\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 11.0 s
Input Error: 5.7
Output Error: 5.7
Log: ⚲
Profile: 🕒
\(\log_* (1 + {e}^{\left(\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)\right)})\)
  1. Started with
    \[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    5.7
  2. Using strategy rm
    5.7
  3. Applied add-exp-log to get
    \[\log_* (1 + \color{red}{{\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}}) \leadsto \log_* (1 + \color{blue}{e^{\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)}})\]
    5.7
  4. Using strategy rm
    5.7
  5. Applied *-un-lft-identity to get
    \[\log_* (1 + e^{\color{red}{\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)}}) \leadsto \log_* (1 + e^{\color{blue}{1 \cdot \log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)}})\]
    5.7
  6. Applied exp-prod to get
    \[\log_* (1 + \color{red}{e^{1 \cdot \log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)}}) \leadsto \log_* (1 + \color{blue}{{\left(e^{1}\right)}^{\left(\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)\right)}})\]
    5.7
  7. Applied simplify to get
    \[\log_* (1 + {\color{red}{\left(e^{1}\right)}}^{\left(\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)\right)}) \leadsto \log_* (1 + {\color{blue}{e}}^{\left(\log \left({\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}\right)\right)})\]
    5.7

Original test:


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