\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 27.6 s
Input Error: 9.4
Output Error: 9.4
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}}\right)}^3\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    9.4
  2. Using strategy rm
    9.4
  3. Applied flip-- to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\]
    9.4
  4. Using strategy rm
    9.4
  5. Applied add-cube-cbrt to get
    \[\color{red}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3}\]
    9.5
  6. Applied simplify to get
    \[{\color{red}{\left(\sqrt[3]{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}}\right)}}^3\]
    9.4
  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))))