\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 27.4 s
Input Error: 9.6
Output Error: 9.7
Log: ⚲
Profile: 🕒
\({\left({\left(\log \left(e^{\sqrt[3]{\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}}\right)\right)}^3\right)}^3\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    9.6
  2. Using strategy rm
    9.6
  3. Applied add-cube-cbrt to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\]
    9.6
  4. Using strategy rm
    9.6
  5. Applied add-cube-cbrt to get
    \[{\color{red}{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}}^3 \leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3\right)}}^3\]
    9.7
  6. Using strategy rm
    9.7
  7. Applied add-log-exp to get
    \[{\left({\color{red}{\left(\sqrt[3]{\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3\right)}^3 \leadsto {\left({\color{blue}{\left(\log \left(e^{\sqrt[3]{\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}}\right)\right)}}^3\right)}^3\]
    9.7
  8. 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))))