\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
Test:
math.log/1 on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Time: 3.1 s
Input Error: 14.6
Output Error: 14.6
Log: ⚲
Profile: 🕒
\(\frac{1}{2} \cdot \log \left({re}^2 + im \cdot im\right)\)
  1. Started with
    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
    14.6
  2. Applied simplify to get
    \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
    14.6
  3. Using strategy rm
    14.6
  4. Applied pow1/2 to get
    \[\log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)} \leadsto \log \color{blue}{\left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)}\]
    14.6
  5. Applied log-pow to get
    \[\color{red}{\log \left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)} \leadsto \color{blue}{\frac{1}{2} \cdot \log \left({re}^2 + im \cdot im\right)}\]
    14.6

Original test:


(lambda ((re default) (im default))
  #:name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))