\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Test:
math.log10 on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 8.1 s
Input Error: 31.5
Output Error: 31.5
Log: ⚲
Profile: 🕒
\(\frac{\log \left({\left(e^{\log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}\right)}^3\right)}{\log 10}\)
  1. Started with
    \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    31.5
  2. Applied simplify to get
    \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
    31.5
  3. Using strategy rm
    31.5
  4. Applied add-cube-cbrt to get
    \[\frac{\log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)}}{\log 10} \leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)}}{\log 10}\]
    31.5
  5. Using strategy rm
    31.5
  6. Applied add-exp-log to get
    \[\frac{\log \left({\color{red}{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}}^3\right)}{\log 10} \leadsto \frac{\log \left({\color{blue}{\left(e^{\log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}\right)}}^3\right)}{\log 10}\]
    31.5

Original test:


(lambda ((re default) (im default))
  #:name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))