• 0 to 1:

$\exp(0)=1$.

• 1 to 2:

$\cos^2(\tan^{-1}(1))=\frac{1}{1^2+1}=\frac{1}{2}$; take the inverse to get $2$.

• 2 to 3:

$\tan^2(\cos^{-1}(2^{-1}))=\Big(\frac{1}{2^{-1}}\Big)^2-1=3$.

• 3 to -3:

$\log((\exp(3))^{-1})=-3$.

• 0 to 1:

  $\exp(0)=1$.

• 1 to 2:

  $\cos^2(\tan^{-1}(1))=\frac{1}{1^2+1}=\frac{1}{2}$; take the inverse to get $2$.

• 2 to 3:

  $\tan^2(\cos^{-1}(2^{-1}))=\Big(\frac{1}{2^{-1}}\Big)^2-1=3$.

• 3 to -3:

  $\log((\exp(3))^{-1})=-3$.