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 0 0.2
\[\leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)}\right|\]
- Using strategy
rm Applied add-sqr-sqrt0.2
\[\leadsto \left|\sqrt{\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \sqrt{\frac{1}{\pi}}}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)\right|\]
Applied sqrt-prod0.2
\[\leadsto \left|\color{blue}{\left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \sqrt{\sqrt{\frac{1}{\pi}}}\right)} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)\right|\]
Applied associate-*l*0.5
\[\leadsto \left|\color{blue}{\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5} + \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)\right)}\right|\]
- Using strategy
rm Applied distribute-lft-in0.5
\[\leadsto \left|\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \color{blue}{\left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5}\right) + \sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)}\right|\]
Applied distribute-lft-in0.5
\[\leadsto \left|\color{blue}{\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5}\right)\right) + \sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(2 \cdot \left|x\right| + \left(\frac{2}{3} \cdot {\left(\left|x\right|\right)}^{3} + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right)\right)\right)}\right|\]
Simplified0.2
\[\leadsto \left|\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left(\frac{1}{5} \cdot {\left(\left|x\right|\right)}^{5}\right)\right) + \color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left(\left(\frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7} + \left(\frac{2}{3} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) + \left|x\right| \cdot 2\right)}\right|\]
Final simplification0.2
\[\leadsto \left|\left(\sqrt{\sqrt{\frac{1}{\pi}}} \cdot \left({\left(\left|x\right|\right)}^{5} \cdot \frac{1}{5}\right)\right) \cdot \sqrt{\sqrt{\frac{1}{\pi}}} + \left(\left(\left(\frac{2}{3} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \frac{1}{21} \cdot {\left(\left|x\right|\right)}^{7}\right) + 2 \cdot \left|x\right|\right) \cdot \sqrt{\frac{1}{\pi}}\right|\]
