Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Initial simplification0.5
\[\leadsto \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)\]
- Using strategy
rm Applied expm1-log1p-u0.5
\[\leadsto \color{blue}{(e^{\log_* (1 + \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right))} - 1)^*}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto (e^{\log_* (1 + \cos^{-1} \left(\frac{\color{blue}{1 \cdot (\left(-5 \cdot v\right) \cdot v + 1)_*}}{(v \cdot v + -1)_*}\right))} - 1)^*\]
Applied associate-/l*0.6
\[\leadsto (e^{\log_* (1 + \cos^{-1} \color{blue}{\left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(-5 \cdot v\right) \cdot v + 1)_*}}\right)})} - 1)^*\]
- Using strategy
rm Applied add-cbrt-cube0.6
\[\leadsto (e^{\log_* (1 + \color{blue}{\sqrt[3]{\left(\cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(-5 \cdot v\right) \cdot v + 1)_*}}\right) \cdot \cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(-5 \cdot v\right) \cdot v + 1)_*}}\right)\right) \cdot \cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(-5 \cdot v\right) \cdot v + 1)_*}}\right)}})} - 1)^*\]
Final simplification0.6
\[\leadsto (e^{\log_* (1 + \sqrt[3]{\cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(v \cdot -5\right) \cdot v + 1)_*}}\right) \cdot \left(\cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(v \cdot -5\right) \cdot v + 1)_*}}\right) \cdot \cos^{-1} \left(\frac{1}{\frac{(v \cdot v + -1)_*}{(\left(v \cdot -5\right) \cdot v + 1)_*}}\right)\right)})} - 1)^*\]
