better readme

lib/SimpleNonlinearSolve/README.md

@@ -9,10 +9,10 @@
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-
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 Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
+SimpleNonlinearSolve.jl focuses on low-dependency implementations of very fast methods for
+very small and simple problems. For the full set of solvers, see NonlinearSolve.jl, of which
+SimpleNonlinearSolve.jl is just one solver set.
 
 For information on using the package,
 [see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
@@ -22,17 +22,17 @@ the documentation which contains the unreleased features.
 ## High Level Examples
 
 ```julia
-using NonlinearSolve, StaticArrays
+using SimpleNonlinearSolve, StaticArrays
 
 f(u,p) = u .* u .- 2
 u0 = @SVector[1.0, 1.0]
 probN = NonlinearProblem{false}(f, u0)
-solver = solve(probN, NewtonRaphson(), tol = 1e-9)
+solver = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
 
 ## Bracketing Methods
 
 f(u, p) = u .* u .- 2.0
 u0 = (1.0, 2.0) # brackets
-probB = NonlinearProblem(f, u0)
+probB = IntervalNonlinearProblem(f, u0)
 sol = solve(probB, Falsi())
 ```