\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;re \le -3.5169395164413523 \cdot 10^{+139}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 3.0686185096665187 \cdot 10^{+60}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

double f(double re, double im) {
        double r1675684 = re;
        double r1675685 = r1675684 * r1675684;
        double r1675686 = im;
        double r1675687 = r1675686 * r1675686;
        double r1675688 = r1675685 + r1675687;
        double r1675689 = sqrt(r1675688);
        double r1675690 = log(r1675689);
        return r1675690;
}

↓

double f(double re, double im) {
        double r1675691 = re;
        double r1675692 = -3.5169395164413523e+139;
        bool r1675693 = r1675691 <= r1675692;
        double r1675694 = -r1675691;
        double r1675695 = log(r1675694);
        double r1675696 = 3.0686185096665187e+60;
        bool r1675697 = r1675691 <= r1675696;
        double r1675698 = im;
        double r1675699 = r1675698 * r1675698;
        double r1675700 = r1675691 * r1675691;
        double r1675701 = r1675699 + r1675700;
        double r1675702 = sqrt(r1675701);
        double r1675703 = log(r1675702);
        double r1675704 = log(r1675691);
        double r1675705 = r1675697 ? r1675703 : r1675704;
        double r1675706 = r1675693 ? r1675695 : r1675705;
        return r1675706;
}

\log \left(\sqrt{re \cdot re + im \cdot im}\right)

↓

\begin{array}{l}
\mathbf{if}\;re \le -3.5169395164413523 \cdot 10^{+139}:\\
\;\;\;\;\log \left(-re\right)\\

\mathbf{elif}\;re \le 3.0686185096665187 \cdot 10^{+60}:\\
\;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\

\mathbf{else}:\\
\;\;\;\;\log re\\

\end{array}

Derivation

Split input into 3 regimes
if re < -3.5169395164413523e+139
1. Initial program 58.4
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around -inf 7.4
  \[\leadsto \log \color{blue}{\left(-1 \cdot re\right)}\]
3. Simplified7.4
  \[\leadsto \log \color{blue}{\left(-re\right)}\]
if -3.5169395164413523e+139 < re < 3.0686185096665187e+60
1. Initial program 21.2
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
if 3.0686185096665187e+60 < re
1. Initial program 44.8
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around inf 10.8
  \[\leadsto \log \color{blue}{re}\]
Recombined 3 regimes into one program.
Final simplification17.3
\[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.5169395164413523 \cdot 10^{+139}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 3.0686185096665187 \cdot 10^{+60}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Error

Derivation

`if re < -3.5169395164413523e+139`

`if -3.5169395164413523e+139 < re < 3.0686185096665187e+60`

`if 3.0686185096665187e+60 < re`

Reproduce