Use TaylorDiff

GaussTuranExampleTemp/example.jl

@@ -1,14 +1,13 @@
 using Optim
+using TaylorDiff
 using PreallocationTools
 using Integrals
 using DoubleFloats
 
-include("high_order_derivatives.jl")
-
 # This fix is needed to avoid crashing: https://github.com/JuliaLang/julia/pull/54201
 include("linear_algebra_fix.jl")
 
-FT = Double64
+FT = Float64 # Double64
 n = 5
 s = 1
 a = FT(0.0)
@@ -17,7 +16,7 @@ b = FT(1.0)
 """
     Example functions ϕⱼ from [1]
 """
-function f(x::T, j::Int)::T where {T<:Number}
+function f(x::T, j::Int)::T where {T <: Number}
     pow = if j % 2 == 0
         j / 2 - 1
     else
@@ -26,10 +25,8 @@ function f(x::T, j::Int)::T where {T<:Number}
     x^pow
 end
 
-deriv! = @generate_derivs(2)
 I = Integrals.GaussTuran(
     f,
-    deriv!,
     a,
     b,
     n,
@@ -39,25 +36,26 @@ I = Integrals.GaussTuran(
         g_tol = FT(1e-250),
         show_trace = true,
         show_every = 100,
-        iterations = 10_000,
-    ),
+        iterations = 10_000
+    )
 )
 
 # Integration error |I(fⱼ) - ₐ∫ᵇfⱼ(x)dx| first N functions fⱼ
-max_int_error_upper =
-    maximum(abs(I(x -> f(x, j)) - I.cache.rhs_upper[j]) for j = 1:I.cache.N)
+max_int_error_upper = maximum(abs(I(x -> f(x, j)) - I.cache.rhs_upper[j])
+for j in 1:(I.cache.N))
 @show max_int_error_upper
-# max_int_error_upper = 3.0814879110195774e-32
+# max_int_error_upper = 2.220446049250313e-16
 
 # Integration error |I(fⱼ) - ₐ∫ᵇfⱼ(x)dx| last n functions fⱼ
 max_int_error_lower = maximum(
-    abs(I(x -> f(x, j)) - I.cache.rhs_lower[j-I.cache.N]) for
-    j = (I.cache.N+1):(I.cache.N+I.cache.n)
+    abs(I(x -> f(x, j)) - I.cache.rhs_lower[j - I.cache.N])
+for
+j in (I.cache.N + 1):(I.cache.N + I.cache.n)
 )
 @show max_int_error_lower
-# max_int_error_lower = 2.8858134286698342e-30
+# max_int_error_lower = 2.0211055051788662e-12
 
 # Example with eˣ
 exp_error = abs(I(Base.exp) - (Base.exp(1) - 1))
 @show exp_error;
-# exp_error = -6.436621416953051e-18
+# exp_error = 1.5543122344752192e-15