\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 8.6 s
Input Error: 5.7
Output Error: 5.8
Log: ⚲
Profile: 🕒
\({e}^{\left(\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)\right)}\)
  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
    \[\color{red}{\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})} \leadsto \color{blue}{e^{\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}}\]
    5.8
  4. Using strategy rm
    5.8
  5. Applied pow1 to get
    \[e^{\log \color{red}{\left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}} \leadsto e^{\log \color{blue}{\left({\left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}^{1}\right)}}\]
    5.8
  6. Applied log-pow to get
    \[e^{\color{red}{\log \left({\left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}^{1}\right)}} \leadsto e^{\color{blue}{1 \cdot \log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}}\]
    5.8
  7. Applied exp-prod to get
    \[\color{red}{e^{1 \cdot \log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)}} \leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)\right)}}\]
    5.8
  8. Applied simplify to get
    \[{\color{red}{\left(e^{1}\right)}}^{\left(\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)\right)} \leadsto {\color{blue}{e}}^{\left(\log \left(\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\right)\right)}\]
    5.8

Original test:


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