Initial program 0.2
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
- Using strategy
rm Applied associate-/l*0.2
\[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot m\]
- Using strategy
rm Applied flip--0.2
\[\leadsto \left(\frac{m}{\frac{v}{\color{blue}{\frac{1 \cdot 1 - m \cdot m}{1 + m}}}} - 1\right) \cdot m\]
Applied associate-/r/0.2
\[\leadsto \left(\frac{m}{\color{blue}{\frac{v}{1 \cdot 1 - m \cdot m} \cdot \left(1 + m\right)}} - 1\right) \cdot m\]
Applied associate-/r*0.2
\[\leadsto \left(\color{blue}{\frac{\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m}}}{1 + m}} - 1\right) \cdot m\]
Taylor expanded around 0 6.9
\[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]
- Using strategy
rm Applied add-sqr-sqrt7.2
\[\leadsto \frac{{m}^{2}}{v} - \color{blue}{\sqrt{m + \frac{{m}^{3}}{v}} \cdot \sqrt{m + \frac{{m}^{3}}{v}}}\]
Applied *-un-lft-identity7.2
\[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v}} - \sqrt{m + \frac{{m}^{3}}{v}} \cdot \sqrt{m + \frac{{m}^{3}}{v}}\]
Applied prod-diff7.2
\[\leadsto \color{blue}{(1 \cdot \left(\frac{{m}^{2}}{v}\right) + \left(-\sqrt{m + \frac{{m}^{3}}{v}} \cdot \sqrt{m + \frac{{m}^{3}}{v}}\right))_* + (\left(-\sqrt{m + \frac{{m}^{3}}{v}}\right) \cdot \left(\sqrt{m + \frac{{m}^{3}}{v}}\right) + \left(\sqrt{m + \frac{{m}^{3}}{v}} \cdot \sqrt{m + \frac{{m}^{3}}{v}}\right))_*}\]
Simplified0.2
\[\leadsto \color{blue}{(\left(\frac{m}{\frac{v}{m}}\right) \cdot \left(1 - m\right) + \left(-m\right))_*} + (\left(-\sqrt{m + \frac{{m}^{3}}{v}}\right) \cdot \left(\sqrt{m + \frac{{m}^{3}}{v}}\right) + \left(\sqrt{m + \frac{{m}^{3}}{v}} \cdot \sqrt{m + \frac{{m}^{3}}{v}}\right))_*\]
Simplified0.2
\[\leadsto (\left(\frac{m}{\frac{v}{m}}\right) \cdot \left(1 - m\right) + \left(-m\right))_* + \color{blue}{0}\]
Final simplification0.2
\[\leadsto (\left(\frac{m}{\frac{v}{m}}\right) \cdot \left(1 - m\right) + \left(-m\right))_*\]
