\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Test:
math.log10 on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 8.5 s
Input Error: 31.1
Output Error: 31.1
Log: ⚲
Profile: 🕒
\(\frac{1}{\log 10 \cdot \frac{1}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}\)
  1. Started with
    \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    31.1
  2. Applied simplify to get
    \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
    31.1
  3. Using strategy rm
    31.1
  4. Applied clear-num to get
    \[\color{red}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{1}{\frac{\log 10}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}}\]
    31.1
  5. Using strategy rm
    31.1
  6. Applied div-inv to get
    \[\frac{1}{\color{red}{\frac{\log 10}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}} \leadsto \frac{1}{\color{blue}{\log 10 \cdot \frac{1}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}}\]
    31.1

Original test:


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