Average Error: 30.4 → 0.6
Time: 38.7s
Precision: 64
\[\sqrt[3]{x + 1.0} - \sqrt[3]{x}\]
↓
\[\frac{1.0}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1.0} \cdot \left(\sqrt[3]{x + 1.0} + \sqrt[3]{x}\right)}\]
\sqrt[3]{x + 1.0} - \sqrt[3]{x}
↓
\frac{1.0}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1.0} \cdot \left(\sqrt[3]{x + 1.0} + \sqrt[3]{x}\right)}
double f(double x) {
        double r2741432 = x;
        double r2741433 = 1.0;
        double r2741434 = r2741432 + r2741433;
        double r2741435 = cbrt(r2741434);
        double r2741436 = cbrt(r2741432);
        double r2741437 = r2741435 - r2741436;
        return r2741437;
}
↓
double f(double x) {
        double r2741438 = 1.0;
        double r2741439 = x;
        double r2741440 = cbrt(r2741439);
        double r2741441 = r2741440 * r2741440;
        double r2741442 = r2741439 + r2741438;
        double r2741443 = cbrt(r2741442);
        double r2741444 = r2741443 + r2741440;
        double r2741445 = r2741443 * r2741444;
        double r2741446 = r2741441 + r2741445;
        double r2741447 = r2741438 / r2741446;
        return r2741447;
}

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

    \[\sqrt[3]{x + 1.0} - \sqrt[3]{x}\]
  2. Using strategy rm

  3. Applied flip3--30.3

    \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + 1.0}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1.0} \cdot \sqrt[3]{x + 1.0} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1.0} \cdot \sqrt[3]{x}\right)}}\]

  4. Simplified0.6

    \[\leadsto \frac{\color{blue}{1.0}}{\sqrt[3]{x + 1.0} \cdot \sqrt[3]{x + 1.0} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1.0} \cdot \sqrt[3]{x}\right)}\]

  5. Simplified0.6

    \[\leadsto \frac{1.0}{\color{blue}{\sqrt[3]{1.0 + x} \cdot \left(\sqrt[3]{1.0 + x} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}}\]

  6. Final simplification0.6

    \[\leadsto \frac{1.0}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1.0} \cdot \left(\sqrt[3]{x + 1.0} + \sqrt[3]{x}\right)}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1.0)) (cbrt x)))