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
\[\leadsto \cos \left((\left(\frac{2}{3}\right) \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right) \cdot 2\]
- Using strategy
rm Applied add-sqr-sqrt1.0
\[\leadsto \cos \left((\left(\frac{2}{3}\right) \cdot \pi + \left(\frac{\color{blue}{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}{3}\right))_*\right) \cdot 2\]
Applied associate-/l*1.0
\[\leadsto \cos \left((\left(\frac{2}{3}\right) \cdot \pi + \color{blue}{\left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied add-cube-cbrt1.0
\[\leadsto \cos \left((\left(\frac{2}{3}\right) \cdot \pi + \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\color{blue}{\left(\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}}}\right))_*\right) \cdot 2\]
- Using strategy
rm Applied fma-udef1.0
\[\leadsto \cos \color{blue}{\left(\frac{2}{3} \cdot \pi + \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\left(\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}}\right)} \cdot 2\]
Applied cos-sum1.0
\[\leadsto \color{blue}{\left(\cos \left(\frac{2}{3} \cdot \pi\right) \cdot \cos \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\left(\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}}\right) - \sin \left(\frac{2}{3} \cdot \pi\right) \cdot \sin \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\left(\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}}\right)\right)} \cdot 2\]
Simplified0.1
\[\leadsto \left(\color{blue}{\cos \left(\frac{2}{3} \cdot \pi\right) \cdot \cos \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)} - \sin \left(\frac{2}{3} \cdot \pi\right) \cdot \sin \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\frac{3}{\left(\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}\right) \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}}\right)\right) \cdot 2\]
Final simplification0.1
\[\leadsto 2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\frac{2}{3} \cdot \pi\right) - \sin \left(\frac{\sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}}{\frac{3}{\sqrt[3]{\sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}} \cdot \left(\sqrt[3]{\sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}} \cdot \sqrt[3]{\sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}}\right)}}\right) \cdot \sin \left(\frac{2}{3} \cdot \pi\right)\right)\]
