Initial program 1.0
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
Simplified1.0
\[\leadsto \color{blue}{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right) \cdot 2}\]
- Using strategy
rm Applied add-sqr-sqrt1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\color{blue}{\sqrt{3} \cdot \sqrt{3}}}\right))_*\right) \cdot 2\]
Applied add-sqr-sqrt1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\color{blue}{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}}{\sqrt{3} \cdot \sqrt{3}}\right))_*\right) \cdot 2\]
Applied times-frac1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied add-log-exp1.0
\[\leadsto \color{blue}{\log \left(e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right))_*\right)}\right)} \cdot 2\]
- Using strategy
rm Applied div-inv1.0
\[\leadsto \log \left(e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \color{blue}{\left(\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \frac{1}{\sqrt{3}}\right)}\right))_*\right)}\right) \cdot 2\]
Final simplification1.0
\[\leadsto \log \left(e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}}{\sqrt{3}} \cdot \left(\frac{1}{\sqrt{3}} \cdot \sqrt{\cos^{-1} \left(-\frac{g}{h}\right)}\right)\right))_*\right)}\right) \cdot 2\]
