Average Error: 31.1 → 17.1
Time: 3.8s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -9.68163596973405975259895298385316105053 \cdot 10^{102}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 3.545380571942664302984715356869784321431 \cdot 10^{140}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\begin{array}{l}
\mathbf{if}\;re \le -9.68163596973405975259895298385316105053 \cdot 10^{102}:\\
\;\;\;\;\log \left(-re\right)\\

\mathbf{elif}\;re \le 3.545380571942664302984715356869784321431 \cdot 10^{140}:\\
\;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\

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

\end{array}
double f(double re, double im) {
        double r2141995 = re;
        double r2141996 = r2141995 * r2141995;
        double r2141997 = im;
        double r2141998 = r2141997 * r2141997;
        double r2141999 = r2141996 + r2141998;
        double r2142000 = sqrt(r2141999);
        double r2142001 = log(r2142000);
        return r2142001;
}
↓
double f(double re, double im) {
        double r2142002 = re;
        double r2142003 = -9.68163596973406e+102;
        bool r2142004 = r2142002 <= r2142003;
        double r2142005 = -r2142002;
        double r2142006 = log(r2142005);
        double r2142007 = 3.5453805719426643e+140;
        bool r2142008 = r2142002 <= r2142007;
        double r2142009 = im;
        double r2142010 = r2142009 * r2142009;
        double r2142011 = r2142002 * r2142002;
        double r2142012 = r2142010 + r2142011;
        double r2142013 = sqrt(r2142012);
        double r2142014 = log(r2142013);
        double r2142015 = log(r2142002);
        double r2142016 = r2142008 ? r2142014 : r2142015;
        double r2142017 = r2142004 ? r2142006 : r2142016;
        return r2142017;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if re < -9.68163596973406e+102

    1. Initial program 51.9

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

    2. Taylor expanded around -inf 8.5

      \[\leadsto \log \color{blue}{\left(-1 \cdot re\right)}\]

    3. Simplified8.5

      \[\leadsto \log \color{blue}{\left(-re\right)}\]

    if -9.68163596973406e+102 < re < 3.5453805719426643e+140

    1. Initial program 21.0

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

    if 3.5453805719426643e+140 < re

    1. Initial program 59.5

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

    2. Taylor expanded around inf 7.5

      \[\leadsto \log \color{blue}{re}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification17.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -9.68163596973405975259895298385316105053 \cdot 10^{102}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 3.545380571942664302984715356869784321431 \cdot 10^{140}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))