\[\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a} - \log a\]
Test:
(- (atan2 (atan2 a c) a) (log a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 11.3 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\log \left(\frac{{e}^{\left(\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}\right)}}{a}\right)\)
  1. Started with
    \[\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a} - \log a\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied add-log-exp to get
    \[\color{red}{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}} - \log a \leadsto \color{blue}{\log \left(e^{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}\right)} - \log a\]
    0.1
  4. Applied diff-log to get
    \[\color{red}{\log \left(e^{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}\right) - \log a} \leadsto \color{blue}{\log \left(\frac{e^{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}{a}\right)}\]
    0.1
  5. Using strategy rm
    0.1
  6. Applied *-un-lft-identity to get
    \[\log \left(\frac{e^{\color{red}{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}}{a}\right) \leadsto \log \left(\frac{e^{\color{blue}{1 \cdot \tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}}{a}\right)\]
    0.1
  7. Applied exp-prod to get
    \[\log \left(\frac{\color{red}{e^{1 \cdot \tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}}{a}\right) \leadsto \log \left(\frac{\color{blue}{{\left(e^{1}\right)}^{\left(\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}\right)}}}{a}\right)\]
    0.1
  8. Applied simplify to get
    \[\log \left(\frac{{\color{red}{\left(e^{1}\right)}}^{\left(\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}\right)}}{a}\right) \leadsto \log \left(\frac{{\color{blue}{e}}^{\left(\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}\right)}}{a}\right)\]
    0.1
  9. Removed slow pow expressions

Original test:


(lambda ((a default) (b default) (c default) (d default))
  #:name "(- (atan2 (atan2 a c) a) (log a))"
  (- (atan2 (atan2 a c) a) (log a)))