Average Error: 29.4 → 0.5
Time: 11.3s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}
double f(double x) {
        double r239680 = x;
        double r239681 = 1.0;
        double r239682 = r239680 + r239681;
        double r239683 = cbrt(r239682);
        double r239684 = cbrt(r239680);
        double r239685 = r239683 - r239684;
        return r239685;
}
↓
double f(double x) {
        double r239686 = 0.0;
        double r239687 = 1.0;
        double r239688 = r239686 + r239687;
        double r239689 = x;
        double r239690 = r239689 + r239687;
        double r239691 = cbrt(r239690);
        double r239692 = cbrt(r239689);
        double r239693 = r239691 + r239692;
        double r239694 = r239691 * r239693;
        double r239695 = r239692 * r239692;
        double r239696 = r239694 + r239695;
        double r239697 = r239688 / r239696;
        return r239697;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.4

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

  3. Applied flip3--29.4

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

  4. Simplified0.5

    \[\leadsto \frac{\color{blue}{0 + 1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]

  5. Simplified0.5

    \[\leadsto \frac{0 + 1}{\color{blue}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}}\]

  6. Final simplification0.5

    \[\leadsto \frac{0 + 1}{\sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}}\]

Reproduce

herbie shell --seed 350497007 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1)) (cbrt x)))