Average Error: 29.7 → 0.6
Time: 3.2s
Precision: binary64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot {\left(\sqrt[3]{\sqrt[3]{x}}\right)}^{2}\right) + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot {\left(\sqrt[3]{\sqrt[3]{x}}\right)}^{2}\right) + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}
(FPCore (x) :precision binary64 (- (cbrt (+ x 1.0)) (cbrt x)))
↓
(FPCore (x)
 :precision binary64
 (/
  1.0
  (+
   (* (cbrt x) (* (cbrt (cbrt x)) (pow (cbrt (cbrt x)) 2.0)))
   (* (cbrt (+ 1.0 x)) (+ (cbrt x) (cbrt (+ 1.0 x)))))))
double code(double x) {
	return ((double) (((double) cbrt(((double) (x + 1.0)))) - ((double) cbrt(x))));
}
↓
double code(double x) {
	return (1.0 / ((double) (((double) (((double) cbrt(x)) * ((double) (((double) cbrt(((double) cbrt(x)))) * ((double) pow(((double) cbrt(((double) cbrt(x)))), 2.0)))))) + ((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 29.7

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

  3. Applied flip3--29.6

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

  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

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

  7. Applied add-cube-cbrt0.6

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

  8. Simplified0.6

    \[\leadsto \frac{1}{\sqrt[3]{x} \cdot \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{x}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) + \sqrt[3]{x + 1} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}\]

  9. Final simplification0.6

    \[\leadsto \frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x}} \cdot {\left(\sqrt[3]{\sqrt[3]{x}}\right)}^{2}\right) + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))