- Split input into 3 regimes
if (* U (- t (* 2 (/ (pow l 2) Om)))) < -1.1075369580943968e+163 or -5.826898217003288e-228 < (* U (- t (* 2 (/ (pow l 2) Om)))) < 4.537323238075e-313 or 3.5255739183697707e+295 < (* U (- t (* 2 (/ (pow l 2) Om))))
Initial program 43.1
\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
- Using strategy
rm Applied associate-/l*37.9
\[\leadsto \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \color{blue}{\frac{\ell}{\frac{Om}{\ell}}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
if -1.1075369580943968e+163 < (* U (- t (* 2 (/ (pow l 2) Om)))) < -5.826898217003288e-228
Initial program 22.6
\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
- Using strategy
rm Applied associate-/l*22.6
\[\leadsto \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \color{blue}{\frac{\ell}{\frac{Om}{\ell}}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
- Using strategy
rm Applied associate-*l*16.4
\[\leadsto \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}}\]
- Using strategy
rm Applied add-cube-cbrt16.5
\[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(n \cdot {\color{blue}{\left(\left(\sqrt[3]{\frac{\ell}{Om}} \cdot \sqrt[3]{\frac{\ell}{Om}}\right) \cdot \sqrt[3]{\frac{\ell}{Om}}\right)}}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\]
Applied unpow-prod-down16.5
\[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(n \cdot \color{blue}{\left({\left(\sqrt[3]{\frac{\ell}{Om}} \cdot \sqrt[3]{\frac{\ell}{Om}}\right)}^{2} \cdot {\left(\sqrt[3]{\frac{\ell}{Om}}\right)}^{2}\right)}\right) \cdot \left(U - U*\right)\right)\right)}\]
Applied associate-*r*15.3
\[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \color{blue}{\left(\left(n \cdot {\left(\sqrt[3]{\frac{\ell}{Om}} \cdot \sqrt[3]{\frac{\ell}{Om}}\right)}^{2}\right) \cdot {\left(\sqrt[3]{\frac{\ell}{Om}}\right)}^{2}\right)} \cdot \left(U - U*\right)\right)\right)}\]
Applied simplify15.9
\[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(\color{blue}{\left(\frac{\ell}{\frac{Om}{n}} \cdot \sqrt[3]{\frac{\ell}{Om}}\right)} \cdot {\left(\sqrt[3]{\frac{\ell}{Om}}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\]
if 4.537323238075e-313 < (* U (- t (* 2 (/ (pow l 2) Om)))) < 3.5255739183697707e+295
Initial program 24.4
\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
- Using strategy
rm Applied associate-/l*24.4
\[\leadsto \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \color{blue}{\frac{\ell}{\frac{Om}{\ell}}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
- Using strategy
rm Applied associate-*l*18.9
\[\leadsto \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}}\]
- Using strategy
rm Applied sqrt-prod11.5
\[\leadsto \color{blue}{\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}}\]
- Recombined 3 regimes into one program.
Applied simplify24.6
\[\leadsto \color{blue}{\begin{array}{l}
\mathbf{if}\;U \cdot \left(t - 2 \cdot \frac{{\ell}^{2}}{Om}\right) \le -1.1075369580943968 \cdot 10^{+163}:\\
\;\;\;\;\sqrt{\left(\left(t - \frac{\ell}{\frac{Om}{\ell}} \cdot 2\right) - \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right) \cdot \left(U - U*\right)\right) \cdot \left(\left(2 \cdot n\right) \cdot U\right)}\\
\mathbf{if}\;U \cdot \left(t - 2 \cdot \frac{{\ell}^{2}}{Om}\right) \le -5.826898217003288 \cdot 10^{-228}:\\
\;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\left(\left(t - \frac{\ell}{\frac{Om}{\ell}} \cdot 2\right) - \left({\left(\sqrt[3]{\frac{\ell}{Om}}\right)}^{2} \cdot \left(\frac{\ell}{\frac{Om}{n}} \cdot \sqrt[3]{\frac{\ell}{Om}}\right)\right) \cdot \left(U - U*\right)\right) \cdot U\right)}\\
\mathbf{if}\;U \cdot \left(t - 2 \cdot \frac{{\ell}^{2}}{Om}\right) \le 4.537323238075 \cdot 10^{-313} \lor \neg \left(U \cdot \left(t - 2 \cdot \frac{{\ell}^{2}}{Om}\right) \le 3.5255739183697707 \cdot 10^{+295}\right):\\
\;\;\;\;\sqrt{\left(\left(t - \frac{\ell}{\frac{Om}{\ell}} \cdot 2\right) - \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right) \cdot \left(U - U*\right)\right) \cdot \left(\left(2 \cdot n\right) \cdot U\right)}\\
\mathbf{else}:\\
\;\;\;\;\sqrt{U \cdot \left(\left(t - \frac{\ell}{\frac{Om}{\ell}} \cdot 2\right) - \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right) \cdot \left(U - U*\right)\right)} \cdot \sqrt{2 \cdot n}\\
\end{array}}\]