\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
Test:
math.log10 on complex, imaginary part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 2.7 s
Input Error: 0.5
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\frac{{\left(\sqrt[3]{\tan^{-1}_* \frac{im}{re}}\right)}^3}{\log 10}\)
  1. Started with
    \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
    0.5
  2. Using strategy rm
    0.5
  3. Applied add-cube-cbrt to get
    \[\frac{\color{red}{\tan^{-1}_* \frac{im}{re}}}{\log 10} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{im}{re}}\right)}^3}}{\log 10}\]
    0.3

Original test:


(lambda ((re default) (im default))
  #:name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))