\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 7.6 s
Input Error: 8.8
Output Error: 8.8
Log: ⚲
Profile: 🕒
\(\log_* (1 + {\left({\left({\left(\sqrt[3]{\sqrt[3]{\sinh b}}\right)}^{3}\right)}^3\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\)
  1. Started with
    \[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    8.8
  2. Using strategy rm
    8.8
  3. Applied add-cube-cbrt to get
    \[\log_* (1 + {\color{red}{\left(\sinh b\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}) \leadsto \log_* (1 + {\color{blue}{\left({\left(\sqrt[3]{\sinh b}\right)}^3\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    8.8
  4. Using strategy rm
    8.8
  5. Applied add-cube-cbrt to get
    \[\log_* (1 + {\left({\color{red}{\left(\sqrt[3]{\sinh b}\right)}}^3\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}) \leadsto \log_* (1 + {\left({\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\sinh b}}\right)}^3\right)}}^3\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    8.8
  6. Using strategy rm
    8.8
  7. Applied pow3 to get
    \[\log_* (1 + {\left({\color{red}{\left({\left(\sqrt[3]{\sqrt[3]{\sinh b}}\right)}^3\right)}}^3\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}) \leadsto \log_* (1 + {\left({\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\sinh b}}\right)}^{3}\right)}}^3\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    8.8

Original test:


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