Average Error: 30.1 → 0.5
Time: 17.4s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}
double f(double x) {
        double r2296968 = x;
        double r2296969 = 1.0;
        double r2296970 = r2296968 + r2296969;
        double r2296971 = cbrt(r2296970);
        double r2296972 = cbrt(r2296968);
        double r2296973 = r2296971 - r2296972;
        return r2296973;
}
↓
double f(double x) {
        double r2296974 = 1.0;
        double r2296975 = x;
        double r2296976 = r2296975 + r2296974;
        double r2296977 = cbrt(r2296976);
        double r2296978 = r2296977 * r2296977;
        double r2296979 = cbrt(r2296975);
        double r2296980 = r2296977 + r2296979;
        double r2296981 = r2296980 * r2296979;
        double r2296982 = r2296978 + r2296981;
        double r2296983 = r2296974 / r2296982;
        return r2296983;
}

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--30.0

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

  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. Using strategy rm

  7. Applied *-un-lft-identity0.5

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

  8. Applied associate-*r*0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))