\[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
Test:
(- (expm1 (- (tan (* a a)) a)) a)
Bits:
128 bits
Bits error versus a
Time: 4.8 s
Input Error: 10.7
Output Error: 12.9
Log: ⚲
Profile: 🕒
\({\left({\left({\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}}}\right)}^3\right)}^3\right)}^3 - a\)
  1. Started with
    \[(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a\]
    10.7
  2. Applied simplify to get
    \[\color{red}{(e^{\tan \left(a \cdot a\right) - a} - 1)^* - a} \leadsto \color{blue}{(e^{\tan \left({a}^2\right) - a} - 1)^* - a}\]
    10.7
  3. Using strategy rm
    10.7
  4. Applied add-cube-cbrt to get
    \[\color{red}{(e^{\tan \left({a}^2\right) - a} - 1)^*} - a \leadsto \color{blue}{{\left(\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}\right)}^3} - a\]
    11.3
  5. Using strategy rm
    11.3
  6. Applied add-cube-cbrt to get
    \[{\color{red}{\left(\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}\right)}}^3 - a \leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}}\right)}^3\right)}}^3 - a\]
    12.0
  7. Using strategy rm
    12.0
  8. Applied add-cube-cbrt to get
    \[{\left({\color{red}{\left(\sqrt[3]{\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}}\right)}}^3\right)}^3 - a \leadsto {\left({\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{(e^{\tan \left({a}^2\right) - a} - 1)^*}}}\right)}^3\right)}}^3\right)}^3 - a\]
    12.9

Original test:


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