\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 7.7 s
Input Error: 5.4
Output Error: 5.5
Log: ⚲
Profile: 🕒
\(e^{\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}\)
  1. Started with
    \[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    5.4
  2. Using strategy rm
    5.4
  3. Applied add-exp-log to get
    \[\color{red}{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})} \leadsto \color{blue}{e^{\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}}\]
    5.5

Original test:


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