\[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
Test:
(log1p (pow (sinh b) (atan2 a (sin a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 9.6 s
Input Error: 5.7
Output Error: 5.7
Log: ⚲
Profile: 🕒
\(\log_* (1 + {\left(\sqrt[3]{\sinh b}\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)} \cdot {\left(\sqrt[3]{\sinh b} \cdot \sqrt[3]{\sinh b}\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\)
  1. Started with
    \[\log_* (1 + {\left(\sinh b\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    5.7
  2. Using strategy rm
    5.7
  3. Applied add-cube-cbrt to get
    \[\log_* (1 + {\color{red}{\left(\sinh b\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}) \leadsto \log_* (1 + {\color{blue}{\left({\left(\sqrt[3]{\sinh b}\right)}^3\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    5.7
  4. Using strategy rm
    5.7
  5. Applied cube-mult to get
    \[\log_* (1 + {\color{red}{\left({\left(\sqrt[3]{\sinh b}\right)}^3\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}) \leadsto \log_* (1 + {\color{blue}{\left(\sqrt[3]{\sinh b} \cdot \left(\sqrt[3]{\sinh b} \cdot \sqrt[3]{\sinh b}\right)\right)}}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)})\]
    5.7
  6. Applied unpow-prod-down to get
    \[\log_* (1 + \color{red}{{\left(\sqrt[3]{\sinh b} \cdot \left(\sqrt[3]{\sinh b} \cdot \sqrt[3]{\sinh b}\right)\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}}) \leadsto \log_* (1 + \color{blue}{{\left(\sqrt[3]{\sinh b}\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)} \cdot {\left(\sqrt[3]{\sinh b} \cdot \sqrt[3]{\sinh b}\right)}^{\left(\tan^{-1}_* \frac{a}{\sin a}\right)}})\]
    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)))))