Improve type-stability in newton

[jishnub]

After this, the following is type-inferred

julia> x=Fun(Chebyshev(0..1))
Fun(Chebyshev(0..1),[0.5, 0.5])

julia> u1 = 0.5*one(x)
Fun(Chebyshev(0..1),[0.5])

julia> u2 = 0.5*one(x)
Fun(Chebyshev(0..1),[0.5])

julia> N_dep = (u1,u2) -> [
                       u1(0)*u1(0)*u1(0) - 0.125;
                       u2(0) - 1;
                       u1' - u1*u1;  
                       u2' + u1*u1*u2;
                   ]
#1 (generic function with 1 method)

julia> @inferred newton(N_dep, [u1,u2]);

[codecov[bot]]

Codecov Report

Base: 39.58% // Head: 39.50% // Decreases project coverage by -0.08% :warning:

Coverage data is based on head (8997503) compared to base (81b94a7). Patch coverage: 90.90% of modified lines in pull request are covered.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #783      +/-   ##
==========================================
- Coverage   39.58%   39.50%   -0.09%     
==========================================
  Files          14       14              
  Lines         682      681       -1     
==========================================
- Hits          270      269       -1     
  Misses        412      412              

Impacted Files	Coverage Δ
src/ApproxFun.jl	50.00% <ø> (ø)
src/Extras/autodifferentiation.jl	62.06% <90.90%> (-0.44%)	:arrow_down:

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[jishnub]

Closing at stale