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

↓

\[\begin{array}{l} \mathbf{if}\;re \le -1.9839400233753306 \cdot 10^{+87}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 7057901.046632865:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

double f(double re, double im) {
        double r1101657 = re;
        double r1101658 = r1101657 * r1101657;
        double r1101659 = im;
        double r1101660 = r1101659 * r1101659;
        double r1101661 = r1101658 + r1101660;
        double r1101662 = sqrt(r1101661);
        double r1101663 = log(r1101662);
        return r1101663;
}

↓

double f(double re, double im) {
        double r1101664 = re;
        double r1101665 = -1.9839400233753306e+87;
        bool r1101666 = r1101664 <= r1101665;
        double r1101667 = -r1101664;
        double r1101668 = log(r1101667);
        double r1101669 = 7057901.046632865;
        bool r1101670 = r1101664 <= r1101669;
        double r1101671 = im;
        double r1101672 = r1101671 * r1101671;
        double r1101673 = r1101664 * r1101664;
        double r1101674 = r1101672 + r1101673;
        double r1101675 = sqrt(r1101674);
        double r1101676 = log(r1101675);
        double r1101677 = log(r1101664);
        double r1101678 = r1101670 ? r1101676 : r1101677;
        double r1101679 = r1101666 ? r1101668 : r1101678;
        return r1101679;
}

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

↓

\begin{array}{l}
\mathbf{if}\;re \le -1.9839400233753306 \cdot 10^{+87}:\\
\;\;\;\;\log \left(-re\right)\\

\mathbf{elif}\;re \le 7057901.046632865:\\
\;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\

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

\end{array}

Derivation

Split input into 3 regimes
if re < -1.9839400233753306e+87
1. Initial program 47.8
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around -inf 8.8
  \[\leadsto \log \color{blue}{\left(-1 \cdot re\right)}\]
3. Simplified8.8
  \[\leadsto \log \color{blue}{\left(-re\right)}\]
if -1.9839400233753306e+87 < re < 7057901.046632865
1. Initial program 21.4
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
if 7057901.046632865 < re
1. Initial program 38.4
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around inf 12.7
  \[\leadsto \log \color{blue}{re}\]
Recombined 3 regimes into one program.
Final simplification17.1
\[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.9839400233753306 \cdot 10^{+87}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 7057901.046632865:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Error

Derivation

`if re < -1.9839400233753306e+87`

`if -1.9839400233753306e+87 < re < 7057901.046632865`

`if 7057901.046632865 < re`

Reproduce