Average Error: 29.8 → 0.5
Time: 17.7s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}
double f(double x) {
        double r1601313 = x;
        double r1601314 = 1.0;
        double r1601315 = r1601313 + r1601314;
        double r1601316 = cbrt(r1601315);
        double r1601317 = cbrt(r1601313);
        double r1601318 = r1601316 - r1601317;
        return r1601318;
}
↓
double f(double x) {
        double r1601319 = 1.0;
        double r1601320 = x;
        double r1601321 = cbrt(r1601320);
        double r1601322 = r1601320 + r1601319;
        double r1601323 = cbrt(r1601322);
        double r1601324 = r1601323 + r1601321;
        double r1601325 = r1601321 * r1601324;
        double r1601326 = r1601323 * r1601323;
        double r1601327 = r1601325 + r1601326;
        double r1601328 = r1601319 / r1601327;
        return r1601328;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.8

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

  3. Applied flip3--29.7

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

  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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019138 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))