Initial program 0.2
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
- Using strategy
rm Applied add-sqr-sqrt0.2
\[\leadsto \left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \color{blue}{\left(\sqrt{\left|x\right|} \cdot \sqrt{\left|x\right|}\right)}\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
Applied associate-*r*0.2
\[\leadsto \left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\color{blue}{\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \sqrt{\left|x\right|}\right) \cdot \sqrt{\left|x\right|}\right)} \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
- Using strategy
rm Applied pow10.2
\[\leadsto \left|\frac{1}{\sqrt{\pi}} \cdot \color{blue}{{\left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \sqrt{\left|x\right|}\right) \cdot \sqrt{\left|x\right|}\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)}^{1}}\right|\]
Applied pow10.2
\[\leadsto \left|\color{blue}{{\left(\frac{1}{\sqrt{\pi}}\right)}^{1}} \cdot {\left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \sqrt{\left|x\right|}\right) \cdot \sqrt{\left|x\right|}\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)}^{1}\right|\]
Applied pow-prod-down0.2
\[\leadsto \left|\color{blue}{{\left(\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \sqrt{\left|x\right|}\right) \cdot \sqrt{\left|x\right|}\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right)}^{1}}\right|\]
Simplified0.2
\[\leadsto \left|{\color{blue}{\left((\left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left(\frac{2}{3} \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) \cdot \left(\frac{1}{\sqrt{\pi}}\right) + \left(\left(\frac{\frac{1}{21}}{\sqrt{\pi}} \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot {\left(\left|x\right|\right)}^{3}\right)\right))_*\right)}}^{1}\right|\]
Simplified0.1
\[\leadsto \color{blue}{\left|(\left((\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left((\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(\frac{2}{3} \cdot \left|x\right|\right))_*\right) + \left(\left|x\right| \cdot 2\right))_*\right) \cdot \left(\frac{1}{\sqrt{\pi}}\right) + \left(\frac{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{5}}{\frac{\sqrt{\pi}}{\left|x\right| \cdot \left|x\right|}}\right))_*\right|}\]
Final simplification0.1
\[\leadsto \left|(\left((\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left((\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(\frac{2}{3} \cdot \left|x\right|\right))_*\right) + \left(2 \cdot \left|x\right|\right))_*\right) \cdot \left(\frac{1}{\sqrt{\pi}}\right) + \left(\frac{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{5}}{\frac{\sqrt{\pi}}{\left|x\right| \cdot \left|x\right|}}\right))_*\right|\]
