\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 7.0 s
Input Error: 3.3
Output Error: 4.5
Log: ⚲
Profile: 🕒
\((e^{{\left(\frac{\sqrt{1}}{\sqrt{\cot \left({a}^2\right)}}\right)}^2 - a} - 1)^* - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    3.3
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    3.3
  3. Using strategy rm
    3.3
  4. Applied add-sqr-sqrt to get
    \[(e^{\color{red}{\tan \left({a}^2\right)} - a} - 1)^* - a \leadsto (e^{\color{blue}{{\left(\sqrt{\tan \left({a}^2\right)}\right)}^2} - a} - 1)^* - a\]
    4.5
  5. Using strategy rm
    4.5
  6. Applied tan-cotan to get
    \[(e^{{\left(\sqrt{\color{red}{\tan \left({a}^2\right)}}\right)}^2 - a} - 1)^* - a \leadsto (e^{{\left(\sqrt{\color{blue}{\frac{1}{\cot \left({a}^2\right)}}}\right)}^2 - a} - 1)^* - a\]
    4.5
  7. Applied sqrt-div to get
    \[(e^{{\color{red}{\left(\sqrt{\frac{1}{\cot \left({a}^2\right)}}\right)}}^2 - a} - 1)^* - a \leadsto (e^{{\color{blue}{\left(\frac{\sqrt{1}}{\sqrt{\cot \left({a}^2\right)}}\right)}}^2 - a} - 1)^* - a\]
    4.5

Original test:


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