Average Error: 30.8 → 17.7
Time: 2.9s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.2183670066001296 \cdot 10^{+58}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.0476517714411159 \cdot 10^{+58}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.2183670066001296 \cdot 10^{+58}:\\
\;\;\;\;\log \left(-re\right)\\

\mathbf{elif}\;re \le 1.0476517714411159 \cdot 10^{+58}:\\
\;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\

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

\end{array}
double f(double re, double im) {
        double r592529 = re;
        double r592530 = r592529 * r592529;
        double r592531 = im;
        double r592532 = r592531 * r592531;
        double r592533 = r592530 + r592532;
        double r592534 = sqrt(r592533);
        double r592535 = log(r592534);
        return r592535;
}
↓
double f(double re, double im) {
        double r592536 = re;
        double r592537 = -1.2183670066001296e+58;
        bool r592538 = r592536 <= r592537;
        double r592539 = -r592536;
        double r592540 = log(r592539);
        double r592541 = 1.0476517714411159e+58;
        bool r592542 = r592536 <= r592541;
        double r592543 = im;
        double r592544 = r592543 * r592543;
        double r592545 = r592536 * r592536;
        double r592546 = r592544 + r592545;
        double r592547 = sqrt(r592546);
        double r592548 = log(r592547);
        double r592549 = log(r592536);
        double r592550 = r592542 ? r592548 : r592549;
        double r592551 = r592538 ? r592540 : r592550;
        return r592551;
}

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 < -1.2183670066001296e+58

    1. Initial program 43.5

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

    2. Taylor expanded around -inf 11.3

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

    3. Simplified11.3

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

    if -1.2183670066001296e+58 < re < 1.0476517714411159e+58

    1. Initial program 22.0

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

    if 1.0476517714411159e+58 < re

    1. Initial program 43.8

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

    2. Taylor expanded around inf 11.6

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

  4. Final simplification17.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.2183670066001296 \cdot 10^{+58}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.0476517714411159 \cdot 10^{+58}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))