laphi instantiated
test_laphi.c running on 0<x<1 for N=5
 L_order,point  order is highest power of x, point 0..n 
      L_n,j(x) = product i=0,n i!=j (x-x_i)/(x_j-x_i)  
      for points x_0, x_1, ... , x_n 
      generate L_n,j(x) for n=1,5  j=0,n and derivatives to 4th 
xg[0]=0.0
xg[1]=1.0
L_1,0(0.0)=1.0, yp=-1.0, ypp=-0.0, yppp=-0.0, ypppp=-0.0
L_1,0(0.25)=0.75, yp=-1.0, ypp=-0.0, yppp=-0.0, ypppp=-0.0
L_1,0(0.5)=0.5, yp=-1.0, ypp=-0.0, yppp=-0.0, ypppp=-0.0
L_1,0(0.75)=0.25, yp=-1.0, ypp=-0.0, yppp=-0.0, ypppp=-0.0
L_1,0(1.0)=-0.0, yp=-1.0, ypp=-0.0, yppp=-0.0, ypppp=-0.0

L_1,1(0.0)=0.0, yp=1.0, ypp=0.0, yppp=0.0, ypppp=0.0
L_1,1(0.25)=0.25, yp=1.0, ypp=0.0, yppp=0.0, ypppp=0.0
L_1,1(0.5)=0.5, yp=1.0, ypp=0.0, yppp=0.0, ypppp=0.0
L_1,1(0.75)=0.75, yp=1.0, ypp=0.0, yppp=0.0, ypppp=0.0
L_1,1(1.0)=1.0, yp=1.0, ypp=0.0, yppp=0.0, ypppp=0.0


xg[0]=0.0
xg[1]=0.5
xg[2]=1.0
L_2,0(0.0)=1.0, yp=-3.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.125)=0.65625, yp=-2.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.25)=0.375, yp=-2.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.375)=0.15625, yp=-1.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.5)=-0.0, yp=-1.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.625)=-0.09375, yp=-0.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.75)=-0.125, yp=0.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(0.875)=-0.09375, yp=0.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,0(1.0)=0.0, yp=1.0, ypp=4.0, yppp=0.0, ypppp=0.0

L_2,1(0.0)=0.0, yp=4.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.125)=0.4375, yp=3.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.25)=0.75, yp=2.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.375)=0.9375, yp=1.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.5)=1.0, yp=-0.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.625)=0.9375, yp=-1.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.75)=0.75, yp=-2.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(0.875)=0.4375, yp=-3.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0
L_2,1(1.0)=-0.0, yp=-4.0, ypp=-8.0, yppp=-0.0, ypppp=-0.0

L_2,2(0.0)=-0.0, yp=-1.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.125)=-0.09375, yp=-0.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.25)=-0.125, yp=0.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.375)=-0.09375, yp=0.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.5)=0.0, yp=1.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.625)=0.15625, yp=1.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.75)=0.375, yp=2.0, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(0.875)=0.65625, yp=2.5, ypp=4.0, yppp=0.0, ypppp=0.0
L_2,2(1.0)=1.0, yp=3.0, ypp=4.0, yppp=0.0, ypppp=0.0


xg[0]=0.0
xg[1]=0.3333333333333333
xg[2]=0.6666666666666666
xg[3]=1.0
L_3,0(0.0)=1.0, yp=-5.500000000000001, ypp=18.0, yppp=-27.0, ypppp=-0.0
L_3,0(0.08333333333333333)=0.6015624999999999, yp=-4.09375, ypp=15.75, yppp=-27.0, ypppp=-0.0
L_3,0(0.16666666666666666)=0.31250000000000006, yp=-2.8750000000000004, ypp=13.5, yppp=-27.0, ypppp=-0.0
L_3,0(0.25)=0.11718749999999996, yp=-1.84375, ypp=11.25, yppp=-27.0, ypppp=-0.0
L_3,0(0.3333333333333333)=-0.0, yp=-1.0000000000000002, ypp=9.0, yppp=-27.0, ypppp=-0.0
L_3,0(0.41666666666666663)=-0.05468749999999999, yp=-0.3437500000000001, ypp=6.750000000000002, yppp=-27.0, ypppp=-0.0
L_3,0(0.5)=-0.0625, yp=0.12500000000000014, ypp=4.499999999999999, yppp=-27.0, ypppp=-0.0
L_3,0(0.5833333333333333)=-0.03906250000000002, yp=0.40624999999999994, ypp=2.250000000000002, yppp=-27.0, ypppp=-0.0
L_3,0(0.6666666666666666)=0.0, yp=0.5000000000000001, ypp=4.996003610813204E-16, yppp=-27.0, ypppp=-0.0
L_3,0(0.75)=0.03906250000000002, yp=0.40624999999999994, ypp=-2.2500000000000004, yppp=-27.0, ypppp=-0.0
L_3,0(0.8333333333333333)=0.06250000000000001, yp=0.12500000000000025, ypp=-4.499999999999999, yppp=-27.0, ypppp=-0.0
L_3,0(0.9166666666666666)=0.05468750000000002, yp=-0.3437499999999998, ypp=-6.749999999999999, yppp=-27.0, ypppp=-0.0
L_3,0(1.0)=-0.0, yp=-1.0000000000000002, ypp=-9.0, yppp=-27.0, ypppp=-0.0

L_3,1(0.0)=0.0, yp=8.999999999999998, ypp=-44.99999999999999, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.08333333333333333)=0.6015624999999998, yp=5.531249999999997, ypp=-38.249999999999986, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.16666666666666666)=0.9374999999999999, yp=2.625, ypp=-31.500000000000004, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.25)=1.0546874999999998, yp=0.2812500000000001, ypp=-24.749999999999993, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.3333333333333333)=1.0, yp=-1.4999999999999998, ypp=-18.0, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.41666666666666663)=0.8203124999999999, yp=-2.7187499999999996, ypp=-11.249999999999998, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.5)=0.5624999999999998, yp=-3.3749999999999996, ypp=-4.499999999999997, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.5833333333333333)=0.2734375000000001, yp=-3.46875, ypp=2.2499999999999947, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.6666666666666666)=-0.0, yp=-3.0, ypp=8.999999999999996, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.75)=-0.21093750000000006, yp=-1.9687499999999996, ypp=15.749999999999998, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.8333333333333333)=-0.3125, yp=-0.3750000000000016, ypp=22.499999999999993, yppp=80.99999999999999, ypppp=0.0
L_3,1(0.9166666666666666)=-0.25781250000000006, yp=1.7812499999999991, ypp=29.249999999999993, yppp=80.99999999999999, ypppp=0.0
L_3,1(1.0)=0.0, yp=4.5, ypp=36.0, yppp=80.99999999999999, ypppp=0.0

L_3,2(0.0)=-0.0, yp=-4.499999999999999, ypp=35.99999999999999, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.08333333333333333)=-0.25781249999999994, yp=-1.7812499999999998, ypp=29.249999999999993, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.16666666666666666)=-0.31249999999999994, yp=0.37499999999999994, ypp=22.499999999999996, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.25)=-0.21093749999999992, yp=1.9687499999999996, ypp=15.749999999999996, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.3333333333333333)=0.0, yp=3.0, ypp=9.000000000000004, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.41666666666666663)=0.2734374999999999, yp=3.468749999999999, ypp=2.250000000000002, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.5)=0.5625, yp=3.3749999999999996, ypp=-4.500000000000001, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.5833333333333333)=0.8203124999999998, yp=2.71875, ypp=-11.249999999999995, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.6666666666666666)=1.0, yp=1.5000000000000004, ypp=-17.999999999999993, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.75)=1.0546874999999998, yp=-0.2812499999999997, ypp=-24.75, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.8333333333333333)=0.9375000000000001, yp=-2.624999999999997, ypp=-31.499999999999993, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(0.9166666666666666)=0.6015625000000001, yp=-5.5312499999999964, ypp=-38.24999999999999, yppp=-80.99999999999999, ypppp=-0.0
L_3,2(1.0)=-0.0, yp=-9.0, ypp=-44.99999999999999, yppp=-80.99999999999999, ypppp=-0.0

L_3,3(0.0)=0.0, yp=0.9999999999999998, ypp=-8.999999999999996, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.08333333333333333)=0.05468749999999998, yp=0.3437499999999999, ypp=-6.749999999999999, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.16666666666666666)=0.062499999999999986, yp=-0.12499999999999997, ypp=-4.499999999999998, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.25)=0.03906249999999998, yp=-0.4062499999999999, ypp=-2.2499999999999987, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.3333333333333333)=-0.0, yp=-0.4999999999999999, ypp=0.0, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.41666666666666663)=-0.03906249999999998, yp=-0.4062499999999999, ypp=2.249999999999999, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.5)=-0.062499999999999986, yp=-0.12499999999999985, ypp=4.499999999999999, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.5833333333333333)=-0.0546875, yp=0.34374999999999967, ypp=6.749999999999997, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.6666666666666666)=0.0, yp=0.9999999999999998, ypp=8.999999999999998, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.75)=0.11718750000000003, yp=1.8437499999999998, ypp=11.249999999999998, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.8333333333333333)=0.31249999999999983, yp=2.8749999999999987, ypp=13.499999999999998, yppp=26.999999999999996, ypppp=0.0
L_3,3(0.9166666666666666)=0.6015624999999998, yp=4.093749999999998, ypp=15.749999999999995, yppp=26.999999999999996, ypppp=0.0
L_3,3(1.0)=1.0, yp=5.499999999999999, ypp=17.999999999999996, yppp=26.999999999999996, ypppp=0.0


xg[0]=0.0
xg[1]=0.25
xg[2]=0.5
xg[3]=0.75
xg[4]=1.0
L_4,0(0.0)=1.0, yp=-8.333333333333334, ypp=46.666666666666664, yppp=-160.0, ypppp=256.0
L_4,0(0.0625)=0.56396484375, yp=-5.71875, ypp=37.166666666666664, yppp=-144.0, ypppp=256.0
L_4,0(0.125)=0.2734375, yp=-3.6666666666666665, ypp=28.666666666666668, yppp=-128.0, ypppp=256.0
L_4,0(0.1875)=0.09521484375, yp=-2.1145833333333335, ypp=21.166666666666668, yppp=-112.0, ypppp=256.0
L_4,0(0.25)=-0.0, yp=-1.0, ypp=14.666666666666666, yppp=-96.0, ypppp=256.0
L_4,0(0.3125)=-0.03759765625, yp=-0.2604166666666667, ypp=9.166666666666666, yppp=-80.0, ypppp=256.0
L_4,0(0.375)=-0.0390625, yp=0.16666666666666666, ypp=4.666666666666667, yppp=-64.0, ypppp=256.0
L_4,0(0.4375)=-0.02197265625, yp=0.34375, ypp=1.1666666666666667, yppp=-48.0, ypppp=256.0
L_4,0(0.5)=0.0, yp=0.3333333333333333, ypp=-1.3333333333333333, yppp=-32.0, ypppp=256.0
L_4,0(0.5625)=0.01708984375, yp=0.19791666666666666, ypp=-2.8333333333333335, yppp=-16.0, ypppp=256.0
L_4,0(0.625)=0.0234375, yp=0.0, ypp=-3.3333333333333335, yppp=0.0, ypppp=256.0
L_4,0(0.6875)=0.01708984375, yp=-0.19791666666666666, ypp=-2.8333333333333335, yppp=16.0, ypppp=256.0
L_4,0(0.75)=-0.0, yp=-0.3333333333333333, ypp=-1.3333333333333333, yppp=32.0, ypppp=256.0
L_4,0(0.8125)=-0.02197265625, yp=-0.34375, ypp=1.1666666666666667, yppp=48.0, ypppp=256.0
L_4,0(0.875)=-0.0390625, yp=-0.16666666666666666, ypp=4.666666666666667, yppp=64.0, ypppp=256.0
L_4,0(0.9375)=-0.03759765625, yp=0.2604166666666667, ypp=9.166666666666666, yppp=80.0, ypppp=256.0
L_4,0(1.0)=0.0, yp=1.0, ypp=14.666666666666666, yppp=96.0, ypppp=256.0

L_4,1(0.0)=0.0, yp=16.0, ypp=-138.66666666666666, yppp=576.0, ypppp=-1024.0
L_4,1(0.0625)=0.751953125, yp=8.416666666666666, ypp=-104.66666666666667, yppp=512.0, ypppp=-1024.0
L_4,1(0.125)=1.09375, yp=2.8333333333333335, ypp=-74.66666666666667, yppp=448.0, ypppp=-1024.0
L_4,1(0.1875)=1.142578125, yp=-1.0, ypp=-48.666666666666664, yppp=384.0, ypppp=-1024.0
L_4,1(0.25)=1.0, yp=-3.3333333333333335, ypp=-26.666666666666668, yppp=320.0, ypppp=-1024.0
L_4,1(0.3125)=0.751953125, yp=-4.416666666666667, ypp=-8.666666666666666, yppp=256.0, ypppp=-1024.0
L_4,1(0.375)=0.46875, yp=-4.5, ypp=5.333333333333333, yppp=192.0, ypppp=-1024.0
L_4,1(0.4375)=0.205078125, yp=-3.8333333333333335, ypp=15.333333333333334, yppp=128.0, ypppp=-1024.0
L_4,1(0.5)=-0.0, yp=-2.6666666666666665, ypp=21.333333333333332, yppp=64.0, ypppp=-1024.0
L_4,1(0.5625)=-0.123046875, yp=-1.25, ypp=23.333333333333332, yppp=-0.0, ypppp=-1024.0
L_4,1(0.625)=-0.15625, yp=0.16666666666666666, ypp=21.333333333333332, yppp=-64.0, ypppp=-1024.0
L_4,1(0.6875)=-0.107421875, yp=1.3333333333333333, ypp=15.333333333333334, yppp=-128.0, ypppp=-1024.0
L_4,1(0.75)=0.0, yp=2.0, ypp=5.333333333333333, yppp=-192.0, ypppp=-1024.0
L_4,1(0.8125)=0.126953125, yp=1.9166666666666667, ypp=-8.666666666666666, yppp=-256.0, ypppp=-1024.0
L_4,1(0.875)=0.21875, yp=0.8333333333333334, ypp=-26.666666666666668, yppp=-320.0, ypppp=-1024.0
L_4,1(0.9375)=0.205078125, yp=-1.5, ypp=-48.666666666666664, yppp=-384.0, ypppp=-1024.0
L_4,1(1.0)=-0.0, yp=-5.333333333333333, ypp=-74.66666666666667, yppp=-448.0, ypppp=-1024.0

L_4,2(0.0)=-0.0, yp=-12.0, ypp=152.0, yppp=-768.0, ypppp=1536.0
L_4,2(0.0625)=-0.4833984375, yp=-3.9375, ypp=107.0, yppp=-672.0, ypppp=1536.0
L_4,2(0.125)=-0.546875, yp=1.5, ypp=68.0, yppp=-576.0, ypppp=1536.0
L_4,2(0.1875)=-0.3427734375, yp=4.6875, ypp=35.0, yppp=-480.0, ypppp=1536.0
L_4,2(0.25)=0.0, yp=6.0, ypp=8.0, yppp=-384.0, ypppp=1536.0
L_4,2(0.3125)=0.3759765625, yp=5.8125, ypp=-13.0, yppp=-288.0, ypppp=1536.0
L_4,2(0.375)=0.703125, yp=4.5, ypp=-28.0, yppp=-192.0, ypppp=1536.0
L_4,2(0.4375)=0.9228515625, yp=2.4375, ypp=-37.0, yppp=-96.0, ypppp=1536.0
L_4,2(0.5)=1.0, yp=0.0, ypp=-40.0, yppp=0.0, ypppp=1536.0
L_4,2(0.5625)=0.9228515625, yp=-2.4375, ypp=-37.0, yppp=96.0, ypppp=1536.0
L_4,2(0.625)=0.703125, yp=-4.5, ypp=-28.0, yppp=192.0, ypppp=1536.0
L_4,2(0.6875)=0.3759765625, yp=-5.8125, ypp=-13.0, yppp=288.0, ypppp=1536.0
L_4,2(0.75)=-0.0, yp=-6.0, ypp=8.0, yppp=384.0, ypppp=1536.0
L_4,2(0.8125)=-0.3427734375, yp=-4.6875, ypp=35.0, yppp=480.0, ypppp=1536.0
L_4,2(0.875)=-0.546875, yp=-1.5, ypp=68.0, yppp=576.0, ypppp=1536.0
L_4,2(0.9375)=-0.4833984375, yp=3.9375, ypp=107.0, yppp=672.0, ypppp=1536.0
L_4,2(1.0)=0.0, yp=12.0, ypp=152.0, yppp=768.0, ypppp=1536.0

L_4,3(0.0)=0.0, yp=5.333333333333333, ypp=-74.66666666666667, yppp=448.0, ypppp=-1024.0
L_4,3(0.0625)=0.205078125, yp=1.5, ypp=-48.666666666666664, yppp=384.0, ypppp=-1024.0
L_4,3(0.125)=0.21875, yp=-0.8333333333333334, ypp=-26.666666666666668, yppp=320.0, ypppp=-1024.0
L_4,3(0.1875)=0.126953125, yp=-1.9166666666666667, ypp=-8.666666666666666, yppp=256.0, ypppp=-1024.0
L_4,3(0.25)=-0.0, yp=-2.0, ypp=5.333333333333333, yppp=192.0, ypppp=-1024.0
L_4,3(0.3125)=-0.107421875, yp=-1.3333333333333333, ypp=15.333333333333334, yppp=128.0, ypppp=-1024.0
L_4,3(0.375)=-0.15625, yp=-0.16666666666666666, ypp=21.333333333333332, yppp=64.0, ypppp=-1024.0
L_4,3(0.4375)=-0.123046875, yp=1.25, ypp=23.333333333333332, yppp=-0.0, ypppp=-1024.0
L_4,3(0.5)=0.0, yp=2.6666666666666665, ypp=21.333333333333332, yppp=-64.0, ypppp=-1024.0
L_4,3(0.5625)=0.205078125, yp=3.8333333333333335, ypp=15.333333333333334, yppp=-128.0, ypppp=-1024.0
L_4,3(0.625)=0.46875, yp=4.5, ypp=5.333333333333333, yppp=-192.0, ypppp=-1024.0
L_4,3(0.6875)=0.751953125, yp=4.416666666666667, ypp=-8.666666666666666, yppp=-256.0, ypppp=-1024.0
L_4,3(0.75)=1.0, yp=3.3333333333333335, ypp=-26.666666666666668, yppp=-320.0, ypppp=-1024.0
L_4,3(0.8125)=1.142578125, yp=1.0, ypp=-48.666666666666664, yppp=-384.0, ypppp=-1024.0
L_4,3(0.875)=1.09375, yp=-2.8333333333333335, ypp=-74.66666666666667, yppp=-448.0, ypppp=-1024.0
L_4,3(0.9375)=0.751953125, yp=-8.416666666666666, ypp=-104.66666666666667, yppp=-512.0, ypppp=-1024.0
L_4,3(1.0)=-0.0, yp=-16.0, ypp=-138.66666666666666, yppp=-576.0, ypppp=-1024.0

L_4,4(0.0)=-0.0, yp=-1.0, ypp=14.666666666666666, yppp=-96.0, ypppp=256.0
L_4,4(0.0625)=-0.03759765625, yp=-0.2604166666666667, ypp=9.166666666666666, yppp=-80.0, ypppp=256.0
L_4,4(0.125)=-0.0390625, yp=0.16666666666666666, ypp=4.666666666666667, yppp=-64.0, ypppp=256.0
L_4,4(0.1875)=-0.02197265625, yp=0.34375, ypp=1.1666666666666667, yppp=-48.0, ypppp=256.0
L_4,4(0.25)=0.0, yp=0.3333333333333333, ypp=-1.3333333333333333, yppp=-32.0, ypppp=256.0
L_4,4(0.3125)=0.01708984375, yp=0.19791666666666666, ypp=-2.8333333333333335, yppp=-16.0, ypppp=256.0
L_4,4(0.375)=0.0234375, yp=0.0, ypp=-3.3333333333333335, yppp=0.0, ypppp=256.0
L_4,4(0.4375)=0.01708984375, yp=-0.19791666666666666, ypp=-2.8333333333333335, yppp=16.0, ypppp=256.0
L_4,4(0.5)=-0.0, yp=-0.3333333333333333, ypp=-1.3333333333333333, yppp=32.0, ypppp=256.0
L_4,4(0.5625)=-0.02197265625, yp=-0.34375, ypp=1.1666666666666667, yppp=48.0, ypppp=256.0
L_4,4(0.625)=-0.0390625, yp=-0.16666666666666666, ypp=4.666666666666667, yppp=64.0, ypppp=256.0
L_4,4(0.6875)=-0.03759765625, yp=0.2604166666666667, ypp=9.166666666666666, yppp=80.0, ypppp=256.0
L_4,4(0.75)=0.0, yp=1.0, ypp=14.666666666666666, yppp=96.0, ypppp=256.0
L_4,4(0.8125)=0.09521484375, yp=2.1145833333333335, ypp=21.166666666666668, yppp=112.0, ypppp=256.0
L_4,4(0.875)=0.2734375, yp=3.6666666666666665, ypp=28.666666666666668, yppp=128.0, ypppp=256.0
L_4,4(0.9375)=0.56396484375, yp=5.71875, ypp=37.166666666666664, yppp=144.0, ypppp=256.0
L_4,4(1.0)=1.0, yp=8.333333333333334, ypp=46.666666666666664, yppp=160.0, ypppp=256.0


xg[0]=0.0
xg[1]=0.2
xg[2]=0.4
xg[3]=0.6000000000000001
xg[4]=0.8
xg[5]=1.0
L_5,0(0.0)=1.0, yp=-11.416666666666664, ypp=93.75, yppp=-531.2499999999997, ypppp=1875.0
L_5,0(0.05)=0.5357666015624999, yp=-7.354980468749997, ypp=69.46614583333334, yppp=-441.4062499999996, ypppp=1718.7499999999989
L_5,0(0.1)=0.24609375000000003, yp=-4.3984375, ypp=49.47916666666663, yppp=-359.3749999999999, ypppp=1562.499999999999
L_5,0(0.15000000000000002)=0.08093261718749996, yp=-2.3419596354166656, ypp=33.39843749999999, yppp=-285.1562500000001, ypppp=1406.249999999999
L_5,0(0.2)=-0.0, yp=-1.0, ypp=20.833333333333332, yppp=-218.75, ypppp=1250.0
L_5,0(0.25)=-0.028198242187499993, yp=-0.20654296875000006, ypp=11.393229166666666, yppp=-160.15624999999997, ypppp=1093.7499999999998
L_5,0(0.30000000000000004)=-0.027343749999999993, yp=0.18489583333333343, ypp=4.6874999999999964, yppp=-109.37500000000004, ypppp=937.499999999999
L_5,0(0.35000000000000003)=-0.014282226562499997, yp=0.3012695312499999, ypp=0.32552083333333354, yppp=-66.40624999999999, ypppp=781.2499999999999
L_5,0(0.4)=0.0, yp=0.25, ypp=-2.0833333333333326, yppp=-31.24999999999998, ypppp=624.9999999999998
L_5,0(0.45)=0.0093994140625, yp=0.11897786458333337, ypp=-2.9296874999999996, yppp=-3.9062500000000204, ypppp=468.7499999999996
L_5,0(0.5)=0.011718750000000003, yp=-0.023437499999999858, ypp=-2.6041666666666665, yppp=15.624999999999984, ypppp=312.49999999999983
L_5,0(0.55)=0.0076904296875000035, yp=-0.12841796874999994, ypp=-1.4973958333333324, yppp=27.343749999999993, ypppp=156.24999999999994
L_5,0(0.6000000000000001)=-0.0, yp=-0.1666666666666666, ypp=2.71050543121376E-16, yppp=31.24999999999999, ypppp=-2.847837706395257E-13
L_5,0(0.65)=-0.007690429687499987, yp=-0.12841796875, ypp=1.4973958333333317, yppp=27.34375, ypppp=-156.24999999999991
L_5,0(0.7000000000000001)=-0.011718749999999988, yp=-0.023437499999999962, ypp=2.6041666666666647, yppp=15.624999999999986, ypppp=-312.5
L_5,0(0.75)=-0.0093994140625, yp=0.11897786458333312, ypp=2.9296874999999982, yppp=-3.906249999999981, ypppp=-468.7499999999998
L_5,0(0.8)=0.0, yp=0.2499999999999998, ypp=2.0833333333333326, yppp=-31.249999999999996, ypppp=-624.9999999999997
L_5,0(0.8500000000000001)=0.014282226562500002, yp=0.3012695312499997, ypp=-0.3255208333333369, yppp=-66.40625000000001, ypppp=-781.2499999999993
L_5,0(0.9)=0.027343749999999962, yp=0.18489583333333318, ypp=-4.6874999999999964, yppp=-109.37499999999991, ypppp=-937.4999999999995
L_5,0(0.9500000000000001)=0.02819824218749996, yp=-0.20654296875000047, ypp=-11.393229166666668, yppp=-160.15624999999997, ypppp=-1093.7499999999993
L_5,0(1.0)=-0.0, yp=-0.9999999999999991, ypp=-20.833333333333318, yppp=-218.75, ypppp=-1249.9999999999995

L_5,1(0.0)=0.0, yp=24.99999999999999, ypp=-320.83333333333314, yppp=2218.749999999999, ypppp=-8749.999999999993
L_5,1(0.05)=0.8929443359374996, yp=11.553548177083329, ypp=-220.50781249999986, yppp=1800.7812499999986, ypppp=-7968.750000000003
L_5,1(0.1)=1.2304687499999998, yp=2.6171875000000004, ypp=-140.1041666666667, yppp=1421.8749999999995, ypppp=-7187.499999999985
L_5,1(0.15000000000000002)=1.2139892578124993, yp=-2.75634765625, ypp=-77.66927083333326, yppp=1082.0312499999995, ypppp=-6406.250000000004
L_5,1(0.2)=1.0, yp=-5.416666666666665, ypp=-31.249999999999975, yppp=781.2499999999999, ypppp=-5624.999999999995
L_5,1(0.25)=0.7049560546874998, yp=-6.115722656249997, ypp=1.1067708333333361, yppp=519.5312499999995, ypppp=-4843.749999999996
L_5,1(0.30000000000000004)=0.4101562499999997, yp=-5.5078124999999964, ypp=21.354166666666664, yppp=296.8749999999999, ypppp=-4062.4999999999986
L_5,1(0.35000000000000003)=0.1666259765624999, yp=-4.149576822916664, ypp=31.445312499999982, yppp=113.28124999999983, ypppp=-3281.249999999993
L_5,1(0.4)=-0.0, yp=-2.4999999999999996, ypp=33.333333333333314, yppp=-31.249999999999993, ypppp=-2499.9999999999986
L_5,1(0.45)=-0.0845947265625, yp=-0.9204101562500004, ypp=28.971354166666657, yppp=-136.7187499999999, ypppp=-1718.750000000001
L_5,1(0.5)=-0.09765625000000001, yp=0.3255208333333324, ypp=20.312499999999996, yppp=-203.1249999999998, ypppp=-937.5000000000011
L_5,1(0.55)=-0.060424804687500014, yp=1.0717773437499993, ypp=9.309895833333327, yppp=-230.46874999999994, ypppp=-156.2499999999999
L_5,1(0.6000000000000001)=0.0, yp=1.2499999999999991, ypp=-2.0833333333333397, yppp=-218.74999999999986, ypppp=625.0000000000008
L_5,1(0.65)=0.0555419921874999, yp=0.8894856770833331, ypp=-11.914062499999986, yppp=-167.96874999999983, ypppp=1406.2499999999989
L_5,1(0.7000000000000001)=0.08203124999999992, yp=0.11718749999999972, ypp=-18.229166666666657, yppp=-78.12499999999989, ypppp=2187.4999999999986
L_5,1(0.75)=0.06408691406249997, yp=-0.8422851562499981, ypp=-19.075520833333314, yppp=50.781249999999865, ypppp=2968.7499999999973
L_5,1(0.8)=-0.0, yp=-1.6666666666666652, ypp=-12.499999999999988, yppp=218.7499999999999, ypppp=3749.999999999997
L_5,1(0.8500000000000001)=-0.0933837890625, yp=-1.936035156249998, ypp=3.450520833333354, yppp=425.7812499999999, ypppp=4531.25
L_5,1(0.9)=-0.17578124999999978, yp=-1.1328124999999987, ypp=30.729166666666643, yppp=671.8749999999993, ypppp=5312.499999999994
L_5,1(0.9500000000000001)=-0.17858886718749967, yp=1.3582356770833355, ypp=71.28906249999999, yppp=957.0312499999997, ypppp=6093.749999999995
L_5,1(1.0)=0.0, yp=6.249999999999992, ypp=127.08333333333321, yppp=1281.249999999999, ypppp=6874.999999999997

L_5,2(0.0)=-0.0, yp=-25.0, ypp=445.8333333333333, yppp=-3687.499999999998, ypppp=16250.000000000007
L_5,2(0.05)=-0.7653808593749999, yp=-6.987304687499996, ypp=281.11979166666663, yppp=-2914.0624999999986, ypppp=14687.499999999998
L_5,2(0.1)=-0.8203125000000001, yp=3.7239583333333335, ypp=153.125, yppp=-2218.75, ypppp=13124.99999999999
L_5,2(0.15000000000000002)=-0.4855957031249999, yp=8.8720703125, ypp=57.94270833333329, yppp=-1601.562499999999, ypppp=11562.500000000005
L_5,2(0.2)=0.0, yp=10.000000000000002, ypp=-8.333333333333327, yppp=-1062.4999999999995, ypppp=9999.999999999993
L_5,2(0.25)=0.4699707031249999, yp=8.455403645833334, ypp=-49.609375, yppp=-601.5625, ypppp=8437.500000000004
L_5,2(0.30000000000000004)=0.8203125, yp=5.390624999999999, ypp=-69.79166666666664, yppp=-218.74999999999977, ypppp=6874.999999999987
L_5,2(0.35000000000000003)=0.999755859375, yp=1.762695312499999, ypp=-72.78645833333331, yppp=85.93749999999991, ypppp=5312.499999999991
L_5,2(0.4)=1.0, yp=-1.6666666666666659, ypp=-62.49999999999999, yppp=312.49999999999983, ypppp=3749.9999999999964
L_5,2(0.45)=0.8459472656250002, yp=-4.331054687499998, ypp=-42.838541666666664, yppp=460.93749999999983, ypppp=2187.5000000000064
L_5,2(0.5)=0.5859375000000004, yp=-5.859374999999997, ypp=-17.70833333333335, yppp=531.2499999999999, ypppp=625.0000000000006
L_5,2(0.55)=0.28198242187500017, yp=-6.075846354166666, ypp=8.984375, yppp=523.4374999999999, ypppp=-937.4999999999986
L_5,2(0.6000000000000001)=-0.0, yp=-4.9999999999999964, ypp=33.33333333333333, yppp=437.4999999999999, ypppp=-2500.000000000001
L_5,2(0.65)=-0.19995117187499972, yp=-2.8466796875000013, ypp=51.43229166666666, yppp=273.4375, ypppp=-4062.4999999999995
L_5,2(0.7000000000000001)=-0.2734374999999998, yp=-0.026041666666666272, ypp=59.374999999999964, yppp=31.249999999999755, ypppp=-5624.999999999995
L_5,2(0.75)=-0.20141601562500003, yp=2.856445312499996, ypp=53.255208333333314, yppp=-289.0624999999998, ypppp=-7187.499999999995
L_5,2(0.8)=0.0, yp=4.9999999999999964, ypp=29.16666666666664, yppp=-687.5, ypppp=-8750.000000000004
L_5,2(0.8500000000000001)=0.26977539062500006, yp=5.408528645833329, ypp=-16.79687500000008, yppp=-1164.0625000000005, ypppp=-10312.5
L_5,2(0.9)=0.49218749999999944, yp=2.890624999999998, ypp=-88.54166666666661, yppp=-1718.7499999999995, ypppp=-11874.99999999999
L_5,2(0.9500000000000001)=0.4870605468749992, yp=-3.940429687500006, ypp=-189.97395833333334, yppp=-2351.5624999999995, ypppp=-13437.499999999998
L_5,2(1.0)=-0.0, yp=-16.666666666666654, ypp=-324.99999999999983, yppp=-3062.4999999999986, ypppp=-14999.999999999985

L_5,3(0.0)=0.0, yp=16.666666666666668, ypp=-325.0, yppp=3062.4999999999995, ypppp=-14999.999999999995
L_5,3(0.05)=0.48706054687499994, yp=3.940429687499999, ypp=-189.97395833333326, yppp=2351.5624999999995, ypppp=-13437.500000000011
L_5,3(0.1)=0.49218750000000006, yp=-2.8906250000000004, ypp=-88.54166666666667, yppp=1718.75, ypppp=-11874.999999999984
L_5,3(0.15000000000000002)=0.26977539062499994, yp=-5.408528645833335, ypp=-16.79687499999995, yppp=1164.0624999999995, ypppp=-10312.500000000002
L_5,3(0.2)=-0.0, yp=-5.000000000000001, ypp=29.166666666666668, yppp=687.4999999999998, ypppp=-8750.000000000004
L_5,3(0.25)=-0.20141601562499997, yp=-2.8564453125, ypp=53.25520833333333, yppp=289.0624999999996, ypppp=-7187.4999999999945
L_5,3(0.30000000000000004)=-0.27343749999999994, yp=0.026041666666668253, ypp=59.37499999999999, yppp=-31.250000000000167, ypppp=-5624.99999999999
L_5,3(0.35000000000000003)=-0.19995117187499994, yp=2.8466796874999996, ypp=51.43229166666664, yppp=-273.4375, ypppp=-4062.4999999999977
L_5,3(0.4)=0.0, yp=5.0, ypp=33.33333333333333, yppp=-437.49999999999994, ypppp=-2500.0
L_5,3(0.45)=0.28198242187499994, yp=6.075846354166666, ypp=8.984375000000018, yppp=-523.4375, ypppp=-937.4999999999999
L_5,3(0.5)=0.5859374999999998, yp=5.859374999999999, ypp=-17.708333333333314, yppp=-531.2500000000002, ypppp=624.999999999999
L_5,3(0.55)=0.8459472656249999, yp=4.3310546875, ypp=-42.83854166666666, yppp=-460.93749999999983, ypppp=2187.4999999999995
L_5,3(0.6000000000000001)=1.0, yp=1.6666666666666616, ypp=-62.49999999999999, yppp=-312.4999999999996, ypppp=3750.000000000001
L_5,3(0.65)=0.999755859375, yp=-1.7626953124999987, ypp=-72.78645833333333, yppp=-85.9374999999999, ypppp=5312.499999999997
L_5,3(0.7000000000000001)=0.8203124999999997, yp=-5.390625000000001, ypp=-69.79166666666663, yppp=218.7500000000003, ypppp=6874.999999999996
L_5,3(0.75)=0.4699707031250003, yp=-8.45540364583333, ypp=-49.60937499999998, yppp=601.5624999999997, ypppp=8437.500000000002
L_5,3(0.8)=-0.0, yp=-9.999999999999998, ypp=-8.333333333333309, yppp=1062.5000000000002, ypppp=9999.999999999998
L_5,3(0.8500000000000001)=-0.4855957031250003, yp=-8.872070312499993, ypp=57.94270833333344, yppp=1601.562500000001, ypppp=11562.499999999998
L_5,3(0.9)=-0.8203124999999994, yp=-3.723958333333331, ypp=153.12499999999997, yppp=2218.7499999999995, ypppp=13124.999999999996
L_5,3(0.9500000000000001)=-0.765380859374999, yp=6.9873046875000115, ypp=281.1197916666667, yppp=2914.0625000000005, ypppp=14687.499999999993
L_5,3(1.0)=0.0, yp=24.999999999999986, ypp=445.83333333333314, yppp=3687.4999999999986, ypppp=16249.999999999996

L_5,4(0.0)=-0.0, yp=-6.250000000000003, ypp=127.08333333333337, yppp=-1281.25, ypppp=6875.0000000000055
L_5,4(0.05)=-0.17858886718750006, yp=-1.358235677083334, ypp=71.28906249999999, yppp=-957.03125, ypppp=6093.750000000005
L_5,4(0.1)=-0.17578125000000014, yp=1.1328125000000004, ypp=30.729166666666668, yppp=-671.8750000000007, ypppp=5312.4999999999945
L_5,4(0.15000000000000002)=-0.09338378906250001, yp=1.9360351562500009, ypp=3.450520833333334, yppp=-425.78125000000017, ypppp=4531.2500000000055
L_5,4(0.2)=0.0, yp=1.6666666666666676, ypp=-12.500000000000005, yppp=-218.74999999999991, ypppp=3750.0000000000005
L_5,4(0.25)=0.06408691406250001, yp=0.8422851562500006, ypp=-19.075520833333346, yppp=-50.7812500000001, ypppp=2968.7499999999986
L_5,4(0.30000000000000004)=0.08203125000000003, yp=-0.11718750000000028, ypp=-18.22916666666667, yppp=78.12500000000004, ypppp=2187.499999999998
L_5,4(0.35000000000000003)=0.05554199218750001, yp=-0.8894856770833337, ypp=-11.914062500000004, yppp=167.9687500000001, ypppp=1406.2500000000023
L_5,4(0.4)=-0.0, yp=-1.2500000000000007, ypp=-2.0833333333333335, yppp=218.74999999999994, ypppp=624.9999999999989
L_5,4(0.45)=-0.060424804687500035, yp=-1.0717773437500009, ypp=9.30989583333333, yppp=230.4687500000001, ypppp=-156.24999999999977
L_5,4(0.5)=-0.09765625000000007, yp=-0.3255208333333348, ypp=20.312499999999996, yppp=203.12500000000006, ypppp=-937.4999999999997
L_5,4(0.55)=-0.0845947265625001, yp=0.9204101562499996, ypp=28.97135416666668, yppp=136.71875000000003, ypppp=-1718.7500000000005
L_5,4(0.6000000000000001)=0.0, yp=2.5000000000000013, ypp=33.33333333333332, yppp=31.24999999999984, ypppp=-2500.0000000000005
L_5,4(0.65)=0.16662597656249978, yp=4.149576822916666, ypp=31.44531250000001, yppp=-113.28124999999997, ypppp=-3281.249999999999
L_5,4(0.7000000000000001)=0.41015625, yp=5.507812499999999, ypp=21.354166666666643, yppp=-296.87500000000017, ypppp=-4062.4999999999995
L_5,4(0.75)=0.7049560546874997, yp=6.115722656250001, ypp=1.1067708333333452, yppp=-519.5312499999999, ypppp=-4843.750000000002
L_5,4(0.8)=1.0, yp=5.416666666666665, ypp=-31.250000000000025, yppp=-781.2500000000005, ypppp=-5625.000000000003
L_5,4(0.8500000000000001)=1.2139892578125, yp=2.756347656249994, ypp=-77.66927083333341, yppp=-1082.0312500000007, ypppp=-6406.250000000005
L_5,4(0.9)=1.2304687499999993, yp=-2.617187500000001, ypp=-140.10416666666666, yppp=-1421.8749999999998, ypppp=-7187.499999999997
L_5,4(0.9500000000000001)=0.892944335937499, yp=-11.553548177083343, ypp=-220.50781250000006, yppp=-1800.7812500000005, ypppp=-7968.750000000004
L_5,4(1.0)=-0.0, yp=-24.999999999999996, ypp=-320.8333333333333, yppp=-2218.7500000000005, ypppp=-8749.999999999996

L_5,5(0.0)=0.0, yp=1.0000000000000009, ypp=-20.83333333333335, yppp=218.7500000000002, ypppp=-1250.0000000000011
L_5,5(0.05)=0.028198242187500017, yp=0.20654296875000017, ypp=-11.393229166666675, yppp=160.1562500000001, ypppp=-1093.750000000001
L_5,5(0.1)=0.027343750000000035, yp=-0.1848958333333335, ypp=-4.6875000000000036, yppp=109.37500000000014, ypppp=-937.4999999999999
L_5,5(0.15000000000000002)=0.014282226562500009, yp=-0.3012695312500002, ypp=-0.3255208333333334, yppp=66.40625000000006, ypppp=-781.2500000000007
L_5,5(0.2)=-0.0, yp=-0.2500000000000003, ypp=2.0833333333333353, yppp=31.25, ypppp=-625.0000000000005
L_5,5(0.25)=-0.009399414062500007, yp=-0.11897786458333347, ypp=2.9296875000000018, yppp=3.9062500000000298, ypppp=-468.7500000000001
L_5,5(0.30000000000000004)=-0.011718750000000009, yp=0.02343750000000006, ypp=2.6041666666666687, yppp=-15.625000000000016, ypppp=-312.49999999999994
L_5,5(0.35000000000000003)=-0.007690429687500005, yp=0.1284179687500001, ypp=1.4973958333333337, yppp=-27.343750000000014, ypppp=-156.25000000000009
L_5,5(0.4)=0.0, yp=0.16666666666666682, ypp=1.807003620809175E-16, yppp=-31.250000000000032, ypppp=7.2280144832367E-15
L_5,5(0.45)=0.007690429687500008, yp=0.12841796875000014, ypp=-1.4973958333333337, yppp=-27.343750000000025, ypppp=156.25000000000003
L_5,5(0.5)=0.011718750000000014, yp=0.023437500000000173, ypp=-2.6041666666666674, yppp=-15.625000000000018, ypppp=312.5000000000001
L_5,5(0.55)=0.009399414062500016, yp=-0.11897786458333336, ypp=-2.9296875000000027, yppp=3.9062499999999987, ypppp=468.7500000000002
L_5,5(0.6000000000000001)=-0.0, yp=-0.2500000000000002, ypp=-2.083333333333332, yppp=31.250000000000036, ypppp=625.0000000000002
L_5,5(0.65)=-0.014282226562499991, yp=-0.3012695312500002, ypp=0.325520833333332, yppp=66.40625000000003, ypppp=781.2499999999999
L_5,5(0.7000000000000001)=-0.02734375000000001, yp=-0.18489583333333334, ypp=4.6875000000000036, yppp=109.37500000000001, ypppp=937.5000000000005
L_5,5(0.75)=-0.028198242187500024, yp=0.20654296874999958, ypp=11.393229166666666, yppp=160.15625, ypppp=1093.7500000000002
L_5,5(0.8)=0.0, yp=1.0000000000000004, ypp=20.833333333333343, yppp=218.7500000000002, ypppp=1250.0000000000007
L_5,5(0.8500000000000001)=0.08093261718750015, yp=2.3419596354166696, ypp=33.39843750000003, yppp=285.1562500000003, ypppp=1406.2500000000014
L_5,5(0.9)=0.24609374999999997, yp=4.3984375, ypp=49.47916666666668, yppp=359.37500000000006, ypppp=1562.500000000001
L_5,5(0.9500000000000001)=0.5357666015625003, yp=7.3549804687500036, ypp=69.46614583333337, yppp=441.4062500000003, ypppp=1718.7500000000007
L_5,5(1.0)=1.0, yp=11.416666666666668, ypp=93.75000000000001, yppp=531.2500000000003, ypppp=1874.9999999999998


end test_laphi.java