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 add-cube-cbrt1.0
\[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)} \cdot \sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)}\right) \cdot \sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)}\right)} \cdot 2\]
- Using strategy
rm Applied cbrt-unprod0.0
\[\leadsto \left(\color{blue}{\sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right) \cdot \cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)}} \cdot \sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)}\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\sqrt[3]{\color{blue}{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right) \cdot \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right)}} \cdot \sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)}\right) \cdot 2\]
Final simplification0.0
\[\leadsto 2 \cdot \left(\sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right) \cdot \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right)} \cdot \sqrt[3]{\cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}} \cdot \sqrt{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}}\right))_*\right)}\right)\]
