Alphabetizing tests; upd comp test scr; bumping ver to 0.4.1

Project.toml

@@ -1,7 +1,7 @@
 name = "FunctionIntegrator"
 uuid = "7685536e-2581-4f83-bef1-2ba363c9cb91"
 authors = ["Brenton Horne <[email protected]>"]
-version = "0.4.0"
+version = "0.4.1"
 
 [deps]
 FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"

test/Computation_times_Travis_92.2.jl

@@ -1,37 +1,22 @@
-# Taken from https://travis-ci.com/github/fusion809/FunctionIntegrator.jl/jobs/358878829
+# Taken from https://travis-ci.com/github/fusion809/FunctionIntegrator.jl/jobs/359262615
 # 10th entry is simppen
-L_adaptive_simpsons = [0.153903;
-0.045990;
-0.000090;
-
-L_chebyshev1=[1.493455; # AiryAi(x)
-0.291795; # besselj
-0.041686; # cos_cot
-0.104719; #
-0.116603;
-0.090129;
-0.088141;
-0.114219;
-0.162800;
-0.441775;
-0.102337;
-0.050055;
-0.048896];
-L_chebyshev2=[0.176496; 0.060008; 0.041355; 0.099813; 0.111966; 0.125740; 0.103428; 0.098729; 0.064575; 8.991385; 0.096214; 0.052295; 0.049748];
-L_chebyshev3 = [0.150834; 0.072039; 0.049798; 0.111535; 0.099392; 0.101607; 0.111045; 0.111373; 0.070177; 3.208550; 0.092763; 0.057960; 0.055562];
-L_chebyshev4 = [0.125087; 0.070966; 0.049619; 0.092735; 0.098091; 0.100671; 0.099425; 0.099531; 0.070195; 4.146543; 0.094798; 0.056763; 0.053876];
-L_jacobi = [20.655073; 0.741378; 0.079454; 0.468545; 0.220772; 2.786482; 0.531896; 0.446746; 0.479568; 22.058539; 0.242638; 1.933591; 0.694156];
-L_legendre=[0.122725; 0.076702; 0.030384; 0.071562; 0.078758; 0.078509; 0.088236; 0.090079; 0.043331; 4.383104; 0.059413; 0.036632; 0.033564];
-L_lobatto=[0.169799; 0.012460; 0.000103; 0.080504; 0.143451; 0.117507; 0.086438; 0.091315; 0.000142; 21.927058; 0.025977; 0.000409; 0.000141];
-L_radau = [0.151726; 0.012143; 0.000040; 0.094062; 0.129707; 0.104701; 0.086289; 0.087083; 0.000057; 22.282400; 0.025089; 0.000345; 0.000109];
-L_rectangle_midpoint = [0.073208; 0.000017; 0.000330; 0.019159; 0.022585; 0.030032; 0.018576; 0.021532; 0.000027; 1.863286; 0.035673; 0.000545; 0.000903];
-L_simpsons=[0.080275; 0.040657; 0.000012; 0.023218; 0.041971; 0.028887; 0.025965; 0.031452; 0.018607; 13.831230; 0.047495; 0.000064; 0.000078];
-L_simpsons38=[0.068510; ]
-L_trapezoidal=[0.149524; 0.034553; 0.000577; 0.017627; 0.032416; 0.022288; 0.019312; 0.023317; 0.013583; 13.361007; 0.077226; 0.001042; 0.001420];
-
+L_adaptive_simpsons = [0.144420; 0.048034; 0.000163; 0.019791; 0.031644; 0.022732; 0.022157; 0.023056; 0.000081; 12.635982; 0.002164; 0.000840; 0.000220];
+L_chebyshev1 = [1.374153; 0.295273; 0.042028; 0.097700; 0.085278; 0.091216; 0.085430; 0.086918; 0.136373; 0.405410; 0.088461; 0.048735; 0.045503];
+L_chebyshev2 = [0.189887; 0.063260; 0.041871; 0.095741; 0.109335; 0.101715; 0.111041; 0.100269; 0.082595; 8.732129; 0.090618; 0.050086; 0.045789];
+L_chebyshev3 = [0.166648; 0.067508; 0.048010; 0.090679; 0.093410; 0.123339; 0.094715; 0.107830; 0.068438; 3.184987; 0.088439; 0.056318; 0.051559];
+L_chebyshev4 = [0.133982; 0.067320; 0.048107; 0.093402; 0.105892; 0.101815; 0.095580; 0.095526; 0.067627; 4.097529; 0.090069; 0.054310; 0.050882];
+L_jacobi = [20.730626; 0.696972; 0.074401; 0.472530; 0.214534; 2.607443; 0.521480; 0.440099; 0.493098; 21.869202; 0.162223; 1.875650; 0.579464];
+L_legendre = [0.104126; 0.075988; 0.029669; 0.069286; 0.074264; 0.075576; 0.072840; 0.071971; 0.043136; 4.255756; 0.058376; 0.034468; 0.030826];
+L_lobatto = [0.191745; 0.012332; 0.000122; 0.090188; 0.139901; 0.105984; 0.083651; 0.081196; 0.000138; 21.580829; 0.092406; 0.000301; 0.000141];
+L_radau = [0.140783; 0.012576; 0.000053; 0.079066; 0.108806; 0.111685; 0.096150; 0.081501; 0.000065; 21.579555; 0.023179; 0.000421; 0.000113];
+L_rectangle_midpoint = [0.074701; 0.000019; 0.000266; 0.018933; 0.020185; 0.018622; 0.018862; 0.018857; 0.000027; 1.564159; 0.029700; 0.000414; 0.000740];
+L_simpsons = [0.057260; 0.018206; 0.000013; 0.020936; 0.029926; 0.022812; 0.023652; 0.024098; 0.018203; 13.383746; 0.036649; 0.000066; 0.000052];
+L_simpsons38 = [0.056655; 0.040500; 0.000012; 0.023536; 0.031635; 0.026131; 0.024863; 0.025426; 0.017806; 14.101716; 0.040174; 0.000060; 0.000041];
+L_trapezoidal = [0.141598; 0.034595; 0.000494; 0.015096; 0.021626; 0.017495; 0.016807; 0.017933; 0.012839; 12.977622; 0.069035; 0.000937; 0.001293];
 N = length(L_simpsons);
 
 # RMS of times
+rms_adaptive_simpsons_wo_simppen = sqrt((L_adaptive_simpsons[1:9]'*L_adaptive_simpsons[1:9]+L_adaptive_simpsons[11:N]'*L_adaptive_simpsons[11:N])/(N-1));
 rms_chebyshev1 = sqrt(L_chebyshev1'*L_chebyshev1/N);
 rms_chebyshev1_wo_simppen = sqrt((L_chebyshev1[1:9]'*L_chebyshev1[1:9]+L_chebyshev1[11:N]'*L_chebyshev1[11:N])/(N-1));
 rms_chebyshev2 = sqrt(L_chebyshev2'*L_chebyshev2/N);
@@ -49,6 +34,7 @@ rms_radau_wo_simppen = sqrt((L_radau[1:9]'*L_radau[1:9]+L_radau[11:N]'*L_radau[1
 rms_rectangle_midpoint = sqrt(L_rectangle_midpoint'*L_rectangle_midpoint/N);
 rms_rectangle_midpoint_wo_simppen = sqrt((L_rectangle_midpoint[1:9]'*L_rectangle_midpoint[1:9]+L_rectangle_midpoint[11:N]'*L_rectangle_midpoint[11:N])/(N-1));
 rms_simpsons_wo_simppen = sqrt((L_simpsons[1:9]'*L_simpsons[1:9]+L_simpsons[11:N]'*L_simpsons[11:N])/(N-1));
+rms_simpsons38_wo_simppen = sqrt((L_simpsons38[1:9]'*L_simpsons38[1:9]+L_simpsons38[11:N]'*L_simpsons38[11:N])/(N-1));
 rms_trapezoidal_wo_simppen = sqrt((L_trapezoidal[1:9]'*L_trapezoidal[1:9]+L_trapezoidal[11:N]'*L_trapezoidal[11:N])/(N-1));
 
 rms_wo_simppen = [rms_chebyshev1_wo_simppen; rms_chebyshev2_wo_simppen; rms_chebyshev3_wo_simppen; rms_chebyshev4_wo_simppen; rms_jacobi_wo_simppen; rms_legendre_wo_simppen; rms_lobatto_wo_simppen; rms_radau_wo_simppen; rms_rectangle_midpoint_wo_simppen; rms_simpsons_wo_simppen; rms_trapezoidal_wo_simppen];
@@ -60,6 +46,7 @@ println("rms_chebyshev4 is $(rms_chebyshev4)")
 println("rms_jacobi     is $(rms_jacobi)")
 println("rms_legendre   is $(rms_legendre)")
 
+println("rms_adaptive_simpsons_wo_simppen is    $(rms_adaptive_simpsons_wo_simppen)")
 println("rms_chebyshev1_wo_simppen is  $(rms_chebyshev1_wo_simppen)")
 println("rms_chebyshev2_wo_simppen is  $(rms_chebyshev2_wo_simppen)")
 println("rms_chebyshev3_wo_simppen is  $(rms_chebyshev3_wo_simppen)")
@@ -70,4 +57,5 @@ println("rms_lobatto_wo_simppen is     $(rms_lobatto_wo_simppen)")
 println("rms_radau_wo_simppen is       $(rms_radau_wo_simppen)")
 println("rms_rectangle_midpoint_wo_simppen is $(rms_rectangle_midpoint_wo_simppen)")
 println("rms_simpsons_wo_simppen is    $(rms_simpsons_wo_simppen)")
+println("rms_simpsons38_wo_simppen is    $(rms_simpsons38_wo_simppen)")
 println("rms_trapezoidal_wo_simppen is $(rms_trapezoidal_wo_simppen)")

test/airyai.jl

@@ -1,6 +1,8 @@
 # AiryAi(x)
 printstyled("Performing the Airy Ai(x) test, where Ai(x) is integrated on the semi-infinite domain, or an approximation of it, namely [0,100] and the result is compared to the analytical result 1/3.\n"; color = :red)
 @testset "Airy Ai(x)" begin
+    printstyled("Running: adaptive_simpsons_rule\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> airyai(x), 0, 100, 1e-8) ≈ 1.0/3.0
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> airyai(x), 38337, 1, 0, 100) ≈ 1.0/3.0
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -29,8 +31,6 @@ printstyled("Performing the Airy Ai(x) test, where Ai(x) is integrated on the se
     @time @test simpsons_rule(x -> airyai(x), 2512, 0, 100) ≈ 1.0/3.0
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> airyai(x), 3075, 0, 100) ≈ 1.0/3.0
-    printstyled("Running: adaptive_simpsons_rule\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> airyai(x), 0, 100, 1e-8) ≈ 1.0/3.0
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> airyai(x), 208381, 0, 100) ≈ 1.0/3.0
 end

test/besselj.jl

@@ -5,6 +5,8 @@ end
 
 printstyled("Performing the besselj test, where BesselJ_1(2) is approximated and the result is compared to the value obtained from SpecialFunctions' besselj function.\n"; color = :red)
 @testset "besselj" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(besselj_integrand, 0, pi/2, 1e-7) ≈ besselj(1,2)
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(besselj_integrand, 4665, 1, 0, pi/2) ≈ besselj(1,2)
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -31,8 +33,6 @@ printstyled("Performing the besselj test, where BesselJ_1(2) is approximated and
     @time @test simpsons_rule(besselj_integrand, 6, 0, pi/2) ≈ besselj(1,2)
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(besselj_integrand, 9, 0, pi/2) ≈ besselj(1,2)
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(besselj_integrand, 0, pi/2, 1e-7) ≈ besselj(1,2)
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(besselj_integrand, 4, 0, pi/2) ≈ besselj(1,2)
 end

test/cos_cot_integral.jl

@@ -7,6 +7,8 @@ end
 
 printstyled("Integrating cos^2(x)/(1+cot(x)) from 0 to pi/2 and comparing the results to the analytical result 0.25.\n"; color = :red)
 @testset "coscotint" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(cos_cot_fn, 0, pi/2, 1e-7) ≈ 0.25
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(cos_cot_fn, 88, 1, 0, pi/2) ≈ 0.25
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -33,8 +35,6 @@ printstyled("Integrating cos^2(x)/(1+cot(x)) from 0 to pi/2 and comparing the re
     @time @test simpsons_rule(cos_cot_fn, 78, 0, pi/2) ≈ 0.25
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(cos_cot_fn, 96, 0, pi/2) ≈ 0.25
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(cos_cot_fn, 0, pi/2, 1e-7) ≈ 0.25
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(cos_cot_fn, 7430, 0, pi/2) ≈ 0.25
 end

test/cosine.jl

@@ -1,6 +1,8 @@
 # cosine test
 printstyled("Integrating cosine from 0 to pi/2 and comparing the result to the analytical result of 1.\n"; color = :red)
 @testset "Cosine" begin
+    printstyled("Running: adaptive_simpsons_rule\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> cos(x), 0, pi/2, 1e-7) ≈ 1
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> cos(x), 4656, 1, 0, pi/2) ≈ 1
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -27,8 +29,6 @@ printstyled("Integrating cosine from 0 to pi/2 and comparing the result to the a
     @time @test simpsons_rule(x -> cos(x), 40, 0, pi/2) ≈ 1
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> cos(x), 48, 0, pi/2) ≈ 1
-    printstyled("Running: adaptive_simpsons_rule\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> cos(x), 0, pi/2, 1e-7) ≈ 1
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> cos(x), 3715, 0, pi/2) ≈ 1
 end

test/expnx2datan.jl

@@ -3,6 +3,8 @@ sol_9 = exp(1)*pi*erfc(1);
 
 printstyled("Integrating e^(-x^2)/(1+x^2) on the infinite domain [-inf, inf], or failing that on [-100,100], and comparing it to the analytical result exp(1)*pi*erfc(1)\n"; color = :red)
 @testset "expnx2datan" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> exp(-x^2)/(x^2+1), -100, 100, 1e-7) ≈ sol_9
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> exp(-x^2)/(x^2+1), 1029, 1, -100, 100) ≈ sol_9
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -33,8 +35,6 @@ printstyled("Integrating e^(-x^2)/(1+x^2) on the infinite domain [-inf, inf], or
     @time @test simpsons_rule(x -> exp(-x^2)/(x^2+1), 1240, -100, 100) ≈ sol_9
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> exp(-x^2)/(x^2+1), 1767, -100, 100) ≈ sol_9
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> exp(-x^2)/(x^2+1), -100, 100, 1e-7) ≈ sol_9
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> exp(-x^2)/(x^2+1), 655, -100, 100) ≈ sol_9
 end

test/gaussian.jl

@@ -1,6 +1,8 @@
 # Gaussian curve test
 printstyled("Integrate exp(-x^2) from minus infinity to positive infinity and comparing the result to the analytical solution, sqrt(pi)\n"; color = :red)
 @testset "Gaussian" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> exp(-x^2), -100, 100, 1e-7) ≈ sqrt(pi)
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> exp(-x^2), 433, 1, -100, 100) ≈ sqrt(pi)
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -33,8 +35,6 @@ printstyled("Integrate exp(-x^2) from minus infinity to positive infinity and co
     @time @test simpsons_rule(x -> exp(-x^2), 536, -100, 100) ≈ sqrt(pi)
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> exp(-x^2), 780, -100, 100) ≈ sqrt(pi)
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> exp(-x^2), -100, 100, 1e-7) ≈ sqrt(pi)
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> exp(-x^2), 276, -100, 100) ≈ sqrt(pi)
 end

test/logarithm.jl

@@ -1,6 +1,8 @@
 # logarithm test
 printstyled("Integrating 1/x from 1 to e and comparing the result to the analytical solution, 1.\n"; color = :red)
 @testset "1/x" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> x^(-1), 1, exp(1), 1e-7) ≈ 1
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> x^(-1), 5695, 1, 1, exp(1)) ≈ 1
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -27,8 +29,6 @@ printstyled("Integrating 1/x from 1 to e and comparing the result to the analyti
     @time @test simpsons_rule(x -> x^(-1), 70, 1, exp(1)) ≈ 1
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> x^(-1), 84, 1, exp(1)) ≈ 1
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> x^(-1), 1, exp(1), 1e-7) ≈ 1
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> x^(-1), 3779, 1, exp(1)) ≈ 1
 end

test/logoverx.jl

@@ -1,5 +1,7 @@
 printstyled("Integrating log(x)/x from 1 to e and comparing the result to the analytical solution of 0.5.\n"; color = :red)
 @testset "log(x)/x" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(x -> log(x)/x, 1, exp(1), 1e-8) ≈ 0.5
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> log(x)/x, 4177, 1, 1, exp(1)) ≈ 0.5
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -26,8 +28,6 @@ printstyled("Integrating log(x)/x from 1 to e and comparing the result to the an
     @time @test simpsons_rule(x -> log(x)/x, 100, 1, exp(1)) ≈ 0.5
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(x -> log(x)/x, 114, 1, exp(1)) ≈ 0.5
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(x -> log(x)/x, 1, exp(1), 1e-8) ≈ 0.5
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(x -> log(x)/x, 5747, 1, exp(1)) ≈ 0.5
 end

test/modbessel0.jl

@@ -9,6 +9,8 @@ end
 
 printstyled("Approximating the modified bessel function I_1(1) and comparing it to the result obtained by SpecialFunctions.\n"; color = :red)
 @testset "modbessel0" begin
+    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
+    @time @test adaptive_simpsons_rule(dmodified_bessel_1, 0, pi/2, 1e-7) ≈ besseli(x,1)
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(dmodified_bessel_1, 4942, 1, 0, pi/2) ≈ besseli(x,1)
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -35,8 +37,6 @@ printstyled("Approximating the modified bessel function I_1(1) and comparing it
     @time @test simpsons_rule(dmodified_bessel_1, 6, 0, pi/2) ≈ besseli(x,1)
     printstyled("Running: simpsons38_rule\n"; color = :magenta)
     @time @test simpsons38_rule(dmodified_bessel_1, 9, 0, pi/2) ≈ besseli(x,1)
-    printstyled("Running: adaptive_simpsons_rule with ε=1e-7\n"; color = :magenta)
-    @time @test adaptive_simpsons_rule(dmodified_bessel_1, 0, pi/2, 1e-7) ≈ besseli(x,1)
     printstyled("Running: trapezoidal_rule\n"; color = :magenta)
     @time @test trapezoidal_rule(dmodified_bessel_1, 3, 0, pi/2) ≈ besseli(x,1)
 end

test/simppen.jl

@@ -1,6 +1,8 @@
 # Simple pendulum test
 printstyled("Integrating 1/sqrt(-19.6 sin(x)) from -pi to 0 and comparing the result to the analytical solution of ellipk(1/2)/sqrt(2.45) The integrand has singularities at x = -pi and x=0, so for some of these functions the integration domain has to be itself approximated.\n"; color = :red)
 @testset "Simppen" begin
+    printstyled("Running: adaptive_simpsons_rule on [-pi+1e-8, -1e-8]. Only a rough approximation can be realistically achieved with this function, due to the singularities.\n"; color = :magenta)
+    @time @test abs(adaptive_simpsons_rule(x -> (-19.6*sin(x))^(-0.5), -pi+1e-8, -1e-8, 1e-5) - ellipk(1/2)/sqrt(2.45)) < 1e-4
     printstyled("Running: chebyshev_quadrature with k=1\n"; color = :magenta)
     @time @test chebyshev_quadrature(x -> (-19.6*sin(x))^(-0.5), 6, 1, -pi, 0) ≈ ellipk(1/2)/sqrt(2.45)
     printstyled("Running: chebyshev_quadrature with k=2\n"; color = :magenta)
@@ -29,8 +31,6 @@ printstyled("Integrating 1/sqrt(-19.6 sin(x)) from -pi to 0 and comparing the re
     @time @test abs(simpsons_rule(x -> (-19.6*sin(x))^(-0.5), 1e8, -pi+1e-8, -1e-8) - ellipk(1/2)/sqrt(2.45)) < 1e-4
     printstyled("Running: simpsons38_rule on [-pi+1e-8, -1e-8]. Only a rough approximation can be realistically achieved with this function, due to the singularities.\n"; color = :magenta)
     @time @test abs(simpsons38_rule(x -> (-19.6*sin(x))^(-0.5), 1e8+2, -pi+1e-8, -1e-8) - ellipk(1/2)/sqrt(2.45)) < 1e-4
-    printstyled("Running: adaptive_simpsons_rule on [-pi+1e-8, -1e-8]. Only a rough approximation can be realistically achieved with this function, due to the singularities.\n"; color = :magenta)
-    @time @test abs(adaptive_simpsons_rule(x -> (-19.6*sin(x))^(-0.5), -pi+1e-8, -1e-8, 1e-5) - ellipk(1/2)/sqrt(2.45)) < 1e-4
     printstyled("Running: trapezoidal_rule on [-pi+1e-8, -1e-8]. Only a rough approximation can be realistically achieved with this function, due to the singularities.\n"; color = :magenta)
     @time @test abs(trapezoidal_rule(x -> (-19.6*sin(x))^(-0.5), 1e8, -pi+1e-8, -1e-8) - ellipk(1/2)/sqrt(2.45)) < 1e-4
 end