\[(e^{a} - 1)^* \cdot \cot a\]
Test:
(* (expm1 a) (cotan a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 4.2 s
Input Error: 0.2
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\frac{\cos a}{\frac{\sin a}{(e^{a} - 1)^*}}\)
  1. Started with
    \[(e^{a} - 1)^* \cdot \cot a\]
    0.2
  2. Using strategy rm
    0.2
  3. Applied cotan-quot to get
    \[(e^{a} - 1)^* \cdot \color{red}{\cot a} \leadsto (e^{a} - 1)^* \cdot \color{blue}{\frac{\cos a}{\sin a}}\]
    0.2
  4. Applied taylor to get
    \[(e^{a} - 1)^* \cdot \frac{\cos a}{\sin a} \leadsto (e^{a} - 1)^* \cdot \frac{\cos a}{\sin a}\]
    0.2
  5. Taylor expanded around 0 to get
    \[\color{red}{(e^{a} - 1)^*} \cdot \frac{\cos a}{\sin a} \leadsto \color{blue}{(e^{a} - 1)^*} \cdot \frac{\cos a}{\sin a}\]
    0.2
  6. Applied simplify to get
    \[(e^{a} - 1)^* \cdot \frac{\cos a}{\sin a} \leadsto \frac{\cos a}{\frac{\sin a}{(e^{a} - 1)^*}}\]
    0.1
  7. Applied final simplification
  8. Removed slow pow expressions

Original test:


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