Initial program 0.1
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
- Using strategy
rm Applied sub-neg0.1
\[\leadsto \left(\frac{m \cdot \color{blue}{\left(1 + \left(-m\right)\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]
Applied distribute-lft-in0.1
\[\leadsto \left(\frac{\color{blue}{m \cdot 1 + m \cdot \left(-m\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]
- Using strategy
rm Applied sub-neg0.1
\[\leadsto \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot \color{blue}{\left(1 + \left(-m\right)\right)}\]
Applied distribute-lft-in0.1
\[\leadsto \color{blue}{\left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot \left(-m\right)}\]
Simplified0.1
\[\leadsto \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot 1 + \color{blue}{(\left(\frac{-1 + m}{\frac{v}{m}}\right) \cdot m + m)_*}\]
Taylor expanded around -inf 0.1
\[\leadsto \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot 1 + \color{blue}{\left(\left(m + \frac{{m}^{3}}{v}\right) - \frac{{m}^{2}}{v}\right)}\]
Simplified0.1
\[\leadsto \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot 1 + \color{blue}{(\left(\frac{m}{v}\right) \cdot \left(m \cdot m - m\right) + m)_*}\]
- Using strategy
rm Applied fma-neg0.1
\[\leadsto \left(\frac{m \cdot 1 + m \cdot \left(-m\right)}{v} - 1\right) \cdot 1 + (\left(\frac{m}{v}\right) \cdot \color{blue}{\left((m \cdot m + \left(-m\right))_*\right)} + m)_*\]
Final simplification0.1
\[\leadsto (\left(\frac{m}{v}\right) \cdot \left((m \cdot m + \left(-m\right))_*\right) + m)_* + \left(\frac{m + \left(-m\right) \cdot m}{v} - 1\right)\]
