diff --git a/src/DerivativeFree/sidi.jl b/src/DerivativeFree/sidi.jl
index d0b2af6..b9037b3 100644
--- a/src/DerivativeFree/sidi.jl
+++ b/src/DerivativeFree/sidi.jl
@@ -36,8 +36,8 @@ end
 
 function init_state(M::Sidi{k}, F::Callable_Function, x) where {k}
     x₀, x₁ = x₀x₁(x)
-    fx₀, xs, fs = _init_sidi(F, (x₀, x₁),  k)
-    state = SidiState(xs[k], xs[k+1], fx₀, fs[1], xs, fs)
+    fx₀, xs, fs = _init_sidi(F, (x₀, x₁), k)
+    state = SidiState(xs[k], xs[k + 1], fx₀, fs[1], xs, fs)
 end
 
 function update_state(
@@ -46,15 +46,14 @@ function update_state(
     o::SidiState{T,S},
     options,
     l=NullTracks(),
-) where {k, T, S}
-
+) where {k,T,S}
     xs, fs = o.xs, o.fs
     fxn1 = o.fxn1
     _update_sidi!(F, xs, fs)
 
     incfn(l)
     @reset o.xn0 = xs[k]
-    @reset o.xn1 = xs[k+1]
+    @reset o.xn1 = xs[k + 1]
     @reset o.fxn0 = o.fxn1
     @reset o.fxn1 = fs[1]
     @reset o.xs = xs
@@ -79,7 +78,7 @@ function _init_sidi(f, x, k)
     x₀ = first(x)
     fx₀ = f(x₀)
 
-    xs = Vector{typeof( x₀)}(undef, k+1)
+    xs = Vector{typeof(x₀)}(undef, k+1)
     fs = Vector{typeof(fx₀)}(undef, k+1)
 
     n = length(x)
@@ -93,64 +92,62 @@ function _init_sidi(f, x, k)
     fs[2] = (fx₀ - fs[1]) / (xs[1] - xs[2])
 
     # build up diagonal by diagonal
-    for j ∈ 3:(k+1)
+    for j in 3:(k + 1)
         if j ≤ n # xⱼ was specified
             xⱼ = xs[j]
         else
-            xⱼ₋₁ = xs[j-1]
-            pk′ = evaluate_pk′(view(xs, 1:j-1), view(fs, 1:j-1))
+            xⱼ₋₁ = xs[j - 1]
+            pk′ = evaluate_pk′(view(xs, 1:(j - 1)), view(fs, 1:(j - 1)))
             xⱼ = xs[j] = xⱼ₋₁ - fs[1] / pk′
         end
         Δ = f(xⱼ)
-        for i ∈ 2:j
-            Δ₀ = fs[i-1]
-            fs[i-1] = Δ
-            Δ = (Δ₀ - Δ) / (xs[j-i+1] - xs[j])
+        for i in 2:j
+            Δ₀ = fs[i - 1]
+            fs[i - 1] = Δ
+            Δ = (Δ₀ - Δ) / (xs[j - i + 1] - xs[j])
         end
         fs[j] = Δ
     end
 
     # return fx₀ for bookkeeping purposes
     fx₀, xs, fs
-
 end
 
 # update step: compute xn, fxn, update the xs,fs tableau
 function _update_sidi!(f, xs, fs)
     xₙ₋₁, fxₙ₋₁ = xs[end], fs[1]
     fn′ = evaluate_pk′(xs, fs)
-    xn =  xₙ₋₁ -  fxₙ₋₁ / fn′
+    xn = xₙ₋₁ - fxₙ₋₁ / fn′
     fxn = f(xn)
     update_tableau!(xn, fxn, xs, fs)
 end
 
 # formula (10) in paper to evaluate derivative of interpolating polynomial
 function evaluate_pk′(xs1, fs1)
-    δ = xs1[end] - xs1[end-1]
+    δ = xs1[end] - xs1[end - 1]
     Σ = fs1[2]
     k = length(xs1)
-    for i ∈ 3:k
+    for i in 3:k
         Σ = Σ + fs1[i] * δ
-        δ = δ * (xs1[end] - xs1[end-i+1])
+        δ = δ * (xs1[end] - xs1[end - i + 1])
     end
     Σ
 end
 
-
 # update tableau's lower part
 # leaves [xn-k, xn-k+1, xn-k+2, ..., xn]
 #        [fn, f(n-1,n), f(n-2, n-1, n), ..., f(n-k,n-k+1, ..., n)]
 function update_tableau!(xn, fxn, xs0, fs0)
     k = length(xs0)
-    for i in 1:k-1
-        xs0[i] = xs0[i+1]
+    for i in 1:(k - 1)
+        xs0[i] = xs0[i + 1]
     end
     xs0[end] = xn
     Δ = fxn
     for i in 2:k
-        Δ₀ = fs0[i-1]
-        fs0[i-1] = Δ
-        Δ = (Δ₀ - Δ) / (xs0[end-i+1] - xn)
+        Δ₀ = fs0[i - 1]
+        fs0[i - 1] = Δ
+        Δ = (Δ₀ - Δ) / (xs0[end - i + 1] - xn)
     end
     fs0[end] = Δ
     xs0, fs0
diff --git a/src/find_zero.jl b/src/find_zero.jl
index ecb2811..50e73ec 100644
--- a/src/find_zero.jl
+++ b/src/find_zero.jl
@@ -319,9 +319,9 @@ function init(
 end
 
 # helper for development use only
-function __init(f,x,M,p=nothing; kwargs...)
-    s = init(ZeroProblem(f,x), M, p;kwargs...)
-    (M=s.M, F=s.F, state=s.state, options=s.options,logger=s.logger)
+function __init(f, x, M, p=nothing; kwargs...)
+    s = init(ZeroProblem(f, x), M, p; kwargs...)
+    (M=s.M, F=s.F, state=s.state, options=s.options, logger=s.logger)
 end
 
 """
diff --git a/test/test_derivative_free.jl b/test/test_derivative_free.jl
index 1cca4ac..4d8fa93 100644
--- a/test/test_derivative_free.jl
+++ b/test/test_derivative_free.jl
@@ -307,7 +307,7 @@ if !isinteractive()
             Roots.Order8(),
             Roots.Order16(),
             Roots.Sidi(2),
-            Roots.Sidi(3)
+            Roots.Sidi(3),
         ]
         results = [run_df_tests((f, b) -> find_zero(f, b, M), name="$M") for M in Ms]
 
@@ -358,7 +358,7 @@ if !isinteractive()
             Roots.Order5(),
             Roots.Order8(),
             Roots.Order16(),
-            Roots.Sidi(2)
+            Roots.Sidi(2),
         ]
         Ts = [Float16, Float32, BigFloat]
 
diff --git a/test/test_find_zero.jl b/test/test_find_zero.jl
index 4b8dd4a..3199d33 100644
--- a/test/test_find_zero.jl
+++ b/test/test_find_zero.jl
@@ -28,7 +28,7 @@ struct Order3_Test <: Roots.AbstractSecantMethod end
         Roots.Thukral16(),
         Roots.LithBoonkkampIJzerman(3, 0),
         Roots.LithBoonkkampIJzerman(4, 0),
-        Roots.Sidi(2)
+        Roots.Sidi(2),
     ]
 
     ## different types of initial values
@@ -597,8 +597,8 @@ end
 end
 
 @testset "similar methods" begin
-    Lsidi,Lsec = Roots.Tracks(),Roots.Tracks()
+    Lsidi, Lsec = Roots.Tracks(), Roots.Tracks()
     find_zero(sin, 3.0, Roots.Sidi(1); tracks=Lsidi)
     find_zero(sin, 3.0, Roots.Secant(); tracks=Lsec)
-    @test Lsidi.xfₛ[3:end] ==  Lsec.xfₛ[3:end] # drop x₀x₁ ordering
+    @test Lsidi.xfₛ[3:end] == Lsec.xfₛ[3:end] # drop x₀x₁ ordering
 end