Initial program 29.7
\[\sqrt{x + 1} - \sqrt{x}\]
- Using strategy
rm Applied add-cube-cbrt29.8
\[\leadsto \color{blue}{\left(\sqrt[3]{\sqrt{x + 1}} \cdot \sqrt[3]{\sqrt{x + 1}}\right) \cdot \sqrt[3]{\sqrt{x + 1}}} - \sqrt{x}\]
Applied fma-neg29.8
\[\leadsto \color{blue}{(\left(\sqrt[3]{\sqrt{x + 1}} \cdot \sqrt[3]{\sqrt{x + 1}}\right) \cdot \left(\sqrt[3]{\sqrt{x + 1}}\right) + \left(-\sqrt{x}\right))_*}\]
- Using strategy
rm Applied cbrt-unprod29.7
\[\leadsto (\color{blue}{\left(\sqrt[3]{\sqrt{x + 1} \cdot \sqrt{x + 1}}\right)} \cdot \left(\sqrt[3]{\sqrt{x + 1}}\right) + \left(-\sqrt{x}\right))_*\]
- Using strategy
rm Applied expm1-log1p-u29.6
\[\leadsto \color{blue}{(e^{\log_* (1 + (\left(\sqrt[3]{\sqrt{x + 1} \cdot \sqrt{x + 1}}\right) \cdot \left(\sqrt[3]{\sqrt{x + 1}}\right) + \left(-\sqrt{x}\right))_*)} - 1)^*}\]
- Using strategy
rm Applied add-cube-cbrt29.6
\[\leadsto (e^{\log_* (1 + (\left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{\sqrt{x + 1} \cdot \sqrt{x + 1}} \cdot \sqrt[3]{\sqrt{x + 1} \cdot \sqrt{x + 1}}\right) \cdot \sqrt[3]{\sqrt{x + 1} \cdot \sqrt{x + 1}}}}\right) \cdot \left(\sqrt[3]{\sqrt{x + 1}}\right) + \left(-\sqrt{x}\right))_*)} - 1)^*\]
Final simplification29.6
\[\leadsto (e^{\log_* (1 + (\left(\sqrt[3]{\sqrt[3]{\sqrt{1 + x} \cdot \sqrt{1 + x}} \cdot \left(\sqrt[3]{\sqrt{1 + x} \cdot \sqrt{1 + x}} \cdot \sqrt[3]{\sqrt{1 + x} \cdot \sqrt{1 + x}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{1 + x}}\right) + \left(-\sqrt{x}\right))_*)} - 1)^*\]
