Initial program 15.3
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
Initial simplification15.2
\[\leadsto \frac{\cos \left((\left(\frac{K}{2}\right) \cdot \left(m + n\right) + \left(-M\right))_*\right)}{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}\]
Taylor expanded around 0 1.3
\[\leadsto \frac{\color{blue}{1}}{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}\]
- Using strategy
rm Applied add-cube-cbrt1.3
\[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}} \cdot \sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}\right) \cdot \sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}}\]
Applied associate-/r*1.3
\[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}} \cdot \sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}}\]
Taylor expanded around -inf 1.3
\[\leadsto \frac{\frac{1}{\color{blue}{e^{\frac{1}{3} \cdot (\left(\left(\frac{1}{2} \cdot m + \frac{1}{2} \cdot n\right) - M\right) \cdot \left(\left(\frac{1}{2} \cdot m + \frac{1}{2} \cdot n\right) - M\right) + \left(\ell - \left|m - n\right|\right))_*}} \cdot \sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}\]
Simplified1.3
\[\leadsto \frac{\frac{1}{\color{blue}{{\left(e^{\frac{1}{3}}\right)}^{\left((\left((\left(m + n\right) \cdot \frac{1}{2} + \left(-M\right))_*\right) \cdot \left((\left(m + n\right) \cdot \frac{1}{2} + \left(-M\right))_*\right) + \ell)_* - \left|m - n\right|\right)}} \cdot \sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}\]
Final simplification1.3
\[\leadsto \frac{\frac{1}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}} \cdot {\left(e^{\frac{1}{3}}\right)}^{\left((\left((\left(m + n\right) \cdot \frac{1}{2} + \left(-M\right))_*\right) \cdot \left((\left(m + n\right) \cdot \frac{1}{2} + \left(-M\right))_*\right) + \ell)_* - \left|m - n\right|\right)}}}{\sqrt[3]{e^{(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right))_*}}}\]
