\[(e^{a} - 1)^* \cdot \cot a\]
Test:
(* (expm1 a) (cotan a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 5.8 s
Input Error: 0.0
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\frac{(e^{a} - 1)^*}{\tan a}\)
  1. Started with
    \[(e^{a} - 1)^* \cdot \cot a\]
    0.0
  2. Using strategy rm
    0.0
  3. Applied cotan-tan to get
    \[(e^{a} - 1)^* \cdot \color{red}{\cot a} \leadsto (e^{a} - 1)^* \cdot \color{blue}{\frac{1}{\tan a}}\]
    0.1
  4. Applied un-div-inv to get
    \[\color{red}{(e^{a} - 1)^* \cdot \frac{1}{\tan a}} \leadsto \color{blue}{\frac{(e^{a} - 1)^*}{\tan a}}\]
    0.1
  5. Removed slow pow expressions

Original test:


(lambda ((a default) (b default))
  #:name "(* (expm1 a) (cotan a))"
  (* (expm1 a) (cotan a)))