math.log/2 on complex, real part

Average Error: 32.1 → 17.3

Time: 24.4s

Precision: 64

Math

\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

↓

\[\begin{array}{l} \mathbf{if}\;im \le -5.802716825709030303495598988914918946689 \cdot 10^{87}:\\ \;\;\;\;-\frac{\log \left(\frac{-1}{im}\right)}{\log base}\\ \mathbf{elif}\;im \le -4.758264364879206199461529726225257410966 \cdot 10^{-176}:\\ \;\;\;\;\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{im \cdot im + re \cdot re}\right) \cdot \log base}{0.0 \cdot 0.0 + \left(\left(\log \left(\sqrt[3]{base}\right) \cdot 2\right) \cdot \log base + \log \left(\sqrt[3]{base}\right) \cdot \log base\right)}\\ \mathbf{elif}\;im \le -2.837677287967872336993894067966499854324 \cdot 10^{-260}:\\ \;\;\;\;\frac{-\log re}{-\log base}\\ \mathbf{elif}\;im \le -7.909982710609458265182257197952783295768 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log base \cdot \log \left(-re\right)}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\\ \mathbf{elif}\;im \le 5.548497518142956227437704972905237987921 \cdot 10^{-237}:\\ \;\;\;\;\frac{-\log re}{-\log base}\\ \mathbf{elif}\;im \le 2.124125077098971279585872547613789818502 \cdot 10^{117}:\\ \;\;\;\;\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{im \cdot im + re \cdot re}\right) \cdot \log base}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\log im}{\log base}\\ \end{array}\]

C

double f(double re, double im, double base) {
        double r55614 = re;
        double r55615 = r55614 * r55614;
        double r55616 = im;
        double r55617 = r55616 * r55616;
        double r55618 = r55615 + r55617;
        double r55619 = sqrt(r55618);
        double r55620 = log(r55619);
        double r55621 = base;
        double r55622 = log(r55621);
        double r55623 = r55620 * r55622;
        double r55624 = atan2(r55616, r55614);
        double r55625 = 0.0;
        double r55626 = r55624 * r55625;
        double r55627 = r55623 + r55626;
        double r55628 = r55622 * r55622;
        double r55629 = r55625 * r55625;
        double r55630 = r55628 + r55629;
        double r55631 = r55627 / r55630;
        return r55631;
}

↓

double f(double re, double im, double base) {
        double r55632 = im;
        double r55633 = -5.80271682570903e+87;
        bool r55634 = r55632 <= r55633;
        double r55635 = -1.0;
        double r55636 = r55635 / r55632;
        double r55637 = log(r55636);
        double r55638 = base;
        double r55639 = log(r55638);
        double r55640 = r55637 / r55639;
        double r55641 = -r55640;
        double r55642 = -4.758264364879206e-176;
        bool r55643 = r55632 <= r55642;
        double r55644 = re;
        double r55645 = atan2(r55632, r55644);
        double r55646 = 0.0;
        double r55647 = r55645 * r55646;
        double r55648 = r55632 * r55632;
        double r55649 = r55644 * r55644;
        double r55650 = r55648 + r55649;
        double r55651 = sqrt(r55650);
        double r55652 = log(r55651);
        double r55653 = r55652 * r55639;
        double r55654 = r55647 + r55653;
        double r55655 = r55646 * r55646;
        double r55656 = cbrt(r55638);
        double r55657 = log(r55656);
        double r55658 = 2.0;
        double r55659 = r55657 * r55658;
        double r55660 = r55659 * r55639;
        double r55661 = r55657 * r55639;
        double r55662 = r55660 + r55661;
        double r55663 = r55655 + r55662;
        double r55664 = r55654 / r55663;
        double r55665 = -2.8376772879678723e-260;
        bool r55666 = r55632 <= r55665;
        double r55667 = log(r55644);
        double r55668 = -r55667;
        double r55669 = -r55639;
        double r55670 = r55668 / r55669;
        double r55671 = -7.909982710609458e-293;
        bool r55672 = r55632 <= r55671;
        double r55673 = 1.0;
        double r55674 = pow(r55639, r55658);
        double r55675 = r55655 + r55674;
        double r55676 = sqrt(r55675);
        double r55677 = r55673 / r55676;
        double r55678 = -r55644;
        double r55679 = log(r55678);
        double r55680 = r55639 * r55679;
        double r55681 = r55647 + r55680;
        double r55682 = r55681 / r55676;
        double r55683 = r55677 * r55682;
        double r55684 = 5.548497518142956e-237;
        bool r55685 = r55632 <= r55684;
        double r55686 = 2.1241250770989713e+117;
        bool r55687 = r55632 <= r55686;
        double r55688 = r55654 / r55676;
        double r55689 = r55688 * r55677;
        double r55690 = log(r55632);
        double r55691 = r55690 / r55639;
        double r55692 = r55687 ? r55689 : r55691;
        double r55693 = r55685 ? r55670 : r55692;
        double r55694 = r55672 ? r55683 : r55693;
        double r55695 = r55666 ? r55670 : r55694;
        double r55696 = r55643 ? r55664 : r55695;
        double r55697 = r55634 ? r55641 : r55696;
        return r55697;
}

Error

Bits error versus re

Bits error versus im

Bits error versus base

Derivation

1. Split input into 6 regimes

2. if im < -5.80271682570903e+87

   1. Initial program 50.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 50.4

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   3. Taylor expanded around -inf 64.0

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

   4. Simplified 9.0

      \[\leadsto \color{blue}{-\frac{\log \left(\frac{-1}{im}\right)}{0 + \log base}}\]

   if -5.80271682570903e+87 < im < -4.758264364879206e-176

   1. Initial program 16.9

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 16.9

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]
   3. Using strategy rm

   4. Applied add-cube-cbrt 16.9

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log \color{blue}{\left(\left(\sqrt[3]{base} \cdot \sqrt[3]{base}\right) \cdot \sqrt[3]{base}\right)} + 0.0 \cdot 0.0}\]

   5. Applied log-prod 16.9

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \color{blue}{\left(\log \left(\sqrt[3]{base} \cdot \sqrt[3]{base}\right) + \log \left(\sqrt[3]{base}\right)\right)} + 0.0 \cdot 0.0}\]

   6. Applied distribute-lft-in 16.9

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\color{blue}{\left(\log base \cdot \log \left(\sqrt[3]{base} \cdot \sqrt[3]{base}\right) + \log base \cdot \log \left(\sqrt[3]{base}\right)\right)} + 0.0 \cdot 0.0}\]

   7. Simplified 16.9

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\left(\color{blue}{\log base \cdot \left(2 \cdot \log \left(\sqrt[3]{base}\right)\right)} + \log base \cdot \log \left(\sqrt[3]{base}\right)\right) + 0.0 \cdot 0.0}\]

   if -4.758264364879206e-176 < im < -2.8376772879678723e-260 or -7.909982710609458e-293 < im < 5.548497518142956e-237

   1. Initial program 31.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 31.4

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 31.4

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\color{blue}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   5. Applied *-un-lft-identity 31.4

      \[\leadsto \frac{\color{blue}{1 \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)}}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   6. Applied times-frac 31.4

      \[\leadsto \color{blue}{\frac{1}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   7. Simplified 31.4

      \[\leadsto \color{blue}{\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   8. Simplified 31.4

      \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}}\]

   9. Taylor expanded around inf 32.9

      \[\leadsto \color{blue}{\frac{\log \left(\frac{1}{re}\right)}{\log \left(\frac{1}{base}\right)}}\]

   10. Simplified 32.9

       \[\leadsto \color{blue}{-\frac{\log re}{-\log base}}\]

   if -2.8376772879678723e-260 < im < -7.909982710609458e-293

   1. Initial program 30.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 30.4

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 30.4

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\color{blue}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   5. Applied *-un-lft-identity 30.4

      \[\leadsto \frac{\color{blue}{1 \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)}}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   6. Applied times-frac 30.4

      \[\leadsto \color{blue}{\frac{1}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   7. Simplified 30.4

      \[\leadsto \color{blue}{\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   8. Simplified 30.4

      \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}}\]

   9. Taylor expanded around -inf 33.7

      \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{\log \color{blue}{\left(-1 \cdot re\right)} \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\]

   10. Simplified 33.7

       \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{\log \color{blue}{\left(-re\right)} \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\]

   if 5.548497518142956e-237 < im < 2.1241250770989713e+117

   1. Initial program 18.9

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 18.9

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 18.9

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\color{blue}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   5. Applied *-un-lft-identity 18.9

      \[\leadsto \frac{\color{blue}{1 \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)}}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   6. Applied times-frac 18.9

      \[\leadsto \color{blue}{\frac{1}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   7. Simplified 18.9

      \[\leadsto \color{blue}{\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   8. Simplified 18.9

      \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}}\]

   if 2.1241250770989713e+117 < im

   1. Initial program 54.3

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\log base \cdot \log base + 0.0 \cdot 0.0}\]

   2. Simplified 54.3

      \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base + 0.0 \cdot 0.0}}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 54.3

      \[\leadsto \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\color{blue}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   5. Applied *-un-lft-identity 54.3

      \[\leadsto \frac{\color{blue}{1 \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)}}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0} \cdot \sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   6. Applied times-frac 54.3

      \[\leadsto \color{blue}{\frac{1}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}}\]

   7. Simplified 54.3

      \[\leadsto \color{blue}{\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\sqrt{\log base \cdot \log base + 0.0 \cdot 0.0}}\]

   8. Simplified 54.3

      \[\leadsto \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0.0}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}}\]

   9. Taylor expanded around 0 8.1

      \[\leadsto \color{blue}{\frac{\log im}{\log base}}\]
3. Recombined 6 regimes into one program.

4. Final simplification 17.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -5.802716825709030303495598988914918946689 \cdot 10^{87}:\\ \;\;\;\;-\frac{\log \left(\frac{-1}{im}\right)}{\log base}\\ \mathbf{elif}\;im \le -4.758264364879206199461529726225257410966 \cdot 10^{-176}:\\ \;\;\;\;\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{im \cdot im + re \cdot re}\right) \cdot \log base}{0.0 \cdot 0.0 + \left(\left(\log \left(\sqrt[3]{base}\right) \cdot 2\right) \cdot \log base + \log \left(\sqrt[3]{base}\right) \cdot \log base\right)}\\ \mathbf{elif}\;im \le -2.837677287967872336993894067966499854324 \cdot 10^{-260}:\\ \;\;\;\;\frac{-\log re}{-\log base}\\ \mathbf{elif}\;im \le -7.909982710609458265182257197952783295768 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log base \cdot \log \left(-re\right)}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\\ \mathbf{elif}\;im \le 5.548497518142956227437704972905237987921 \cdot 10^{-237}:\\ \;\;\;\;\frac{-\log re}{-\log base}\\ \mathbf{elif}\;im \le 2.124125077098971279585872547613789818502 \cdot 10^{117}:\\ \;\;\;\;\frac{\tan^{-1}_* \frac{im}{re} \cdot 0.0 + \log \left(\sqrt{im \cdot im + re \cdot re}\right) \cdot \log base}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}} \cdot \frac{1}{\sqrt{0.0 \cdot 0.0 + {\left(\log base\right)}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\log im}{\log base}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (re im base)
  :name "math.log/2 on complex, real part"
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0))))