Initial program 37.4
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
Initial simplification12.8
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt14.0
\[\leadsto 0.5 \cdot \sqrt{(\color{blue}{\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{re^2 + im^2}^*}\right)} \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt14.4
\[\leadsto 0.5 \cdot \sqrt{(\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \color{blue}{\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied associate-*r*14.3
\[\leadsto 0.5 \cdot \sqrt{(\color{blue}{\left(\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right) \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)} \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
- Using strategy
rm Applied pow114.3
\[\leadsto 0.5 \cdot \sqrt{(\left(\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right) \cdot \color{blue}{{\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)}^{1}}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied pow114.3
\[\leadsto 0.5 \cdot \sqrt{(\left(\color{blue}{{\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)}^{1}} \cdot {\left(\sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)}^{1}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Applied pow-prod-down14.3
\[\leadsto 0.5 \cdot \sqrt{(\color{blue}{\left({\left(\left(\sqrt{\sqrt{re^2 + im^2}^*} \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right) \cdot \sqrt{\sqrt{\sqrt{re^2 + im^2}^*}}\right)}^{1}\right)} \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Simplified12.8
\[\leadsto 0.5 \cdot \sqrt{(\left({\color{blue}{\left(\sqrt{re^2 + im^2}^*\right)}}^{1}\right) \cdot 2.0 + \left(re \cdot 2.0\right))_*}\]
Final simplification12.8
\[\leadsto \sqrt{(\left(\sqrt{re^2 + im^2}^*\right) \cdot 2.0 + \left(2.0 \cdot re\right))_*} \cdot 0.5\]
