\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 24.6 s
Input Error: 9.6
Output Error: 9.6
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left(\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}\right)}^3}\)
  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 add-cbrt-cube to get
    \[\color{red}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} \leadsto \color{blue}{\sqrt[3]{{\left(\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}}\]
    9.6
  6. Applied simplify to get
    \[\sqrt[3]{\color{red}{{\left(\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}\right)}^3}}\]
    9.6
  7. Removed slow pow expressions

Original test:


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