Initial program 0.2
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
Taylor expanded around -inf 0.2
\[\leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)}\right|\]
Simplified0.2
\[\leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left(\left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left|x\right| \cdot \left(2 + \left(\frac{2}{3} \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)}\right|\]
- Using strategy
rm Applied sqrt-div0.2
\[\leadsto \left|\color{blue}{\frac{\sqrt{1}}{\sqrt{\pi}}} \cdot \left(\left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left|x\right| \cdot \left(2 + \left(\frac{2}{3} \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right|\]
Applied associate-*l/0.6
\[\leadsto \left|\color{blue}{\frac{\sqrt{1} \cdot \left(\left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left|x\right| \cdot \left(2 + \left(\frac{2}{3} \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)}{\sqrt{\pi}}}\right|\]
Simplified0.6
\[\leadsto \left|\frac{\color{blue}{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\left|x\right| \cdot \left(2 + \left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{2}{3}\right) + {\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)}}{\sqrt{\pi}}\right|\]
- Using strategy
rm Applied add-sqr-sqrt0.6
\[\leadsto \left|\frac{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\left|x\right| \cdot \left(2 + \left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{2}{3}\right) + {\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)}{\sqrt{\color{blue}{\sqrt{\pi} \cdot \sqrt{\pi}}}}\right|\]
Applied sqrt-prod0.4
\[\leadsto \left|\frac{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\left|x\right| \cdot \left(2 + \left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{2}{3}\right) + {\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)}{\color{blue}{\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}}}\right|\]
Applied *-un-lft-identity0.4
\[\leadsto \left|\frac{\color{blue}{1 \cdot \left(\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\left|x\right| \cdot \left(2 + \left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{2}{3}\right) + {\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)\right)}}{\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}}\right|\]
Applied times-frac0.3
\[\leadsto \left|\color{blue}{\frac{1}{\sqrt{\sqrt{\pi}}} \cdot \frac{\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\left|x\right| \cdot \left(2 + \left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{2}{3}\right) + {\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)}{\sqrt{\sqrt{\pi}}}}\right|\]
Final simplification0.3
\[\leadsto \left|\frac{\left({\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5} + \left(2 + \frac{2}{3} \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left|x\right|\right) + {\left(\left|x\right|\right)}^{7} \cdot \frac{1}{21}}{\sqrt{\sqrt{\pi}}} \cdot \frac{1}{\sqrt{\sqrt{\pi}}}\right|\]
