\(\left(x + \left(\frac{1}{1920} \cdot {x}^{5} + {x}^3 \cdot \frac{1}{24}\right)\right) \cdot \left(x + \left(\frac{1}{1920} \cdot {x}^{5} + {x}^3 \cdot \frac{1}{24}\right)\right)\)
- Started with
\[\left(e^{x} - 2\right) + e^{-x}\]
14.5
- Applied taylor to get
\[\left(e^{x} - 2\right) + e^{-x} \leadsto {x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)\]
2.7
- Taylor expanded around 0 to get
\[\color{red}{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)} \leadsto \color{blue}{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)}\]
2.7
- Using strategy
rm 2.7
- Applied add-sqr-sqrt to get
\[\color{red}{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)} \leadsto \color{blue}{{\left(\sqrt{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)}\right)}^2}\]
2.7
- Applied taylor to get
\[{\left(\sqrt{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)}\right)}^2 \leadsto {\left(\frac{1}{1920} \cdot {x}^{5} + \left(\frac{1}{24} \cdot {x}^{3} + x\right)\right)}^2\]
0.1
- Taylor expanded around 0 to get
\[{\color{red}{\left(\frac{1}{1920} \cdot {x}^{5} + \left(\frac{1}{24} \cdot {x}^{3} + x\right)\right)}}^2 \leadsto {\color{blue}{\left(\frac{1}{1920} \cdot {x}^{5} + \left(\frac{1}{24} \cdot {x}^{3} + x\right)\right)}}^2\]
0.1
- Applied simplify to get
\[{\left(\frac{1}{1920} \cdot {x}^{5} + \left(\frac{1}{24} \cdot {x}^{3} + x\right)\right)}^2 \leadsto \left(x + \left(\frac{1}{1920} \cdot {x}^{5} + {x}^3 \cdot \frac{1}{24}\right)\right) \cdot \left(x + \left(\frac{1}{1920} \cdot {x}^{5} + {x}^3 \cdot \frac{1}{24}\right)\right)\]
0.1
- Applied final simplification
- Removed slow pow expressions
