\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
Test:
math.log10 on complex, imaginary part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 2.1 s
Input Error: 0.8
Output Error: 0.7
Log: ⚲
Profile: 🕒
\(\log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)\)
  1. Started with
    \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
    0.8
  2. Using strategy rm
    0.8
  3. Applied log1p-expm1-u to get
    \[\color{red}{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} \leadsto \color{blue}{\log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)}\]
    0.7

Original test:


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