\[(e^{a} - 1)^* \cdot \cot a\]
Test:
(* (expm1 a) (cotan a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 3.8 s
Input Error: 0.0
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left((e^{a} - 1)^*\right)}^3 \cdot {\left(\cot a\right)}^3}\)
  1. Started with
    \[(e^{a} - 1)^* \cdot \cot a\]
    0.0
  2. Using strategy rm
    0.0
  3. Applied add-cbrt-cube to get
    \[(e^{a} - 1)^* \cdot \color{red}{\cot a} \leadsto (e^{a} - 1)^* \cdot \color{blue}{\sqrt[3]{{\left(\cot a\right)}^3}}\]
    13.1
  4. Applied add-cbrt-cube to get
    \[\color{red}{(e^{a} - 1)^*} \cdot \sqrt[3]{{\left(\cot a\right)}^3} \leadsto \color{blue}{\sqrt[3]{{\left((e^{a} - 1)^*\right)}^3}} \cdot \sqrt[3]{{\left(\cot a\right)}^3}\]
    13.2
  5. Applied cbrt-unprod to get
    \[\color{red}{\sqrt[3]{{\left((e^{a} - 1)^*\right)}^3} \cdot \sqrt[3]{{\left(\cot a\right)}^3}} \leadsto \color{blue}{\sqrt[3]{{\left((e^{a} - 1)^*\right)}^3 \cdot {\left(\cot a\right)}^3}}\]
    0.2

Original test:


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