Initial program 30.0
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re - im \cdot im} + re\right)}\]
- Using strategy
rm Applied difference-of-squares30.0
\[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\color{blue}{\left(re + im\right) \cdot \left(re - im\right)}} + re\right)}\]
Applied sqrt-prod0.1
\[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{\sqrt{re + im} \cdot \sqrt{re - im}} + re\right)}\]
Applied fma-def0.1
\[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \color{blue}{(\left(\sqrt{re + im}\right) \cdot \left(\sqrt{re - im}\right) + re)_*}}\]
- Using strategy
rm Applied sqrt-prod0.5
\[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{2.0} \cdot \sqrt{(\left(\sqrt{re + im}\right) \cdot \left(\sqrt{re - im}\right) + re)_*}\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.5
\[\leadsto 0.5 \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sqrt{2.0}} \cdot \sqrt[3]{\sqrt{2.0}}\right) \cdot \sqrt[3]{\sqrt{2.0}}\right)} \cdot \sqrt{(\left(\sqrt{re + im}\right) \cdot \left(\sqrt{re - im}\right) + re)_*}\right)\]
Applied associate-*l*0.5
\[\leadsto 0.5 \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{2.0}} \cdot \sqrt[3]{\sqrt{2.0}}\right) \cdot \left(\sqrt[3]{\sqrt{2.0}} \cdot \sqrt{(\left(\sqrt{re + im}\right) \cdot \left(\sqrt{re - im}\right) + re)_*}\right)\right)}\]
