Initial program 12.3
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Initial simplification0.4
\[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - (\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]
- Using strategy
rm Applied add-sqr-sqrt1.0
\[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*} \cdot \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}}\]
Applied *-un-lft-identity1.0
\[\leadsto \color{blue}{1 \cdot \left(3 + \frac{2}{r \cdot r}\right)} - \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*} \cdot \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\]
Applied prod-diff1.0
\[\leadsto \color{blue}{(1 \cdot \left(3 + \frac{2}{r \cdot r}\right) + \left(-\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*} \cdot \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right))_* + (\left(-\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right) \cdot \left(\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right) + \left(\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*} \cdot \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right))_*}\]
Simplified0.4
\[\leadsto \color{blue}{(\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right))_*} + (\left(-\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right) \cdot \left(\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right) + \left(\sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*} \cdot \sqrt{(\left(\frac{(-2 \cdot v + 3)_*}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\right))_*\]
Simplified0.3
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right))_* + \color{blue}{0}\]
- Using strategy
rm Applied flip-+0.3
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\color{blue}{\frac{\left(-4.5\right) \cdot \left(-4.5\right) - 3 \cdot 3}{\left(-4.5\right) - 3}} + \frac{\frac{2}{r}}{r}\right))_* + 0\]
Applied frac-add0.5
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \color{blue}{\left(\frac{\left(\left(-4.5\right) \cdot \left(-4.5\right) - 3 \cdot 3\right) \cdot r + \left(\left(-4.5\right) - 3\right) \cdot \frac{2}{r}}{\left(\left(-4.5\right) - 3\right) \cdot r}\right)})_* + 0\]
Simplified0.5
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\frac{\color{blue}{(\left(3 - 4.5\right) \cdot r + \left(\frac{2}{r}\right))_* \cdot \left(-3 - 4.5\right)}}{\left(\left(-4.5\right) - 3\right) \cdot r}\right))_* + 0\]
Simplified0.5
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\frac{(\left(3 - 4.5\right) \cdot r + \left(\frac{2}{r}\right))_* \cdot \left(-3 - 4.5\right)}{\color{blue}{\left(-3 - 4.5\right) \cdot r}}\right))_* + 0\]
- Using strategy
rm Applied flip--0.5
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\frac{(\left(3 - 4.5\right) \cdot r + \left(\frac{2}{r}\right))_* \cdot \color{blue}{\frac{-3 \cdot -3 - 4.5 \cdot 4.5}{-3 + 4.5}}}{\left(-3 - 4.5\right) \cdot r}\right))_* + 0\]
Applied associate-*r/0.6
\[\leadsto (\left(0.125 \cdot \frac{(-2 \cdot v + 3)_*}{1 - v}\right) \cdot \left(-\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\frac{\color{blue}{\frac{(\left(3 - 4.5\right) \cdot r + \left(\frac{2}{r}\right))_* \cdot \left(-3 \cdot -3 - 4.5 \cdot 4.5\right)}{-3 + 4.5}}}{\left(-3 - 4.5\right) \cdot r}\right))_* + 0\]
Final simplification0.6
\[\leadsto (\left(\frac{(-2 \cdot v + 3)_*}{1 - v} \cdot 0.125\right) \cdot \left(\left(-w \cdot r\right) \cdot \left(w \cdot r\right)\right) + \left(\frac{\frac{\left(9 - 4.5 \cdot 4.5\right) \cdot (\left(3 - 4.5\right) \cdot r + \left(\frac{2}{r}\right))_*}{4.5 + -3}}{r \cdot \left(-3 - 4.5\right)}\right))_*\]
