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 log1p-expm1-u1.0
\[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right)})_*\right) \cdot 2\]
- Using strategy
rm Applied add-log-exp1.0
\[\leadsto \color{blue}{\log \left(e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}\right)} \cdot 2\]
- Using strategy
rm Applied add-cube-cbrt0.1
\[\leadsto \log \color{blue}{\left(\left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}} \cdot \sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right) \cdot \sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right)} \cdot 2\]
Applied log-prod0.1
\[\leadsto \color{blue}{\left(\log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}} \cdot \sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right) + \log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right)\right)} \cdot 2\]
Simplified0.1
\[\leadsto \left(\color{blue}{\log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right)}} \cdot \sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right))_*\right)}}\right)} + \log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right)\right) \cdot 2\]
Final simplification0.1
\[\leadsto 2 \cdot \left(\log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\log_* (1 + (e^{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} - 1)^*)\right))_*\right)}}\right) + \log \left(\sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right)}} \cdot \sqrt[3]{e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right)}}\right)\right)\]
