Average Error: 29.6 → 0.5
Time: 18.9s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}
double f(double x) {
        double r1292573 = x;
        double r1292574 = 1.0;
        double r1292575 = r1292573 + r1292574;
        double r1292576 = cbrt(r1292575);
        double r1292577 = cbrt(r1292573);
        double r1292578 = r1292576 - r1292577;
        return r1292578;
}
↓
double f(double x) {
        double r1292579 = 1.0;
        double r1292580 = x;
        double r1292581 = cbrt(r1292580);
        double r1292582 = r1292581 * r1292581;
        double r1292583 = r1292580 + r1292579;
        double r1292584 = cbrt(r1292583);
        double r1292585 = r1292584 + r1292581;
        double r1292586 = r1292584 * r1292585;
        double r1292587 = r1292582 + r1292586;
        double r1292588 = r1292579 / r1292587;
        return r1292588;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

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

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019130 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))