r2630455 = r2630453 + r2630454;
        double r2630456 = r2630444 / r2630455;
        return r2630456;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.1

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

  3. Applied flip3--30.1

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

  4. Simplified0.6

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

  5. Simplified0.6

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

  7. Applied add-cube-cbrt0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1.0)) (cbrt x)))