\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 19.1 s
Input Error: 2.6
Output Error: 3.0
Log: ⚲
Profile: 🕒
\(\left(b - \frac{{b}^{\left(-a\right)}}{e^{\left(a \cdot \frac{1}{3}\right) \cdot {b}^2}}\right) - \sin^{-1} b\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    2.6
  2. Using strategy rm
    2.6
  3. Applied add-exp-log to get
    \[b - \left({\color{red}{\left(\cot b\right)}}^{a} + \sin^{-1} b\right) \leadsto b - \left({\color{blue}{\left(e^{\log \left(\cot b\right)}\right)}}^{a} + \sin^{-1} b\right)\]
    7.5
  4. Applied pow-exp to get
    \[b - \left(\color{red}{{\left(e^{\log \left(\cot b\right)}\right)}^{a}} + \sin^{-1} b\right) \leadsto b - \left(\color{blue}{e^{\log \left(\cot b\right) \cdot a}} + \sin^{-1} b\right)\]
    7.5
  5. Applied taylor to get
    \[b - \left(e^{\log \left(\cot b\right) \cdot a} + \sin^{-1} b\right) \leadsto b - \left(e^{-\left(a \cdot \log b + \frac{1}{3} \cdot \left({b}^2 \cdot a\right)\right)} + \sin^{-1} b\right)\]
    7.5
  6. Taylor expanded around 0 to get
    \[b - \left(e^{\color{red}{-\left(a \cdot \log b + \frac{1}{3} \cdot \left({b}^2 \cdot a\right)\right)}} + \sin^{-1} b\right) \leadsto b - \left(e^{\color{blue}{-\left(a \cdot \log b + \frac{1}{3} \cdot \left({b}^2 \cdot a\right)\right)}} + \sin^{-1} b\right)\]
    7.5
  7. Applied simplify to get
    \[b - \left(e^{-\left(a \cdot \log b + \frac{1}{3} \cdot \left({b}^2 \cdot a\right)\right)} + \sin^{-1} b\right) \leadsto \left(b - \frac{{b}^{\left(-a\right)}}{e^{\left(a \cdot \frac{1}{3}\right) \cdot {b}^2}}\right) - \sin^{-1} b\]
    3.0
  8. Applied final simplification

Original test:


(lambda ((a default) (b default))
  #:name "(- b (+ (pow (cotan b) a) (asin b)))"
  (- b (+ (pow (cotan b) a) (asin b))))