\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 43.1 s
Input Error: 4.0
Output Error: 4.2
Log: ⚲
Profile: 🕒
\(\sqrt[3]{\frac{1}{{\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)}} \cdot \sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    4.0
  2. Using strategy rm
    4.0
  3. Applied add-cbrt-cube to get
    \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\sqrt[3]{{\left(b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^3}}\]
    4.1
  4. Using strategy rm
    4.1
  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. Applied cube-div to get
    \[\sqrt[3]{\color{red}{{\left(\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^3}}}\]
    4.1
  7. Using strategy rm
    4.1
  8. Applied cube-mult to get
    \[\sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\color{red}{{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^3}}} \leadsto \sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\color{blue}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}}}\]
    4.1
  9. Applied *-un-lft-identity to get
    \[\sqrt[3]{\frac{{\color{red}{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}} \leadsto \sqrt[3]{\frac{{\color{blue}{\left(1 \cdot \left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)\right)}}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}}\]
    4.1
  10. Applied cube-prod to get
    \[\sqrt[3]{\frac{\color{red}{{\left(1 \cdot \left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)\right)}^3}}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}} \leadsto \sqrt[3]{\frac{\color{blue}{{1}^3 \cdot {\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}}\]
    4.1
  11. Applied times-frac to get
    \[\sqrt[3]{\color{red}{\frac{{1}^3 \cdot {\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)\right)}}} \leadsto \sqrt[3]{\color{blue}{\frac{{1}^3}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \cdot \frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}}\]
    4.1
  12. Applied cbrt-prod to get
    \[\color{red}{\sqrt[3]{\frac{{1}^3}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \cdot \frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}} \leadsto \color{blue}{\sqrt[3]{\frac{{1}^3}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}} \cdot \sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}}\]
    4.2
  13. Applied simplify to get
    \[\color{red}{\sqrt[3]{\frac{{1}^3}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}} \cdot \sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}} \leadsto \color{blue}{\sqrt[3]{\frac{1}{{\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)}}} \cdot \sqrt[3]{\frac{{\left({b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2\right)}^3}{\left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right) \cdot \left(b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\]
    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))))