\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;t \le -1.0725352664225265 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{1}{\sin k} \cdot \frac{\ell}{t}}{t} \cdot \frac{\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\sin k \cdot t}{\ell}}\\ \mathbf{elif}\;t \le 6.496758686090682 \cdot 10^{-129}:\\ \;\;\;\;\left(\frac{\cos k}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\sin k}{\ell}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t}}{\frac{\sin k}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}}{t \cdot \frac{\sin k \cdot t}{\ell}}\\ \end{array}\]

double f(double t, double l, double k) {
        double r43320576 = 2.0;
        double r43320577 = t;
        double r43320578 = 3.0;
        double r43320579 = pow(r43320577, r43320578);
        double r43320580 = l;
        double r43320581 = r43320580 * r43320580;
        double r43320582 = r43320579 / r43320581;
        double r43320583 = k;
        double r43320584 = sin(r43320583);
        double r43320585 = r43320582 * r43320584;
        double r43320586 = tan(r43320583);
        double r43320587 = r43320585 * r43320586;
        double r43320588 = 1.0;
        double r43320589 = r43320583 / r43320577;
        double r43320590 = pow(r43320589, r43320576);
        double r43320591 = r43320588 + r43320590;
        double r43320592 = r43320591 + r43320588;
        double r43320593 = r43320587 * r43320592;
        double r43320594 = r43320576 / r43320593;
        return r43320594;
}

↓

double f(double t, double l, double k) {
        double r43320595 = t;
        double r43320596 = -1.0725352664225265e-75;
        bool r43320597 = r43320595 <= r43320596;
        double r43320598 = 1.0;
        double r43320599 = k;
        double r43320600 = sin(r43320599);
        double r43320601 = r43320598 / r43320600;
        double r43320602 = l;
        double r43320603 = r43320602 / r43320595;
        double r43320604 = r43320601 * r43320603;
        double r43320605 = r43320604 / r43320595;
        double r43320606 = cos(r43320599);
        double r43320607 = 2.0;
        double r43320608 = r43320599 / r43320595;
        double r43320609 = fma(r43320608, r43320608, r43320607);
        double r43320610 = r43320607 / r43320609;
        double r43320611 = r43320606 * r43320610;
        double r43320612 = r43320600 * r43320595;
        double r43320613 = r43320612 / r43320602;
        double r43320614 = r43320611 / r43320613;
        double r43320615 = r43320605 * r43320614;
        double r43320616 = 6.496758686090682e-129;
        bool r43320617 = r43320595 <= r43320616;
        double r43320618 = r43320606 / r43320595;
        double r43320619 = cbrt(r43320610);
        double r43320620 = r43320600 / r43320602;
        double r43320621 = r43320619 / r43320620;
        double r43320622 = r43320618 * r43320621;
        double r43320623 = r43320619 / r43320595;
        double r43320624 = r43320623 * r43320623;
        double r43320625 = r43320624 / r43320620;
        double r43320626 = r43320622 * r43320625;
        double r43320627 = r43320603 / r43320600;
        double r43320628 = r43320611 * r43320627;
        double r43320629 = r43320595 * r43320613;
        double r43320630 = r43320628 / r43320629;
        double r43320631 = r43320617 ? r43320626 : r43320630;
        double r43320632 = r43320597 ? r43320615 : r43320631;
        return r43320632;
}

\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}

↓

\begin{array}{l}
\mathbf{if}\;t \le -1.0725352664225265 \cdot 10^{-75}:\\
\;\;\;\;\frac{\frac{1}{\sin k} \cdot \frac{\ell}{t}}{t} \cdot \frac{\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\sin k \cdot t}{\ell}}\\

\mathbf{elif}\;t \le 6.496758686090682 \cdot 10^{-129}:\\
\;\;\;\;\left(\frac{\cos k}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\sin k}{\ell}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t}}{\frac{\sin k}{\ell}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}}{t \cdot \frac{\sin k \cdot t}{\ell}}\\

\end{array}

Derivation

Split input into 3 regimes
if t < -1.0725352664225265e-75
1. Initial program 21.6
  \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
2. Simplified17.9
  \[\leadsto \color{blue}{\frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \tan k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}}\]
3. Using strategy rm
4. Applied tan-quot17.9
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \color{blue}{\frac{\sin k}{\cos k}}\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
5. Applied associate-*r/17.9
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\sin k \cdot \sin k}{\cos k}} \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
6. Applied associate-*l/17.9
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\left(\sin k \cdot \sin k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}{\cos k}}}\]
7. Simplified4.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\color{blue}{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}}{\cos k}}\]
8. Using strategy rm
9. Applied *-un-lft-identity4.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}{\color{blue}{1 \cdot \cos k}}}\]
10. Applied times-frac4.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
11. Applied *-un-lft-identity4.2
  \[\leadsto \frac{\frac{2}{\color{blue}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
12. Applied *-un-lft-identity4.2
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot 2}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
13. Applied times-frac4.2
  \[\leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
14. Applied times-frac3.3
  \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1}} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
15. Simplified3.5
  \[\leadsto \color{blue}{\frac{\frac{\ell}{\sin k \cdot t}}{t}} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
16. Simplified3.2
  \[\leadsto \frac{\frac{\ell}{\sin k \cdot t}}{t} \cdot \color{blue}{\frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}}\]
17. Using strategy rm
18. Applied *-un-lft-identity3.2
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \ell}}{\sin k \cdot t}}{t} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}\]
19. Applied times-frac3.5
  \[\leadsto \frac{\color{blue}{\frac{1}{\sin k} \cdot \frac{\ell}{t}}}{t} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}\]
if -1.0725352664225265e-75 < t < 6.496758686090682e-129
1. Initial program 59.3
  \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
2. Simplified44.2
  \[\leadsto \color{blue}{\frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \tan k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}}\]
3. Using strategy rm
4. Applied tan-quot44.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \color{blue}{\frac{\sin k}{\cos k}}\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
5. Applied associate-*r/44.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\sin k \cdot \sin k}{\cos k}} \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
6. Applied associate-*l/44.2
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\left(\sin k \cdot \sin k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}{\cos k}}}\]
7. Simplified43.3
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\color{blue}{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}}{\cos k}}\]
8. Using strategy rm
9. Applied *-un-lft-identity43.3
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}{\color{blue}{1 \cdot \cos k}}}\]
10. Applied times-frac43.3
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
11. Applied add-cube-cbrt43.4
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}} \cdot \sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}\right) \cdot \sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
12. Applied times-frac39.1
  \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}} \cdot \sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1}} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
13. Simplified34.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t}}{\frac{\sin k}{\ell}}} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
14. Simplified34.7
  \[\leadsto \frac{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t}}{\frac{\sin k}{\ell}} \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\sin k}{\ell}} \cdot \frac{\cos k}{t}\right)}\]
if 6.496758686090682e-129 < t
1. Initial program 24.4
  \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
2. Simplified19.4
  \[\leadsto \color{blue}{\frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \tan k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}}\]
3. Using strategy rm
4. Applied tan-quot19.4
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\left(\sin k \cdot \color{blue}{\frac{\sin k}{\cos k}}\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
5. Applied associate-*r/19.4
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\sin k \cdot \sin k}{\cos k}} \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}\]
6. Applied associate-*l/19.4
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{\left(\sin k \cdot \sin k\right) \cdot \frac{t}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}{\cos k}}}\]
7. Simplified6.8
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\color{blue}{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}}{\cos k}}\]
8. Using strategy rm
9. Applied *-un-lft-identity6.8
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\left(t \cdot \frac{\sin k}{\frac{\ell}{t}}\right) \cdot \frac{\sin k}{\frac{\ell}{t}}}{\color{blue}{1 \cdot \cos k}}}\]
10. Applied times-frac6.8
  \[\leadsto \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\color{blue}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
11. Applied *-un-lft-identity6.8
  \[\leadsto \frac{\frac{2}{\color{blue}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
12. Applied *-un-lft-identity6.8
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot 2}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
13. Applied times-frac6.8
  \[\leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1} \cdot \frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
14. Applied times-frac5.4
  \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{t \cdot \frac{\sin k}{\frac{\ell}{t}}}{1}} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}}\]
15. Simplified5.4
  \[\leadsto \color{blue}{\frac{\frac{\ell}{\sin k \cdot t}}{t}} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\frac{\sin k}{\frac{\ell}{t}}}{\cos k}}\]
16. Simplified5.2
  \[\leadsto \frac{\frac{\ell}{\sin k \cdot t}}{t} \cdot \color{blue}{\frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}}\]
17. Using strategy rm
18. Applied *-un-lft-identity5.2
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \ell}}{\sin k \cdot t}}{t} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}\]
19. Applied times-frac5.5
  \[\leadsto \frac{\color{blue}{\frac{1}{\sin k} \cdot \frac{\ell}{t}}}{t} \cdot \frac{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k}{\frac{\sin k \cdot t}{\ell}}\]
20. Using strategy rm
21. Applied frac-times5.4
  \[\leadsto \color{blue}{\frac{\left(\frac{1}{\sin k} \cdot \frac{\ell}{t}\right) \cdot \left(\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k\right)}{t \cdot \frac{\sin k \cdot t}{\ell}}}\]
22. Simplified5.4
  \[\leadsto \frac{\color{blue}{\frac{\frac{\ell}{t}}{\sin k} \cdot \left(\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \cos k\right)}}{t \cdot \frac{\sin k \cdot t}{\ell}}\]
Recombined 3 regimes into one program.
Final simplification11.3
\[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.0725352664225265 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{1}{\sin k} \cdot \frac{\ell}{t}}{t} \cdot \frac{\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\sin k \cdot t}{\ell}}\\ \mathbf{elif}\;t \le 6.496758686090682 \cdot 10^{-129}:\\ \;\;\;\;\left(\frac{\cos k}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{\frac{\sin k}{\ell}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t} \cdot \frac{\sqrt[3]{\frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}}{t}}{\frac{\sin k}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\cos k \cdot \frac{2}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}}{t \cdot \frac{\sin k \cdot t}{\ell}}\\ \end{array}\]

Error

Derivation

`if t < -1.0725352664225265e-75`

`if -1.0725352664225265e-75 < t < 6.496758686090682e-129`

`if 6.496758686090682e-129 < t`

Reproduce