\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 6.5 s
Input Error: 8.5
Output Error: 8.6
Log: ⚲
Profile: 🕒
\({\left({\left(\sqrt{\sqrt{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})}}\right)}^2\right)}^2\)
  1. Started with
    \[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    8.5
  2. Using strategy rm
    8.5
  3. Applied add-sqr-sqrt to get
    \[\color{red}{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})} \leadsto \color{blue}{{\left(\sqrt{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})}\right)}^2}\]
    8.6
  4. Using strategy rm
    8.6
  5. Applied add-sqr-sqrt to get
    \[{\color{red}{\left(\sqrt{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})}\right)}}^2 \leadsto {\color{blue}{\left({\left(\sqrt{\sqrt{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})}}\right)}^2\right)}}^2\]
    8.6
  6. Removed slow pow expressions

Original test:


(lambda ((a default) (b default))
  #:name "(log1p (pow (sinh b) (atan2 a (sin a))))"
  (log1p (pow (sinh b) (atan2 a (sin a)))))