\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 6.1 s
Input Error: 10.6
Output Error: 10.6
Log: ⚲
Profile: 🕒
\((e^{\log_* (1 + \sqrt[3]{{\left((e^{\tan \left({a}^2\right)} - 1)^*\right)}^3}) - a} - 1)^* - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    10.6
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    10.6
  3. Using strategy rm
    10.6
  4. Applied log1p-expm1-u to get
    \[(e^{\color{red}{\tan \left({a}^2\right)} - a} - 1)^* - a \leadsto (e^{\color{blue}{\log_* (1 + (e^{\tan \left({a}^2\right)} - 1)^*)} - a} - 1)^* - a\]
    10.6
  5. Using strategy rm
    10.6
  6. Applied add-cbrt-cube to get
    \[(e^{\log_* (1 + \color{red}{(e^{\tan \left({a}^2\right)} - 1)^*}) - a} - 1)^* - a \leadsto (e^{\log_* (1 + \color{blue}{\sqrt[3]{{\left((e^{\tan \left({a}^2\right)} - 1)^*\right)}^3}}) - a} - 1)^* - a\]
    10.6

Original test:


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