\[\left(-x \cdot \cot B\right) + \frac{1}{\sin B}\]
Test:
VandenBroeck and Keller, Equation (24)
Bits:
128 bits
Bits error versus B
Bits error versus x
Time: 6.5 s
Input Error: 0.1
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(-x \cdot \cot B\right) + {\left(\frac{\sqrt[3]{1}}{\sqrt[3]{\sin B}}\right)}^3\)
  1. Started with
    \[\left(-x \cdot \cot B\right) + \frac{1}{\sin B}\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied add-cube-cbrt to get
    \[\left(-x \cdot \cot B\right) + \color{red}{\frac{1}{\sin B}} \leadsto \left(-x \cdot \cot B\right) + \color{blue}{{\left(\sqrt[3]{\frac{1}{\sin B}}\right)}^3}\]
    0.5
  4. Using strategy rm
    0.5
  5. Applied cbrt-div to get
    \[\left(-x \cdot \cot B\right) + {\color{red}{\left(\sqrt[3]{\frac{1}{\sin B}}\right)}}^3 \leadsto \left(-x \cdot \cot B\right) + {\color{blue}{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{\sin B}}\right)}}^3\]
    0.4
  6. Removed slow pow expressions

Original test:


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