Average Error: 30.1 → 0.4
Time: 3.0s
Precision: binary64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\frac{x}{\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)} + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\frac{x}{\sqrt[3]{\sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)} + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}
double code(double x) {
	return ((double) (((double) cbrt(((double) (x + 1.0)))) - ((double) cbrt(x))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (((double) (x / ((double) (((double) cbrt(((double) cbrt(x)))) * ((double) (((double) cbrt(((double) cbrt(x)))) * ((double) cbrt(((double) cbrt(x)))))))))) + ((double) (((double) cbrt(((double) (1.0 + x)))) * ((double) (((double) cbrt(x)) + ((double) cbrt(((double) (1.0 + x))))))))))));
}

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. Simplified0.6

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

  5. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{\sqrt[3]{x}} + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))