\[\sqrt{re \cdot re + im \cdot im}\]

↓

\[\begin{array}{l} \mathbf{if}\;re \le -5.332347770209516 \cdot 10^{+150}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.9883706818166164 \cdot 10^{+84}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

double f(double re, double im) {
        double r3413662 = re;
        double r3413663 = r3413662 * r3413662;
        double r3413664 = im;
        double r3413665 = r3413664 * r3413664;
        double r3413666 = r3413663 + r3413665;
        double r3413667 = sqrt(r3413666);
        return r3413667;
}

↓

double f(double re, double im) {
        double r3413668 = re;
        double r3413669 = -5.332347770209516e+150;
        bool r3413670 = r3413668 <= r3413669;
        double r3413671 = -r3413668;
        double r3413672 = 2.9883706818166164e+84;
        bool r3413673 = r3413668 <= r3413672;
        double r3413674 = im;
        double r3413675 = r3413674 * r3413674;
        double r3413676 = r3413668 * r3413668;
        double r3413677 = r3413675 + r3413676;
        double r3413678 = sqrt(r3413677);
        double r3413679 = r3413673 ? r3413678 : r3413668;
        double r3413680 = r3413670 ? r3413671 : r3413679;
        return r3413680;
}

\sqrt{re \cdot re + im \cdot im}

↓

\begin{array}{l}
\mathbf{if}\;re \le -5.332347770209516 \cdot 10^{+150}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 2.9883706818166164 \cdot 10^{+84}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}

Derivation

Split input into 3 regimes
if re < -5.332347770209516e+150
1. Initial program 58.3
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Taylor expanded around -inf 8.3
  \[\leadsto \color{blue}{-1 \cdot re}\]
3. Simplified8.3
  \[\leadsto \color{blue}{-re}\]
if -5.332347770209516e+150 < re < 2.9883706818166164e+84
1. Initial program 20.4
  \[\sqrt{re \cdot re + im \cdot im}\]
if 2.9883706818166164e+84 < re
1. Initial program 45.2
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Taylor expanded around inf 11.5
  \[\leadsto \color{blue}{re}\]
Recombined 3 regimes into one program.
Final simplification17.3
\[\leadsto \begin{array}{l} \mathbf{if}\;re \le -5.332347770209516 \cdot 10^{+150}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.9883706818166164 \cdot 10^{+84}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Error

Derivation

`if re < -5.332347770209516e+150`

`if -5.332347770209516e+150 < re < 2.9883706818166164e+84`

`if 2.9883706818166164e+84 < re`

Reproduce