Initial program 0.6
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Initial simplification0.6
\[\leadsto \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)\]
Taylor expanded around 0 0.8
\[\leadsto \cos^{-1} \color{blue}{\left(\left(4 \cdot {v}^{4} + 4 \cdot {v}^{2}\right) - 1\right)}\]
Simplified0.8
\[\leadsto \cos^{-1} \color{blue}{\left((4 \cdot \left((v \cdot v + \left({v}^{4}\right))_*\right) + -1)_*\right)}\]
- Using strategy
rm Applied expm1-log1p-u0.8
\[\leadsto \color{blue}{(e^{\log_* (1 + \cos^{-1} \left((4 \cdot \left((v \cdot v + \left({v}^{4}\right))_*\right) + -1)_*\right))} - 1)^*}\]
- Using strategy
rm Applied expm1-log1p-u0.8
\[\leadsto (e^{\color{blue}{(e^{\log_* (1 + \log_* (1 + \cos^{-1} \left((4 \cdot \left((v \cdot v + \left({v}^{4}\right))_*\right) + -1)_*\right)))} - 1)^*}} - 1)^*\]
- Using strategy
rm Applied add-exp-log0.8
\[\leadsto \color{blue}{e^{\log \left((e^{(e^{\log_* (1 + \log_* (1 + \cos^{-1} \left((4 \cdot \left((v \cdot v + \left({v}^{4}\right))_*\right) + -1)_*\right)))} - 1)^*} - 1)^*\right)}}\]
Final simplification0.8
\[\leadsto e^{\log \left((e^{(e^{\log_* (1 + \log_* (1 + \cos^{-1} \left((4 \cdot \left((v \cdot v + \left({v}^{4}\right))_*\right) + -1)_*\right)))} - 1)^*} - 1)^*\right)}\]
