\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 4.7 s
Input Error: 5.8
Output Error: 6.0
Log: ⚲
Profile: 🕒
\({\left((e^{\log_* (1 + \sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*})} - 1)^*\right)}^3 - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    5.8
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    5.8
  3. Using strategy rm
    5.8
  4. Applied add-cube-cbrt to get
    \[\color{red}{(e^{\tan \left({a}^2\right) - a} - 1)^*} - a \leadsto \color{blue}{{\left(\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}\right)}^3} - a\]
    6.0
  5. Using strategy rm
    6.0
  6. Applied expm1-log1p-u to get
    \[{\color{red}{\left(\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}\right)}}^3 - a \leadsto {\color{blue}{\left((e^{\log_* (1 + \sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*})} - 1)^*\right)}}^3 - a\]
    6.0

Original test:


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