Average Error: 29.9 → 0.5

Time: 18.3s

Precision: 64

Internal Precision: 1344

\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]

↓

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

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Initial program 29.9
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
Initial simplification29.9
\[\leadsto \sqrt[3]{1 + x} - \sqrt[3]{x}\]
Using strategy rm
Applied flip3--29.9
\[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{1 + x}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{1 + x} \cdot \sqrt[3]{x}\right)}}\]
Taylor expanded around -inf 0.5
\[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{1 + x} \cdot \sqrt[3]{x}\right)}\]
Final simplification0.5
\[\leadsto \frac{1}{\left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x} + \sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}\]

herbie shell --seed 2018256 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))