Initial program 1.5
\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
- Using strategy
rm Applied frac-times1.3
\[\leadsto \left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\color{blue}{\frac{1 \cdot 1}{\left|x\right| \cdot \left|x\right|}} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
Simplified1.3
\[\leadsto \left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\frac{\color{blue}{1}}{\left|x\right| \cdot \left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
Simplified1.0
\[\leadsto \color{blue}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right| \cdot \left|x\right|} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)}\]
- Using strategy
rm Applied pow21.0
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\color{blue}{{\left(\left|x\right|\right)}^{2}}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied pow11.0
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \color{blue}{{\left(\left|x\right|\right)}^{1}}}}{{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied pow11.0
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{1}{\left|x\right|}}{\color{blue}{{\left(\left|x\right|\right)}^{1}} \cdot {\left(\left|x\right|\right)}^{1}}}{{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied pow-prod-up1.0
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{1}{\left|x\right|}}{\color{blue}{{\left(\left|x\right|\right)}^{\left(1 + 1\right)}}}}{{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied inv-pow1.0
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\color{blue}{{\left(\left|x\right|\right)}^{-1}}}{{\left(\left|x\right|\right)}^{\left(1 + 1\right)}}}{{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied pow-div0.8
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\color{blue}{{\left(\left|x\right|\right)}^{\left(-1 - \left(1 + 1\right)\right)}}}{{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Applied pow-div0.7
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\color{blue}{{\left(\left|x\right|\right)}^{\left(\left(-1 - \left(1 + 1\right)\right) - 2\right)}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Simplified0.7
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left({\left(\left|x\right|\right)}^{\color{blue}{-5}} \cdot \left(\frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|} + \frac{3}{4}\right) + \left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}\right)\right)\]
Final simplification0.7
\[\leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{\frac{1}{2}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} + \frac{1}{\left|x\right|}\right) + \left(\frac{3}{4} + \frac{\frac{15}{8}}{\left|x\right| \cdot \left|x\right|}\right) \cdot {\left(\left|x\right|\right)}^{-5}\right)\]
