\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Test:
math.log/2 on complex, real part
Bits:
128 bits
Bits error versus re
Bits error versus im
Bits error versus base
Time: 13.9 s
Input Error: 30.5
Output Error: 30.5
Log: ⚲
Profile: 🕒
\(\frac{\log base \cdot \log \left({\left({\left(\sqrt{{re}^2 + im \cdot im}\right)}^{\frac{1}{3}}\right)}^3\right) + 0}{\log base \cdot \log base}\)
  1. Started with
    \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
    30.5
  2. Applied simplify to get
    \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
    30.5
  3. Using strategy rm
    30.5
  4. Applied add-cube-cbrt to get
    \[\frac{\log base \cdot \log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)} + 0}{\log base \cdot \log base}\]
    30.5
  5. Using strategy rm
    30.5
  6. Applied pow1/3 to get
    \[\frac{\log base \cdot \log \left({\color{red}{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}}^3\right) + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \left({\color{blue}{\left({\left(\sqrt{{re}^2 + im \cdot im}\right)}^{\frac{1}{3}}\right)}}^3\right) + 0}{\log base \cdot \log base}\]
    30.5

Original test:


(lambda ((re default) (im default) (base default))
  #:name "math.log/2 on complex, real part"
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))))