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-cube-cbrt1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied log1p-expm1-u1.0
\[\leadsto \color{blue}{\log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)} - 1)^*)} \cdot 2\]
- Using strategy
rm Applied cbrt-div1.0
\[\leadsto \log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \color{blue}{\frac{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt[3]{3}}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)} - 1)^*) \cdot 2\]
- Using strategy
rm Applied add-cube-cbrt1.0
\[\leadsto \log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \frac{\sqrt[3]{\color{blue}{\left(\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}\right) \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}}}{\sqrt[3]{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)} - 1)^*) \cdot 2\]
Applied cbrt-prod1.0
\[\leadsto \log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \frac{\color{blue}{\sqrt[3]{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}}}{\sqrt[3]{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right)} - 1)^*) \cdot 2\]
Final simplification1.0
\[\leadsto 2 \cdot \log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}} \cdot \frac{\sqrt[3]{\sqrt[3]{\cos^{-1} \left(-\frac{g}{h}\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos^{-1} \left(-\frac{g}{h}\right)} \cdot \sqrt[3]{\cos^{-1} \left(-\frac{g}{h}\right)}}}{\sqrt[3]{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}}\right))_*\right)} - 1)^*)\]
