\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 23.2 s
Input Error: 4.1
Output Error: 4.1
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left(\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    4.1
  2. Using strategy rm
    4.1
  3. Applied add-cbrt-cube to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\sqrt[3]{{\left(b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^3}}\]
    4.2
  4. Using strategy rm
    4.2
  5. Applied flip-- to get
    \[\sqrt[3]{{\color{red}{\left(b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}}^3}\]
    4.1
  6. 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))))