Initial program 37.0
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
Simplified12.5
\[\leadsto \color{blue}{0.5 \cdot \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}}\]
- Using strategy
rm Applied add-sqr-sqrt13.5
\[\leadsto 0.5 \cdot \sqrt{(\color{blue}{\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)} \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt13.8
\[\leadsto 0.5 \cdot \sqrt{(\left(\color{blue}{\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied associate-*l*13.8
\[\leadsto 0.5 \cdot \sqrt{(\color{blue}{\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)\right)} \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied add-cube-cbrt13.8
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \left(\sqrt{\sqrt{\color{blue}{\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}}}} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied sqrt-prod13.8
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \left(\sqrt{\color{blue}{\sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}} \cdot \sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*}}}} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied sqrt-prod14.0
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \left(\color{blue}{\left(\sqrt{\sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}}} \cdot \sqrt{\sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*}}}\right)} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Simplified14.0
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \left(\left(\color{blue}{\sqrt{\left|\sqrt[3]{\sqrt{re^2 + im^2}^*}\right|}} \cdot \sqrt{\sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*}}}\right) \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Final simplification14.0
\[\leadsto 0.5 \cdot \sqrt{(\left(\left(\left(\sqrt{\left|\sqrt[3]{\sqrt{re^2 + im^2}^*}\right|} \cdot \sqrt{\sqrt{\sqrt[3]{\sqrt{re^2 + im^2}^*}}}\right) \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
