\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 16.9 s
Input Error: 4.1
Output Error: 4.1
Log: ⚲
Profile: 🕒
\(\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}\)
  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-cube-cbrt to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\]
    4.2
  4. Applied taylor to get
    \[{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3 \leadsto {\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3\]
    4.2
  5. Taylor expanded around 0 to get
    \[{\color{red}{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}}^3\]
    4.2
  6. Applied simplify to get
    \[\color{red}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3} \leadsto \color{blue}{\left(b - \sin^{-1} b\right) - {\left(\cot b\right)}^{a}}\]
    4.1
  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))))