\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 5.1 s
Input Error: 5.6
Output Error: 5.8
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{(e^{{\left(\sqrt[3]{\tan \left({a}^2\right)}\right)}^3 - a} - 1)^*}\right)}^3 - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    5.6
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    5.6
  3. Using strategy rm
    5.6
  4. Applied add-cube-cbrt to get
    \[\color{red}{(e^{\tan \left({a}^2\right) - a} - 1)^*} - a \leadsto \color{blue}{{\left(\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}\right)}^3} - a\]
    5.8
  5. Using strategy rm
    5.8
  6. Applied add-cube-cbrt to get
    \[{\left(\sqrt[3]{(e^{\color{red}{\tan \left({a}^2\right)} - a} - 1)^*}\right)}^3 - a \leadsto {\left(\sqrt[3]{(e^{\color{blue}{{\left(\sqrt[3]{\tan \left({a}^2\right)}\right)}^3} - a} - 1)^*}\right)}^3 - a\]
    5.8

Original test:


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