\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 18.0 s
Input Error: 9.7
Output Error: 9.7
Log: ⚲
Profile: 🕒
\(\left(b - {\left(\left(\frac{1}{b} - b \cdot \frac{1}{3}\right) - {b}^3 \cdot \frac{1}{45}\right)}^{a}\right) - \sin^{-1} b\)
  1. Started with
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
    9.7
  2. Applied taylor to get
    \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right) \leadsto b - \left({\left(\frac{1}{b} - \left(\frac{1}{3} \cdot b + \frac{1}{45} \cdot {b}^{3}\right)\right)}^{a} + \sin^{-1} b\right)\]
    9.7
  3. Taylor expanded around 0 to get
    \[b - \left({\color{red}{\left(\frac{1}{b} - \left(\frac{1}{3} \cdot b + \frac{1}{45} \cdot {b}^{3}\right)\right)}}^{a} + \sin^{-1} b\right) \leadsto b - \left({\color{blue}{\left(\frac{1}{b} - \left(\frac{1}{3} \cdot b + \frac{1}{45} \cdot {b}^{3}\right)\right)}}^{a} + \sin^{-1} b\right)\]
    9.7
  4. Applied simplify to get
    \[\color{red}{b - \left({\left(\frac{1}{b} - \left(\frac{1}{3} \cdot b + \frac{1}{45} \cdot {b}^{3}\right)\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{\left(b - {\left(\left(\frac{1}{b} - b \cdot \frac{1}{3}\right) - {b}^3 \cdot \frac{1}{45}\right)}^{a}\right) - \sin^{-1} b}\]
    9.7
  5. 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))))