Initial program 36.9
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
Initial simplification13.0
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt13.0
\[\leadsto 0.5 \cdot \sqrt{\color{blue}{\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*} \cdot \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}}}\]
Applied sqrt-prod13.4
\[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}} \cdot \sqrt{\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}}\right)}\]
- Using strategy
rm Applied pow1/213.4
\[\leadsto 0.5 \cdot \left(\sqrt{\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}} \cdot \color{blue}{{\left(\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\right)}^{\frac{1}{2}}}\right)\]
Applied pow1/213.4
\[\leadsto 0.5 \cdot \left(\color{blue}{{\left(\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\right)}^{\frac{1}{2}}} \cdot {\left(\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\right)}^{\frac{1}{2}}\right)\]
Applied pow-prod-down13.0
\[\leadsto 0.5 \cdot \color{blue}{{\left(\sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*} \cdot \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\right)}^{\frac{1}{2}}}\]
Simplified13.0
\[\leadsto 0.5 \cdot {\color{blue}{\left((\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(2.0 \cdot re\right))_*\right)}}^{\frac{1}{2}}\]
Final simplification13.0
\[\leadsto 0.5 \cdot {\left((\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*\right)}^{\frac{1}{2}}\]
