\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 22.6 s
Input Error: 4.1
Output Error: 4.2
Log: ⚲
Profile: 🕒
\(\frac{{b}^2 - (\left({\left(\cot b\right)}^{a}\right) * \left((2 * \left(\sin^{-1} b\right) + \left({\left(\cot b\right)}^{a}\right))_*\right) + \left({\left(\sin^{-1} b\right)}^2\right))_*}{\left(\sin^{-1} b + b\right) + {\left(\cot b\right)}^{a}}\)
  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. Using strategy rm
    4.2
  5. Applied flip-- to get
    \[{\left(\sqrt[3]{\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}}\right)}^3\]
    12.5
  6. Applied cbrt-div to get
    \[{\color{red}{\left(\sqrt[3]{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}}{\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3\]
    6.1
  7. Applied cube-div to get
    \[\color{red}{{\left(\frac{\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}}{\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3} \leadsto \color{blue}{\frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{{\left(\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}}\]
    6.1
  8. Applied simplify to get
    \[\frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{\color{red}{{\left(\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}} \leadsto \frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{\color{blue}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)}}\]
    6.1
  9. Applied taylor to get
    \[\frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)} \leadsto \frac{{\left(\sqrt[3]{{b}^2 - \left({\left(\sin^{-1} b\right)}^2 + \left(2 \cdot \left(\sin^{-1} b \cdot {\left(\cot b\right)}^{a}\right) + {\left({\left(\cot b\right)}^{a}\right)}^2\right)\right)}\right)}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)}\]
    6.1
  10. Taylor expanded around 0 to get
    \[\frac{{\color{red}{\left(\sqrt[3]{{b}^2 - \left({\left(\sin^{-1} b\right)}^2 + \left(2 \cdot \left(\sin^{-1} b \cdot {\left(\cot b\right)}^{a}\right) + {\left({\left(\cot b\right)}^{a}\right)}^2\right)\right)}\right)}}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)} \leadsto \frac{{\color{blue}{\left(\sqrt[3]{{b}^2 - \left({\left(\sin^{-1} b\right)}^2 + \left(2 \cdot \left(\sin^{-1} b \cdot {\left(\cot b\right)}^{a}\right) + {\left({\left(\cot b\right)}^{a}\right)}^2\right)\right)}\right)}}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)}\]
    6.1
  11. Applied simplify to get
    \[\frac{{\left(\sqrt[3]{{b}^2 - \left({\left(\sin^{-1} b\right)}^2 + \left(2 \cdot \left(\sin^{-1} b \cdot {\left(\cot b\right)}^{a}\right) + {\left({\left(\cot b\right)}^{a}\right)}^2\right)\right)}\right)}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)} \leadsto \frac{{b}^2 - (\left({\left(\cot b\right)}^{a}\right) * \left((2 * \left(\sin^{-1} b\right) + \left({\left(\cot b\right)}^{a}\right))_*\right) + \left(\sin^{-1} b \cdot \sin^{-1} b\right))_*}{{\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)}\]
    4.2
  12. Applied final simplification
  13. Applied simplify to get
    \[\color{red}{\frac{{b}^2 - (\left({\left(\cot b\right)}^{a}\right) * \left((2 * \left(\sin^{-1} b\right) + \left({\left(\cot b\right)}^{a}\right))_*\right) + \left(\sin^{-1} b \cdot \sin^{-1} b\right))_*}{{\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)}} \leadsto \color{blue}{\frac{{b}^2 - (\left({\left(\cot b\right)}^{a}\right) * \left((2 * \left(\sin^{-1} b\right) + \left({\left(\cot b\right)}^{a}\right))_*\right) + \left({\left(\sin^{-1} b\right)}^2\right))_*}{\left(\sin^{-1} b + b\right) + {\left(\cot b\right)}^{a}}}\]
    4.2
  14. 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))))