Create infix string from Julia expression

infix.jl

let ops_prec = (Symbol=>Int)[], prec=0, _op_str, _op, tight
    ops_by_prec = ["= := += -= *= /= //= .//= .*= ./= \\= .\\= ^= .^= %= .%= |= &= \$= => <<= >>= >>>= ~ .+= .-=",
                   "?",
                   "||",
                   "&&",
                   "-- -->",
                   "> < >= <= == === != !== .> .< .>= .<= .== .!= .= .! <: >:",
                   "|> <|",
                   ": ..",
                   "+ - .+ .- | \$",
                   "<< >> >>> .<< .>> .>>>",
                   "* / ./ % .% & .* \\ .\\",
                   "// .//",
                   "^ .^",
                   "::",
                   "."]

    global infix

    for _op_str in ops_by_prec
        prec += 1
        for _op in split(_op_str)
            ops_prec[symbol(_op)] = prec
        end
    end

    const tight = ops_prec[:(^)]
    
    function infix(x::Expr, prec = 0)
        if x.head != :call
            return string(x)
        end
        
        op = x.args[1]
        args = x.args[2:end]
        op_prec = get(ops_prec, op, 0)

        local ret
        if op_prec == 0
            infargs = join([infix(arg) for arg in args], " ,")
            ret = "$op($infargs)"
        elseif op == :(*) && length(args)==2 && isa(args[1], Real) && !isa(args[2], Real)
            m1 = args[1]
            m2 = infix(args[2])
            ret = "$m1$m2"
        else
            ops = op_prec < tight ? " $op " : "$op"
            ret = join([infix(arg, op_prec) for arg in args], ops)
            if op_prec <= prec
                ret = "($ret_str)"
            end
        end

        ret
    end

    infix(x, prec = 0) = string(x)
end

infix_test.txt

julia> include("infix.jl")
infix (generic function with 4 methods)

julia> ex = :(sqrt(sin(2pi*x)^2+cos(2pi*x)^2))
:(sqrt(+(^(sin(*(*(2,pi),x)),2),^(cos(*(*(2,pi),x)),2))))

julia> infix(ex)
"sqrt(sin(2pi * x)^2 + cos(2pi * x)^2)"

julia> a = :(5+2b)
:(+(5,*(2,b)))

julia> infix(a)
"5 + 2b"