\[\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a} - \log a\]
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: 10.7 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}\right)}^2\right)}^2 - \log a\)
  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-sqr-sqrt to get
    \[\color{red}{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}} - \log a \leadsto \color{blue}{{\left(\sqrt{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}\right)}^2} - \log a\]
    0.1
  4. Using strategy rm
    0.1
  5. Applied add-sqr-sqrt to get
    \[{\color{red}{\left(\sqrt{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}\right)}}^2 - \log a \leadsto {\color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}}\right)}^2\right)}}^2 - \log a\]
    0.1
  6. 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)))