Initial program 0.0
\[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Initial simplification0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\cos y}{e^{x}}\right))_*}{2}\]
- Using strategy
rm Applied fma-udef0.0
\[\leadsto \frac{\color{blue}{\cos y \cdot e^{x} + \frac{\cos y}{e^{x}}}}{2}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \frac{\cos y \cdot \color{blue}{\left(\sqrt{e^{x}} \cdot \sqrt{e^{x}}\right)} + \frac{\cos y}{e^{x}}}{2}\]
Applied associate-*r*0.0
\[\leadsto \frac{\color{blue}{\left(\cos y \cdot \sqrt{e^{x}}\right) \cdot \sqrt{e^{x}}} + \frac{\cos y}{e^{x}}}{2}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \frac{\left(\cos y \cdot \sqrt{e^{x}}\right) \cdot \sqrt{e^{x}} + \frac{\cos y}{\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}}}}{2}\]
Applied associate-/r*0.0
\[\leadsto \frac{\left(\cos y \cdot \sqrt{e^{x}}\right) \cdot \sqrt{e^{x}} + \color{blue}{\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\sqrt{e^{x}}}}}{2}\]
Final simplification0.0
\[\leadsto \frac{\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\sqrt{e^{x}}} + \sqrt{e^{x}} \cdot \left(\cos y \cdot \sqrt{e^{x}}\right)}{2}\]
