Average Error: 30.8 → 17.0
Time: 4.5s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -4.60789516418958 \cdot 10^{+152}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 9.383285093579015 \cdot 10^{+93}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\begin{array}{l}
\mathbf{if}\;re \le -4.60789516418958 \cdot 10^{+152}:\\
\;\;\;\;\log \left(-re\right)\\

\mathbf{elif}\;re \le 9.383285093579015 \cdot 10^{+93}:\\
\;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\

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

\end{array}
double f(double re, double im) {
        double r991959 = re;
        double r991960 = r991959 * r991959;
        double r991961 = im;
        double r991962 = r991961 * r991961;
        double r991963 = r991960 + r991962;
        double r991964 = sqrt(r991963);
        double r991965 = log(r991964);
        return r991965;
}
↓
double f(double re, double im) {
        double r991966 = re;
        double r991967 = -4.60789516418958e+152;
        bool r991968 = r991966 <= r991967;
        double r991969 = -r991966;
        double r991970 = log(r991969);
        double r991971 = 9.383285093579015e+93;
        bool r991972 = r991966 <= r991971;
        double r991973 = im;
        double r991974 = r991973 * r991973;
        double r991975 = r991966 * r991966;
        double r991976 = r991974 + r991975;
        double r991977 = sqrt(r991976);
        double r991978 = log(r991977);
        double r991979 = log(r991966);
        double r991980 = r991972 ? r991978 : r991979;
        double r991981 = r991968 ? r991970 : r991980;
        return r991981;
}

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 < -4.60789516418958e+152

    1. Initial program 61.5

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

    2. Taylor expanded around -inf 6.7

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

    3. Simplified6.7

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

    if -4.60789516418958e+152 < re < 9.383285093579015e+93

    1. Initial program 20.7

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

    if 9.383285093579015e+93 < re

    1. Initial program 49.2

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

    2. Taylor expanded around inf 9.6

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

  4. Final simplification17.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -4.60789516418958 \cdot 10^{+152}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 9.383285093579015 \cdot 10^{+93}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))