\(\left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left(\left({\left(\left|x\right|\right)}^3 \cdot {\left(\left|x\right|\right)}^3\right) \cdot \left|x\right|\right)\right)\right|\)
- Started with
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
0.2
- Applied simplify to get
\[\color{red}{\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|} \leadsto \color{blue}{\left|\frac{(\left(\frac{\left|x\right|}{5} \cdot {\left(\left|x\right|\right)}^3\right) * \left(\left|x\right|\right) + \left((\left(\frac{2}{3}\right) * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{{\left({\left(\left|x\right|\right)}^2\right)}^3}{\frac{21}{\left|x\right|}}}{\sqrt{\pi}}\right|}\]
0.6
- Applied taylor to get
\[\left|\frac{(\left(\frac{\left|x\right|}{5} \cdot {\left(\left|x\right|\right)}^3\right) * \left(\left|x\right|\right) + \left((\left(\frac{2}{3}\right) * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{{\left({\left(\left|x\right|\right)}^2\right)}^3}{\frac{21}{\left|x\right|}}}{\sqrt{\pi}}\right| \leadsto \left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left({\left({\left(\left|x\right|\right)}^2\right)}^3 \cdot \left|x\right|\right)\right)\right|\]
0.2
- Taylor expanded around 0 to get
\[\left|\color{red}{\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left({\left({\left(\left|x\right|\right)}^2\right)}^3 \cdot \left|x\right|\right)\right)}\right| \leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left({\left({\left(\left|x\right|\right)}^2\right)}^3 \cdot \left|x\right|\right)\right)}\right|\]
0.2
- Using strategy
rm 0.2
- Applied square-mult to get
\[\left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left({\color{red}{\left({\left(\left|x\right|\right)}^2\right)}}^3 \cdot \left|x\right|\right)\right)\right| \leadsto \left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left({\color{blue}{\left(\left|x\right| \cdot \left|x\right|\right)}}^3 \cdot \left|x\right|\right)\right)\right|\]
0.2
- Applied cube-prod to get
\[\left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left(\color{red}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3} \cdot \left|x\right|\right)\right)\right| \leadsto \left|\sqrt{\frac{1}{\pi}} \cdot \left((\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot {\left(\left|x\right|\right)}^3\right)\right) * \left(\left|x\right|\right) + \left((\frac{2}{3} * \left({\left(\left|x\right|\right)}^3\right) + \left(2 \cdot \left|x\right|\right))_*\right))_* + \frac{1}{21} \cdot \left(\color{blue}{\left({\left(\left|x\right|\right)}^3 \cdot {\left(\left|x\right|\right)}^3\right)} \cdot \left|x\right|\right)\right)\right|\]
0.2
