Initial program 4.3
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Simplified0.1
\[\leadsto \color{blue}{\sqrt{e^{x} + 1}}\]
- Using strategy
rm Applied add-sqr-sqrt0.1
\[\leadsto \sqrt{\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}} + 1}\]
Applied fma-def0.1
\[\leadsto \sqrt{\color{blue}{(\left(\sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}}\right) + 1)_*}}\]
- Using strategy
rm Applied expm1-log1p-u0.1
\[\leadsto \color{blue}{(e^{\log_* (1 + \sqrt{(\left(\sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}}\right) + 1)_*})} - 1)^*}\]
Final simplification0.1
\[\leadsto (e^{\log_* (1 + \sqrt{(\left(\sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}}\right) + 1)_*})} - 1)^*\]
