\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 27.3 s
Input Error: 9.6
Output Error: 9.6
Log: ⚲
Profile: 🕒
\(\log_* (1 + (e^{\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}} - 1)^*)\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    9.6
  2. Using strategy rm
    9.6
  3. Applied flip-- to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\]
    9.6
  4. Using strategy rm
    9.6
  5. Applied log1p-expm1-u to get
    \[\color{red}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} \leadsto \color{blue}{\log_* (1 + (e^{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} - 1)^*)}\]
    9.6
  6. Applied simplify to get
    \[\log_* (1 + \color{red}{(e^{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} - 1)^*}) \leadsto \log_* (1 + \color{blue}{(e^{\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}} - 1)^*})\]
    9.6

Original test:


(lambda ((a default) (b default))
  #:name "(- b (+ (pow (cotan b) a) (asin b)))"
  (- b (+ (pow (cotan b) a) (asin b))))