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-cube-cbrt0.0
\[\leadsto \frac{\cos y \cdot \color{blue}{\left(\left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right) \cdot \sqrt[3]{e^{x}}\right)} + \frac{\cos y}{e^{x}}}{2}\]
Applied associate-*r*0.0
\[\leadsto \frac{\color{blue}{\left(\cos y \cdot \left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right)\right) \cdot \sqrt[3]{e^{x}}} + \frac{\cos y}{e^{x}}}{2}\]
Taylor expanded around inf 0.0
\[\leadsto \frac{\left(\cos y \cdot \color{blue}{{\left(e^{\frac{1}{3} \cdot x}\right)}^{2}}\right) \cdot \sqrt[3]{e^{x}} + \frac{\cos y}{e^{x}}}{2}\]
Simplified0.0
\[\leadsto \frac{\left(\cos y \cdot \color{blue}{e^{x \cdot \frac{2}{3}}}\right) \cdot \sqrt[3]{e^{x}} + \frac{\cos y}{e^{x}}}{2}\]
Final simplification0.0
\[\leadsto \frac{\frac{\cos y}{e^{x}} + \left(e^{x \cdot \frac{2}{3}} \cdot \cos y\right) \cdot \sqrt[3]{e^{x}}}{2}\]
