\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 4.1 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\((e^{\log_* (1 + \left((e^{\tan \left({a}^2\right) - a} - 1)^* - a\right))} - 1)^*\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    0.1
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    0.1
  3. Using strategy rm
    0.1
  4. Applied expm1-log1p-u to get
    \[\color{red}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\log_* (1 + \left((e^{\tan \left({a}^2\right) - a} - 1)^* - a\right))} - 1)^*}\]
    0.1

Original test:


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