\[\left(-x \cdot \cot B\right) + \frac{1}{\sin B}\]
Test:
VandenBroeck and Keller, Equation (24)
Bits:
128 bits
Bits error versus B
Bits error versus x
Time: 5.5 s
Input Error: 0.2
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\left(-\frac{x}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\)
  1. Started with
    \[\left(-x \cdot \cot B\right) + \frac{1}{\sin B}\]
    0.2
  2. Using strategy rm
    0.2
  3. Applied cotan-tan to get
    \[\left(-x \cdot \color{red}{\cot B}\right) + \frac{1}{\sin B} \leadsto \left(-x \cdot \color{blue}{\frac{1}{\tan B}}\right) + \frac{1}{\sin B}\]
    0.2
  4. Applied un-div-inv to get
    \[\left(-\color{red}{x \cdot \frac{1}{\tan B}}\right) + \frac{1}{\sin B} \leadsto \left(-\color{blue}{\frac{x}{\tan B}}\right) + \frac{1}{\sin B}\]
    0.2
  5. Using strategy rm
    0.2
  6. Applied tan-quot to get
    \[\left(-\frac{x}{\color{red}{\tan B}}\right) + \frac{1}{\sin B} \leadsto \left(-\frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B}\]
    0.2
  7. Applied associate-/r/ to get
    \[\left(-\color{red}{\frac{x}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B} \leadsto \left(-\color{blue}{\frac{x}{\sin B} \cdot \cos B}\right) + \frac{1}{\sin B}\]
    0.2

Original test:


(lambda ((B default) (x default))
  #:name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (cotan B))) (/ 1 (sin B))))