Average Error: 30.1 → 0.5
Time: 16.6s
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 r1122947 = x;
        double r1122948 = 1.0;
        double r1122949 = r1122947 + r1122948;
        double r1122950 = cbrt(r1122949);
        double r1122951 = cbrt(r1122947);
        double r1122952 = r1122950 - r1122951;
        return r1122952;
}
↓
double f(double x) {
        double r1122953 = 1.0;
        double r1122954 = x;
        double r1122955 = r1122954 + r1122953;
        double r1122956 = cbrt(r1122955);
        double r1122957 = r1122956 * r1122956;
        double r1122958 = cbrt(r1122954);
        double r1122959 = r1122956 + r1122958;
        double r1122960 = r1122959 * r1122958;
        double r1122961 = r1122957 + r1122960;
        double r1122962 = r1122953 / r1122961;
        return r1122962;
}

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)))