\[\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a} - \log a\]
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: 6.1 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\log \left(e^{\tan^{-1}_* \frac{\tan^{-1}_* \frac{a}{c}}{a}}\right) - \log a\)
  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-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

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)))