Initial program 15.1
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
Taylor expanded around 0 1.4
\[\leadsto \color{blue}{1} \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
- Using strategy
rm Applied *-un-lft-identity1.4
\[\leadsto 1 \cdot e^{\color{blue}{1 \cdot \left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\]
Applied exp-prod1.4
\[\leadsto 1 \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\]
Applied simplify1.4
\[\leadsto 1 \cdot {\color{blue}{e}}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}\]
- Using strategy
rm Applied add-cbrt-cube1.4
\[\leadsto 1 \cdot \color{blue}{\sqrt[3]{\left({e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)} \cdot {e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}\right) \cdot {e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}}\]
Applied simplify1.4
\[\leadsto 1 \cdot \sqrt[3]{\color{blue}{{\left({e}^{\left(\left(\frac{m + n}{2} - M\right) \cdot \left(-\left(\frac{m + n}{2} - M\right)\right) - \left(\ell - \left|m - n\right|\right)\right)}\right)}^{3}}}\]
