\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{t}{\ell} \le 2.3440785796627555 \cdot 10^{+40}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right) + 1}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\sqrt{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}}{\frac{t \cdot \sqrt{2}}{\ell}}\right)\\ \end{array}\]

double f(double t, double l, double Om, double Omc) {
        double r2986412 = 1.0;
        double r2986413 = Om;
        double r2986414 = Omc;
        double r2986415 = r2986413 / r2986414;
        double r2986416 = 2.0;
        double r2986417 = pow(r2986415, r2986416);
        double r2986418 = r2986412 - r2986417;
        double r2986419 = t;
        double r2986420 = l;
        double r2986421 = r2986419 / r2986420;
        double r2986422 = pow(r2986421, r2986416);
        double r2986423 = r2986416 * r2986422;
        double r2986424 = r2986412 + r2986423;
        double r2986425 = r2986418 / r2986424;
        double r2986426 = sqrt(r2986425);
        double r2986427 = asin(r2986426);
        return r2986427;
}

↓

double f(double t, double l, double Om, double Omc) {
        double r2986428 = t;
        double r2986429 = l;
        double r2986430 = r2986428 / r2986429;
        double r2986431 = 2.3440785796627555e+40;
        bool r2986432 = r2986430 <= r2986431;
        double r2986433 = 1.0;
        double r2986434 = Om;
        double r2986435 = Omc;
        double r2986436 = r2986434 / r2986435;
        double r2986437 = r2986436 * r2986436;
        double r2986438 = r2986433 - r2986437;
        double r2986439 = 2.0;
        double r2986440 = r2986430 * r2986430;
        double r2986441 = r2986439 * r2986440;
        double r2986442 = r2986441 + r2986433;
        double r2986443 = r2986438 / r2986442;
        double r2986444 = sqrt(r2986443);
        double r2986445 = asin(r2986444);
        double r2986446 = sqrt(r2986438);
        double r2986447 = sqrt(r2986439);
        double r2986448 = r2986428 * r2986447;
        double r2986449 = r2986448 / r2986429;
        double r2986450 = r2986446 / r2986449;
        double r2986451 = asin(r2986450);
        double r2986452 = r2986432 ? r2986445 : r2986451;
        return r2986452;
}

\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)

↓

\begin{array}{l}
\mathbf{if}\;\frac{t}{\ell} \le 2.3440785796627555 \cdot 10^{+40}:\\
\;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right) + 1}}\right)\\

\mathbf{else}:\\
\;\;\;\;\sin^{-1} \left(\frac{\sqrt{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}}{\frac{t \cdot \sqrt{2}}{\ell}}\right)\\

\end{array}

Derivation

Split input into 2 regimes
if (/ t l) < 2.3440785796627555e+40
1. Initial program 6.7
  \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
2. Simplified6.7
  \[\leadsto \color{blue}{\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{1 + 2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)}}\right)}\]
if 2.3440785796627555e+40 < (/ t l)
1. Initial program 23.2
  \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
2. Simplified23.2
  \[\leadsto \color{blue}{\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{1 + 2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)}}\right)}\]
3. Using strategy rm
4. Applied sqrt-div23.2
  \[\leadsto \sin^{-1} \color{blue}{\left(\frac{\sqrt{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}}{\sqrt{1 + 2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right)}}\right)}\]
5. Taylor expanded around inf 1.0
  \[\leadsto \sin^{-1} \left(\frac{\sqrt{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}}{\color{blue}{\frac{t \cdot \sqrt{2}}{\ell}}}\right)\]
Recombined 2 regimes into one program.
Final simplification5.4
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t}{\ell} \le 2.3440785796627555 \cdot 10^{+40}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{2 \cdot \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right) + 1}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\sqrt{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}}{\frac{t \cdot \sqrt{2}}{\ell}}\right)\\ \end{array}\]

Error

Derivation

`if (/ t l) < 2.3440785796627555e+40`

`if 2.3440785796627555e+40 < (/ t l)`

Reproduce