\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 4.2 s
Input Error: 5.3
Output Error: 5.3
Log: ⚲
Profile: 🕒
\((e^{{\left({\left({\left(\sqrt[3]{\sqrt[3]{\tan \left({a}^2\right)}}\right)}^3\right)}^3\right)}^{1} - a} - 1)^* - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    5.3
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    5.3
  3. Using strategy rm
    5.3
  4. Applied add-cube-cbrt to get
    \[(e^{\color{red}{\tan \left({a}^2\right)} - a} - 1)^* - a \leadsto (e^{\color{blue}{{\left(\sqrt[3]{\tan \left({a}^2\right)}\right)}^3} - a} - 1)^* - a\]
    5.3
  5. Using strategy rm
    5.3
  6. Applied add-cube-cbrt to get
    \[(e^{{\color{red}{\left(\sqrt[3]{\tan \left({a}^2\right)}\right)}}^3 - a} - 1)^* - a \leadsto (e^{{\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\tan \left({a}^2\right)}}\right)}^3\right)}}^3 - a} - 1)^* - a\]
    5.3
  7. Using strategy rm
    5.3
  8. Applied pow1 to get
    \[(e^{\color{red}{{\left({\left(\sqrt[3]{\sqrt[3]{\tan \left({a}^2\right)}}\right)}^3\right)}^3} - a} - 1)^* - a \leadsto (e^{\color{blue}{{\left({\left({\left(\sqrt[3]{\sqrt[3]{\tan \left({a}^2\right)}}\right)}^3\right)}^3\right)}^{1}} - a} - 1)^* - a\]
    5.3

Original test:


(lambda ((a default))
  #:name "(- (expm1 (- (tan (* a a)) a)) a)"
  (- (expm1 (- (tan (* a a)) a)) a))