\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
Test:
math.log10 on complex, imaginary part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 2.9 s
Input Error: 0.5
Output Error: 0.3
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\tan^{-1}_* \frac{im}{re}} \cdot \sqrt[3]{\frac{1}{\log 10}}\right)}^3\)
  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
    \[\color{red}{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}}\right)}^3}\]
    0.8
  4. Using strategy rm
    0.8
  5. Applied div-inv to get
    \[{\left(\sqrt[3]{\color{red}{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\log 10}}}\right)}^3\]
    0.8
  6. Applied cbrt-prod to get
    \[{\color{red}{\left(\sqrt[3]{\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\log 10}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\tan^{-1}_* \frac{im}{re}} \cdot \sqrt[3]{\frac{1}{\log 10}}\right)}}^3\]
    0.3

Original test:


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