Initial program 1.0
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
Initial simplification1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right) \cdot 2\]
- Using strategy
rm Applied add-sqr-sqrt1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied sqrt-div1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \color{blue}{\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}}\right))_*\right) \cdot 2\]
Applied associate-*r/1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\frac{\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied add-cube-cbrt1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\color{blue}{\left(\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}\right) \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}}}{\sqrt{3}}\right))_*\right) \cdot 2\]
Applied sqrt-prod1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \color{blue}{\left(\sqrt{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}\right)}}{\sqrt{3}}\right))_*\right) \cdot 2\]
Simplified1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \left(\color{blue}{\left|\sqrt[3]{\cos^{-1} \left(-\frac{g}{h}\right)}\right|} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}\right)}{\sqrt{3}}\right))_*\right) \cdot 2\]
Final simplification1.0
\[\leadsto 2 \cdot \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\left(\left|\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}\right| \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}}{\sqrt{3}}\right))_*\right)\]
