Initial program 46.2
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
Simplified15.9
\[\leadsto \color{blue}{\frac{i \cdot i}{\left(4 \cdot \left(i \cdot i\right) - 1.0\right) \cdot 4}}\]
- Using strategy
rm Applied add-sqr-sqrt15.9
\[\leadsto \frac{i \cdot i}{\left(4 \cdot \left(i \cdot i\right) - \color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}}\right) \cdot 4}\]
Applied add-sqr-sqrt16.0
\[\leadsto \frac{i \cdot i}{\left(4 \cdot \left(i \cdot \color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)}\right) - \sqrt{1.0} \cdot \sqrt{1.0}\right) \cdot 4}\]
Applied add-sqr-sqrt16.0
\[\leadsto \frac{i \cdot i}{\left(4 \cdot \left(\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)\right) - \sqrt{1.0} \cdot \sqrt{1.0}\right) \cdot 4}\]
Applied swap-sqr16.0
\[\leadsto \frac{i \cdot i}{\left(4 \cdot \color{blue}{\left(\left(\sqrt{i} \cdot \sqrt{i}\right) \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)\right)} - \sqrt{1.0} \cdot \sqrt{1.0}\right) \cdot 4}\]
Applied add-sqr-sqrt16.0
\[\leadsto \frac{i \cdot i}{\left(\color{blue}{\left(\sqrt{4} \cdot \sqrt{4}\right)} \cdot \left(\left(\sqrt{i} \cdot \sqrt{i}\right) \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)\right) - \sqrt{1.0} \cdot \sqrt{1.0}\right) \cdot 4}\]
Applied unswap-sqr16.0
\[\leadsto \frac{i \cdot i}{\left(\color{blue}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)\right) \cdot \left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)\right)} - \sqrt{1.0} \cdot \sqrt{1.0}\right) \cdot 4}\]
Applied difference-of-squares16.0
\[\leadsto \frac{i \cdot i}{\color{blue}{\left(\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}\right) \cdot \left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right)\right)} \cdot 4}\]
Applied associate-*l*16.0
\[\leadsto \frac{i \cdot i}{\color{blue}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}\right) \cdot \left(\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4\right)}}\]
Applied add-sqr-sqrt16.1
\[\leadsto \frac{i \cdot \color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)}}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}\right) \cdot \left(\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4\right)}\]
Applied add-sqr-sqrt16.0
\[\leadsto \frac{\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}\right) \cdot \left(\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4\right)}\]
Applied unswap-sqr16.0
\[\leadsto \frac{\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right) \cdot \left(\sqrt{i} \cdot \sqrt{i}\right)}}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}\right) \cdot \left(\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\sqrt{i} \cdot \sqrt{i}}{\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}} \cdot \frac{\sqrt{i} \cdot \sqrt{i}}{\left(\sqrt{4} \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4}}\]
Final simplification0.3
\[\leadsto \frac{\sqrt{i} \cdot \sqrt{i}}{2 \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) + \sqrt{1.0}} \cdot \frac{\sqrt{i} \cdot \sqrt{i}}{\left(2 \cdot \left(\sqrt{i} \cdot \sqrt{i}\right) - \sqrt{1.0}\right) \cdot 4}\]
