\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 33.6 s
Input Error: 9.8
Output Error: 10.1
Log: ⚲
Profile: 🕒
\(\log \left(e^{b} \cdot e^{-\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    9.8
  2. Using strategy rm
    9.8
  3. Applied add-log-exp to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\log \left(e^{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}\]
    10.1
  4. Using strategy rm
    10.1
  5. Applied sub-neg to get
    \[\log \left(e^{\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right) \leadsto \log \left(e^{\color{blue}{b + \left(-\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\right)\]
    10.1
  6. Applied exp-sum to get
    \[\log \color{red}{\left(e^{b + \left(-\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}\right)} \leadsto \log \color{blue}{\left(e^{b} \cdot e^{-\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}\]
    10.1

Original test:


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