Average Error: 30.4 → 0.6
Time: 18.0s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\left(\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{x}} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\left(\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{x}} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}
double f(double x) {
        double r768370 = x;
        double r768371 = 1.0;
        double r768372 = r768370 + r768371;
        double r768373 = cbrt(r768372);
        double r768374 = cbrt(r768370);
        double r768375 = r768373 - r768374;
        return r768375;
}
↓
double f(double x) {
        double r768376 = 1.0;
        double r768377 = x;
        double r768378 = cbrt(r768377);
        double r768379 = cbrt(r768378);
        double r768380 = r768379 * r768379;
        double r768381 = r768378 * r768380;
        double r768382 = r768381 * r768379;
        double r768383 = r768377 + r768376;
        double r768384 = cbrt(r768383);
        double r768385 = r768384 + r768378;
        double r768386 = r768384 * r768385;
        double r768387 = r768382 + r768386;
        double r768388 = r768376 / r768387;
        return r768388;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.4

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

  3. Applied flip3--30.3

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

  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

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

  7. Applied add-cube-cbrt0.6

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

  8. Applied associate-*r*0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))