Initial program 0.0
\[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
- Using strategy
rm Applied clear-num0.0
\[\leadsto \Re(\left(\color{blue}{\frac{1}{\frac{2}{e^{x} + e^{-x}}}} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Applied associate-*l/0.0
\[\leadsto \Re(\left(\color{blue}{\frac{1 \cdot \cos y}{\frac{2}{e^{x} + e^{-x}}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Simplified0.0
\[\leadsto \Re(\left(\frac{\color{blue}{\cos y}}{\frac{2}{e^{x} + e^{-x}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
- Using strategy
rm Applied add-cbrt-cube0.1
\[\leadsto \Re(\left(\frac{\cos y}{\frac{2}{\color{blue}{\sqrt[3]{\left(\left(e^{x} + e^{-x}\right) \cdot \left(e^{x} + e^{-x}\right)\right) \cdot \left(e^{x} + e^{-x}\right)}}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Applied add-cbrt-cube0.1
\[\leadsto \Re(\left(\frac{\cos y}{\frac{\color{blue}{\sqrt[3]{\left(2 \cdot 2\right) \cdot 2}}}{\sqrt[3]{\left(\left(e^{x} + e^{-x}\right) \cdot \left(e^{x} + e^{-x}\right)\right) \cdot \left(e^{x} + e^{-x}\right)}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Applied cbrt-undiv0.1
\[\leadsto \Re(\left(\frac{\cos y}{\color{blue}{\sqrt[3]{\frac{\left(2 \cdot 2\right) \cdot 2}{\left(\left(e^{x} + e^{-x}\right) \cdot \left(e^{x} + e^{-x}\right)\right) \cdot \left(e^{x} + e^{-x}\right)}}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Simplified0.1
\[\leadsto \Re(\left(\frac{\cos y}{\sqrt[3]{\color{blue}{{\left(\frac{2}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Final simplification0.1
\[\leadsto \Re(\left(\frac{\cos y}{\sqrt[3]{{\left(\frac{2}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}} + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
