Formulas for numerical computation of derivatives f^(3) means third derivative f^(2)(x[1]) means second derivative computed at point x[1] f(x[2]) means function evaluated at point x[2] Points are x[0], x[1]=x[0]+h, x[2]=x0+2h, ... The error term gives the power of h and derivative order with z chosen for maximum value. The error terms, err=, are for test polynomial sum(x^pwr) with h = 0.125 or smaller, and order = 'pwr' computing order= 1 , npoints= 2 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 1 h^ 1 )( -1 * f(x[ 0 ]) + 1 * f(x[ 1 ] ) + O(h^ 1 )f^( 2 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.0 , pwr= 0 err= 0.0 , h= 0.125 , deriv= 1.0 , x= 1.0 , pwr= 1 err= 1.0 , h= 0.125 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 1.0 , h= 0.0625 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 2.0 , h= 0.125 , deriv= 3.0 , x= 1.0 , pwr= 3 err= 2.0 , h= 0.0625 , deriv= 3.0 , x= 1.0 , pwr= 3 computing order= 1 , npoints= 2 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 1 h^ 1 )( -1 * f(x[ 0 ]) + 1 * f(x[ 1 ] ) + O(h^ 1 )f^( 2 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.125 , pwr= 0 err= 0.0 , h= 0.125 , deriv= 1.0 , x= 1.125 , pwr= 1 err= 1.25 , h= 0.125 , deriv= 2.25 , x= 1.125 , pwr= 2 err= 1.125 , h= 0.0625 , deriv= 2.125 , x= 1.0625 , pwr= 2 err= 2.375 , h= 0.125 , deriv= 3.375 , x= 1.125 , pwr= 3 err= 2.1875 , h= 0.0625 , deriv= 3.1875 , x= 1.0625 , pwr= 3 computing order= 1 , npoints= 3 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 2 h^ 1 )( -3 * f(x[ 0 ]) + 4 * f(x[ 1 ] + -1 * f(x[ 2 ] ) + O(h^ 2 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 1.0 , x= 1.0 , pwr= 1 err= 1.0 , h= 0.125 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 2.0 , h= 0.125 , deriv= 3.0 , x= 1.0 , pwr= 3 err= 2.0 , h= 0.0625 , deriv= 3.0 , x= 1.0 , pwr= 3 err= 3.0 , h= 0.125 , deriv= 4.0 , x= 1.0 , pwr= 4 err= 3.0 , h= 0.0625 , deriv= 4.0 , x= 1.0 , pwr= 4 computing order= 1 , npoints= 3 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 2 h^ 1 )( -1 * f(x[ 0 ]) + 0 * f(x[ 1 ] + 1 * f(x[ 2 ] ) + O(h^ 2 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 1.0 , x= 1.125 , pwr= 1 err= 1.25 , h= 0.125 , deriv= 2.25 , x= 1.125 , pwr= 2 err= 2.375 , h= 0.125 , deriv= 3.375 , x= 1.125 , pwr= 3 err= 2.1875 , h= 0.0625 , deriv= 3.1875 , x= 1.0625 , pwr= 3 err= 3.5 , h= 0.125 , deriv= 4.5 , x= 1.125 , pwr= 4 err= 3.25 , h= 0.0625 , deriv= 4.25 , x= 1.0625 , pwr= 4 computing order= 1 , npoints= 3 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 2 h^ 1 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 3 * f(x[ 2 ] ) + O(h^ 2 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 1.0 , x= 1.25 , pwr= 1 err= 1.5 , h= 0.125 , deriv= 2.5 , x= 1.25 , pwr= 2 err= 2.75 , h= 0.125 , deriv= 3.75 , x= 1.25 , pwr= 3 err= 2.375 , h= 0.0625 , deriv= 3.375 , x= 1.125 , pwr= 3 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.25 , pwr= 4 err= 3.5 , h= 0.0625 , deriv= 4.5 , x= 1.125 , pwr= 4 computing order= 1 , npoints= 4 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 6 h^ 1 )( -11 * f(x[ 0 ]) + 18 * f(x[ 1 ] + -9 * f(x[ 2 ] + 2 * f(x[ 3 ] ) + O(h^ 3 )f^( 4 )(z) err= 1.0 , h= 0.125 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 2.0 , h= 0.125 , deriv= 3.0 , x= 1.0 , pwr= 3 err= 3.0 , h= 0.125 , deriv= 4.0 , x= 1.0 , pwr= 4 err= 3.0 , h= 0.0625 , deriv= 4.0 , x= 1.0 , pwr= 4 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.0 , pwr= 5 err= 4.0 , h= 0.0625 , deriv= 5.0 , x= 1.0 , pwr= 5 computing order= 1 , npoints= 4 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 6 h^ 1 )( -2 * f(x[ 0 ]) + -3 * f(x[ 1 ] + 6 * f(x[ 2 ] + -1 * f(x[ 3 ] ) + O(h^ 3 )f^( 4 )(z) err= 1.25 , h= 0.125 , deriv= 2.25 , x= 1.125 , pwr= 2 err= 2.375 , h= 0.125 , deriv= 3.375 , x= 1.125 , pwr= 3 err= 3.5 , h= 0.125 , deriv= 4.5 , x= 1.125 , pwr= 4 err= 3.25 , h= 0.0625 , deriv= 4.25 , x= 1.0625 , pwr= 4 err= 4.625 , h= 0.125 , deriv= 5.625 , x= 1.125 , pwr= 5 err= 4.3125 , h= 0.0625 , deriv= 5.3125 , x= 1.0625 , pwr= 5 computing order= 1 , npoints= 4 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 6 h^ 1 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 3 * f(x[ 2 ] + 2 * f(x[ 3 ] ) + O(h^ 3 )f^( 4 )(z) err= 1.5 , h= 0.125 , deriv= 2.5 , x= 1.25 , pwr= 2 err= 2.75 , h= 0.125 , deriv= 3.75 , x= 1.25 , pwr= 3 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.25 , pwr= 4 err= 3.5 , h= 0.0625 , deriv= 4.5 , x= 1.125 , pwr= 4 err= 5.25 , h= 0.125 , deriv= 6.25 , x= 1.25 , pwr= 5 err= 4.625 , h= 0.0625 , deriv= 5.625 , x= 1.125 , pwr= 5 computing order= 1 , npoints= 4 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 6 h^ 1 )( -2 * f(x[ 0 ]) + 9 * f(x[ 1 ] + -18 * f(x[ 2 ] + 11 * f(x[ 3 ] ) + O(h^ 3 )f^( 4 )(z) err= 1.75 , h= 0.125 , deriv= 2.75 , x= 1.375 , pwr= 2 err= 3.125 , h= 0.125 , deriv= 4.125 , x= 1.375 , pwr= 3 err= 4.5 , h= 0.125 , deriv= 5.5 , x= 1.375 , pwr= 4 err= 3.75 , h= 0.0625 , deriv= 4.75 , x= 1.1875 , pwr= 4 err= 5.875 , h= 0.125 , deriv= 6.875 , x= 1.375 , pwr= 5 err= 4.9375 , h= 0.0625 , deriv= 5.9375 , x= 1.1875 , pwr= 5 computing order= 1 , npoints= 5 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 12 h^ 1 )( -25 * f(x[ 0 ]) + 48 * f(x[ 1 ] + -36 * f(x[ 2 ] + 16 * f(x[ 3 ] + -3 * f(x[ 4 ] ) + O(h^ 4 )f^( 5 )(z) err= 2.0 , h= 0.125 , deriv= 3.0 , x= 1.0 , pwr= 3 err= 3.0 , h= 0.125 , deriv= 4.0 , x= 1.0 , pwr= 4 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.0 , pwr= 5 err= 4.0 , h= 0.0625 , deriv= 5.0 , x= 1.0 , pwr= 5 err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 6 err= 5.0 , h= 0.0625 , deriv= 6.0 , x= 1.0 , pwr= 6 computing order= 1 , npoints= 5 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 12 h^ 1 )( -3 * f(x[ 0 ]) + -10 * f(x[ 1 ] + 18 * f(x[ 2 ] + -6 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 4 )f^( 5 )(z) err= 2.375 , h= 0.125 , deriv= 3.375 , x= 1.125 , pwr= 3 err= 3.5 , h= 0.125 , deriv= 4.5 , x= 1.125 , pwr= 4 err= 4.625 , h= 0.125 , deriv= 5.625 , x= 1.125 , pwr= 5 err= 4.3125 , h= 0.0625 , deriv= 5.3125 , x= 1.0625 , pwr= 5 err= 5.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 6 err= 5.375 , h= 0.0625 , deriv= 6.375 , x= 1.0625 , pwr= 6 computing order= 1 , npoints= 5 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 12 h^ 1 )( 1 * f(x[ 0 ]) + -8 * f(x[ 1 ] + 0 * f(x[ 2 ] + 8 * f(x[ 3 ] + -1 * f(x[ 4 ] ) + O(h^ 4 )f^( 5 )(z) err= 2.75 , h= 0.125 , deriv= 3.75 , x= 1.25 , pwr= 3 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.25 , pwr= 4 err= 5.25 , h= 0.125 , deriv= 6.25 , x= 1.25 , pwr= 5 err= 4.625 , h= 0.0625 , deriv= 5.625 , x= 1.125 , pwr= 5 err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 6 err= 5.75 , h= 0.0625 , deriv= 6.75 , x= 1.125 , pwr= 6 computing order= 1 , npoints= 5 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 12 h^ 1 )( -1 * f(x[ 0 ]) + 6 * f(x[ 1 ] + -18 * f(x[ 2 ] + 10 * f(x[ 3 ] + 3 * f(x[ 4 ] ) + O(h^ 4 )f^( 5 )(z) err= 3.125 , h= 0.125 , deriv= 4.125 , x= 1.375 , pwr= 3 err= 4.5 , h= 0.125 , deriv= 5.5 , x= 1.375 , pwr= 4 err= 5.875 , h= 0.125 , deriv= 6.875 , x= 1.375 , pwr= 5 err= 4.9375 , h= 0.0625 , deriv= 5.9375 , x= 1.1875 , pwr= 5 err= 7.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 6 err= 6.125 , h= 0.0625 , deriv= 7.125 , x= 1.1875 , pwr= 6 computing order= 1 , npoints= 5 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 12 h^ 1 )( 3 * f(x[ 0 ]) + -16 * f(x[ 1 ] + 36 * f(x[ 2 ] + -48 * f(x[ 3 ] + 25 * f(x[ 4 ] ) + O(h^ 4 )f^( 5 )(z) err= 3.5 , h= 0.125 , deriv= 4.5 , x= 1.5 , pwr= 3 err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.5 , pwr= 4 err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.5 , pwr= 5 err= 5.25 , h= 0.0625 , deriv= 6.25 , x= 1.25 , pwr= 5 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.5 , pwr= 6 err= 6.5 , h= 0.0625 , deriv= 7.5 , x= 1.25 , pwr= 6 computing order= 1 , npoints= 6 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 60 h^ 1 )( -137 * f(x[ 0 ]) + 300 * f(x[ 1 ] + -300 * f(x[ 2 ] + 200 * f(x[ 3 ] + -75 * f(x[ 4 ] + 12 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 3.0 , h= 0.125 , deriv= 4.0 , x= 1.0 , pwr= 4 err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.0 , pwr= 5 err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 6 err= 5.0 , h= 0.0625 , deriv= 6.0 , x= 1.0 , pwr= 6 err= 6.0 , h= 0.125 , deriv= 7.0 , x= 1.0 , pwr= 7 err= 6.0 , h= 0.0625 , deriv= 7.0 , x= 1.0 , pwr= 7 computing order= 1 , npoints= 6 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 60 h^ 1 )( -12 * f(x[ 0 ]) + -65 * f(x[ 1 ] + 120 * f(x[ 2 ] + -60 * f(x[ 3 ] + 20 * f(x[ 4 ] + -3 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 3.5 , h= 0.125 , deriv= 4.5 , x= 1.125 , pwr= 4 err= 4.625 , h= 0.125 , deriv= 5.625 , x= 1.125 , pwr= 5 err= 5.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 6 err= 5.375 , h= 0.0625 , deriv= 6.375 , x= 1.0625 , pwr= 6 err= 6.875 , h= 0.125 , deriv= 7.875 , x= 1.125 , pwr= 7 err= 6.4375 , h= 0.0625 , deriv= 7.4375 , x= 1.0625 , pwr= 7 computing order= 1 , npoints= 6 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 60 h^ 1 )( 3 * f(x[ 0 ]) + -30 * f(x[ 1 ] + -20 * f(x[ 2 ] + 60 * f(x[ 3 ] + -15 * f(x[ 4 ] + 2 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.25 , pwr= 4 err= 5.25 , h= 0.125 , deriv= 6.25 , x= 1.25 , pwr= 5 err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 6 err= 5.75 , h= 0.0625 , deriv= 6.75 , x= 1.125 , pwr= 6 err= 7.75 , h= 0.125 , deriv= 8.75 , x= 1.25 , pwr= 7 err= 6.875 , h= 0.0625 , deriv= 7.875 , x= 1.125 , pwr= 7 computing order= 1 , npoints= 6 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 60 h^ 1 )( -2 * f(x[ 0 ]) + 15 * f(x[ 1 ] + -60 * f(x[ 2 ] + 20 * f(x[ 3 ] + 30 * f(x[ 4 ] + -3 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 4.5 , h= 0.125 , deriv= 5.5 , x= 1.375 , pwr= 4 err= 5.875 , h= 0.125 , deriv= 6.875 , x= 1.375 , pwr= 5 err= 7.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 6 err= 6.125 , h= 0.0625 , deriv= 7.125 , x= 1.1875 , pwr= 6 err= 8.625 , h= 0.125 , deriv= 9.625 , x= 1.375 , pwr= 7 err= 7.3125 , h= 0.0625 , deriv= 8.3125 , x= 1.1875 , pwr= 7 computing order= 1 , npoints= 6 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 60 h^ 1 )( 3 * f(x[ 0 ]) + -20 * f(x[ 1 ] + 60 * f(x[ 2 ] + -120 * f(x[ 3 ] + 65 * f(x[ 4 ] + 12 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.5 , pwr= 4 err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.5 , pwr= 5 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.5 , pwr= 6 err= 6.5 , h= 0.0625 , deriv= 7.5 , x= 1.25 , pwr= 6 err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.5 , pwr= 7 err= 7.75 , h= 0.0625 , deriv= 8.75 , x= 1.25 , pwr= 7 computing order= 1 , npoints= 6 , at term= 5 f^( 1 )(x[ 5 ])=(1/ 60 h^ 1 )( -12 * f(x[ 0 ]) + 75 * f(x[ 1 ] + -200 * f(x[ 2 ] + 300 * f(x[ 3 ] + -300 * f(x[ 4 ] + 137 * f(x[ 5 ] ) + O(h^ 5 )f^( 6 )(z) err= 5.5 , h= 0.125 , deriv= 6.5 , x= 1.625 , pwr= 4 err= 7.125 , h= 0.125 , deriv= 8.125 , x= 1.625 , pwr= 5 err= 8.75 , h= 0.125 , deriv= 9.75 , x= 1.625 , pwr= 6 err= 6.875 , h= 0.0625 , deriv= 7.875 , x= 1.3125 , pwr= 6 err= 10.375 , h= 0.125 , deriv= 11.375 , x= 1.625 , pwr= 7 err= 8.1875 , h= 0.0625 , deriv= 9.1875 , x= 1.3125 , pwr= 7 computing order= 1 , npoints= 7 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 60 h^ 1 )( -147 * f(x[ 0 ]) + 360 * f(x[ 1 ] + -450 * f(x[ 2 ] + 400 * f(x[ 3 ] + -225 * f(x[ 4 ] + 72 * f(x[ 5 ] + -10 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 4.0 , h= 0.125 , deriv= 5.0 , x= 1.0 , pwr= 5 err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 6 err= 6.0 , h= 0.125 , deriv= 7.0 , x= 1.0 , pwr= 7 err= 6.0 , h= 0.0625 , deriv= 7.0 , x= 1.0 , pwr= 7 err= 7.0 , h= 0.125 , deriv= 8.0 , x= 1.0 , pwr= 8 err= 7.0 , h= 0.0625 , deriv= 8.0 , x= 1.0 , pwr= 8 computing order= 1 , npoints= 7 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 60 h^ 1 )( -10 * f(x[ 0 ]) + -77 * f(x[ 1 ] + 150 * f(x[ 2 ] + -100 * f(x[ 3 ] + 50 * f(x[ 4 ] + -15 * f(x[ 5 ] + 2 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 4.625 , h= 0.125 , deriv= 5.625 , x= 1.125 , pwr= 5 err= 5.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 6 err= 6.875 , h= 0.125 , deriv= 7.875 , x= 1.125 , pwr= 7 err= 6.4375 , h= 0.0625 , deriv= 7.4375 , x= 1.0625 , pwr= 7 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.125 , pwr= 8 err= 7.5 , h= 0.0625 , deriv= 8.5 , x= 1.0625 , pwr= 8 computing order= 1 , npoints= 7 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 60 h^ 1 )( 2 * f(x[ 0 ]) + -24 * f(x[ 1 ] + -35 * f(x[ 2 ] + 80 * f(x[ 3 ] + -30 * f(x[ 4 ] + 8 * f(x[ 5 ] + -1 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 5.25 , h= 0.125 , deriv= 6.25 , x= 1.25 , pwr= 5 err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 6 err= 7.75 , h= 0.125 , deriv= 8.75 , x= 1.25 , pwr= 7 err= 6.875 , h= 0.0625 , deriv= 7.875 , x= 1.125 , pwr= 7 err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.25 , pwr= 8 err= 8.0 , h= 0.0625 , deriv= 9.0 , x= 1.125 , pwr= 8 computing order= 1 , npoints= 7 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 60 h^ 1 )( -1 * f(x[ 0 ]) + 9 * f(x[ 1 ] + -45 * f(x[ 2 ] + 0 * f(x[ 3 ] + 45 * f(x[ 4 ] + -9 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 5.875 , h= 0.125 , deriv= 6.875 , x= 1.375 , pwr= 5 err= 7.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 6 err= 8.625 , h= 0.125 , deriv= 9.625 , x= 1.375 , pwr= 7 err= 7.3125 , h= 0.0625 , deriv= 8.3125 , x= 1.1875 , pwr= 7 err= 10.0 , h= 0.125 , deriv= 11.0 , x= 1.375 , pwr= 8 err= 8.5 , h= 0.0625 , deriv= 9.5 , x= 1.1875 , pwr= 8 computing order= 1 , npoints= 7 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 60 h^ 1 )( 1 * f(x[ 0 ]) + -8 * f(x[ 1 ] + 30 * f(x[ 2 ] + -80 * f(x[ 3 ] + 35 * f(x[ 4 ] + 24 * f(x[ 5 ] + -2 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.5 , pwr= 5 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.5 , pwr= 6 err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.5 , pwr= 7 err= 7.75 , h= 0.0625 , deriv= 8.75 , x= 1.25 , pwr= 7 err= 11.0 , h= 0.125 , deriv= 12.0 , x= 1.5 , pwr= 8 err= 9.0 , h= 0.0625 , deriv= 10.0 , x= 1.25 , pwr= 8 computing order= 1 , npoints= 7 , at term= 5 f^( 1 )(x[ 5 ])=(1/ 60 h^ 1 )( -2 * f(x[ 0 ]) + 15 * f(x[ 1 ] + -50 * f(x[ 2 ] + 100 * f(x[ 3 ] + -150 * f(x[ 4 ] + 77 * f(x[ 5 ] + 10 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 7.125 , h= 0.125 , deriv= 8.125 , x= 1.625 , pwr= 5 err= 8.75 , h= 0.125 , deriv= 9.75 , x= 1.625 , pwr= 6 err= 10.375 , h= 0.125 , deriv= 11.375 , x= 1.625 , pwr= 7 err= 8.1875 , h= 0.0625 , deriv= 9.1875 , x= 1.3125 , pwr= 7 err= 12.0 , h= 0.125 , deriv= 13.0 , x= 1.625 , pwr= 8 err= 9.5 , h= 0.0625 , deriv= 10.5 , x= 1.3125 , pwr= 8 computing order= 1 , npoints= 7 , at term= 6 f^( 1 )(x[ 6 ])=(1/ 60 h^ 1 )( 10 * f(x[ 0 ]) + -72 * f(x[ 1 ] + 225 * f(x[ 2 ] + -400 * f(x[ 3 ] + 450 * f(x[ 4 ] + -360 * f(x[ 5 ] + 147 * f(x[ 6 ] ) + O(h^ 6 )f^( 7 )(z) err= 7.75 , h= 0.125 , deriv= 8.75 , x= 1.75 , pwr= 5 err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.75 , pwr= 6 err= 11.25 , h= 0.125 , deriv= 12.25 , x= 1.75 , pwr= 7 err= 8.625 , h= 0.0625 , deriv= 9.625 , x= 1.375 , pwr= 7 err= 13.0 , h= 0.125 , deriv= 14.0 , x= 1.75 , pwr= 8 err= 10.0 , h= 0.0625 , deriv= 11.0 , x= 1.375 , pwr= 8 computing order= 1 , npoints= 8 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 420 h^ 1 )( -1089 * f(x[ 0 ]) + 2940 * f(x[ 1 ] + -4410 * f(x[ 2 ] + 4900 * f(x[ 3 ] + -3675 * f(x[ 4 ] + 1764 * f(x[ 5 ] + -490 * f(x[ 6 ] + 60 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 5.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 6 err= 6.0 , h= 0.125 , deriv= 7.0 , x= 1.0 , pwr= 7 err= 7.0 , h= 0.125 , deriv= 8.0 , x= 1.0 , pwr= 8 err= 7.0 , h= 0.0625 , deriv= 8.0 , x= 1.0 , pwr= 8 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.0 , pwr= 9 err= 8.0 , h= 0.0625 , deriv= 9.0 , x= 1.0 , pwr= 9 computing order= 1 , npoints= 8 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 420 h^ 1 )( -60 * f(x[ 0 ]) + -609 * f(x[ 1 ] + 1260 * f(x[ 2 ] + -1050 * f(x[ 3 ] + 700 * f(x[ 4 ] + -315 * f(x[ 5 ] + 84 * f(x[ 6 ] + -10 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 5.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 6 err= 6.875 , h= 0.125 , deriv= 7.875 , x= 1.125 , pwr= 7 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.125 , pwr= 8 err= 7.5 , h= 0.0625 , deriv= 8.5 , x= 1.0625 , pwr= 8 err= 9.125 , h= 0.125 , deriv= 10.125 , x= 1.125 , pwr= 9 err= 8.5625 , h= 0.0625 , deriv= 9.5625 , x= 1.0625 , pwr= 9 computing order= 1 , npoints= 8 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 420 h^ 1 )( 10 * f(x[ 0 ]) + -140 * f(x[ 1 ] + -329 * f(x[ 2 ] + 700 * f(x[ 3 ] + -350 * f(x[ 4 ] + 140 * f(x[ 5 ] + -35 * f(x[ 6 ] + 4 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 6.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 6 err= 7.75 , h= 0.125 , deriv= 8.75 , x= 1.25 , pwr= 7 err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.25 , pwr= 8 err= 8.0 , h= 0.0625 , deriv= 9.0 , x= 1.125 , pwr= 8 err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.25 , pwr= 9 err= 9.125 , h= 0.0625 , deriv= 10.125 , x= 1.125 , pwr= 9 computing order= 1 , npoints= 8 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 420 h^ 1 )( -4 * f(x[ 0 ]) + 42 * f(x[ 1 ] + -252 * f(x[ 2 ] + -105 * f(x[ 3 ] + 420 * f(x[ 4 ] + -126 * f(x[ 5 ] + 28 * f(x[ 6 ] + -3 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 7.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 6 err= 8.625 , h= 0.125 , deriv= 9.625 , x= 1.375 , pwr= 7 err= 10.0 , h= 0.125 , deriv= 11.0 , x= 1.375 , pwr= 8 err= 8.5 , h= 0.0625 , deriv= 9.5 , x= 1.1875 , pwr= 8 err= 11.375 , h= 0.125 , deriv= 12.375 , x= 1.375 , pwr= 9 err= 9.6875 , h= 0.0625 , deriv= 10.6875 , x= 1.1875 , pwr= 9 computing order= 1 , npoints= 8 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 420 h^ 1 )( 3 * f(x[ 0 ]) + -28 * f(x[ 1 ] + 126 * f(x[ 2 ] + -420 * f(x[ 3 ] + 105 * f(x[ 4 ] + 252 * f(x[ 5 ] + -42 * f(x[ 6 ] + 4 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.5 , pwr= 6 err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.5 , pwr= 7 err= 11.0 , h= 0.125 , deriv= 12.0 , x= 1.5 , pwr= 8 err= 9.0 , h= 0.0625 , deriv= 10.0 , x= 1.25 , pwr= 8 err= 12.5 , h= 0.125 , deriv= 13.5 , x= 1.5 , pwr= 9 err= 10.25 , h= 0.0625 , deriv= 11.25 , x= 1.25 , pwr= 9 computing order= 1 , npoints= 8 , at term= 5 f^( 1 )(x[ 5 ])=(1/ 420 h^ 1 )( -4 * f(x[ 0 ]) + 35 * f(x[ 1 ] + -140 * f(x[ 2 ] + 350 * f(x[ 3 ] + -700 * f(x[ 4 ] + 329 * f(x[ 5 ] + 140 * f(x[ 6 ] + -10 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 8.75 , h= 0.125 , deriv= 9.75 , x= 1.625 , pwr= 6 err= 10.375 , h= 0.125 , deriv= 11.375 , x= 1.625 , pwr= 7 err= 12.0 , h= 0.125 , deriv= 13.0 , x= 1.625 , pwr= 8 err= 9.5 , h= 0.0625 , deriv= 10.5 , x= 1.3125 , pwr= 8 err= 13.625 , h= 0.125 , deriv= 14.625 , x= 1.625 , pwr= 9 err= 10.8125 , h= 0.0625 , deriv= 11.8125 , x= 1.3125 , pwr= 9 computing order= 1 , npoints= 8 , at term= 6 f^( 1 )(x[ 6 ])=(1/ 420 h^ 1 )( 10 * f(x[ 0 ]) + -84 * f(x[ 1 ] + 315 * f(x[ 2 ] + -700 * f(x[ 3 ] + 1050 * f(x[ 4 ] + -1260 * f(x[ 5 ] + 609 * f(x[ 6 ] + 60 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.75 , pwr= 6 err= 11.25 , h= 0.125 , deriv= 12.25 , x= 1.75 , pwr= 7 err= 13.0 , h= 0.125 , deriv= 14.0 , x= 1.75 , pwr= 8 err= 10.0 , h= 0.0625 , deriv= 11.0 , x= 1.375 , pwr= 8 err= 14.75 , h= 0.125 , deriv= 15.75 , x= 1.75 , pwr= 9 err= 11.375 , h= 0.0625 , deriv= 12.375 , x= 1.375 , pwr= 9 computing order= 1 , npoints= 8 , at term= 7 f^( 1 )(x[ 7 ])=(1/ 420 h^ 1 )( -60 * f(x[ 0 ]) + 490 * f(x[ 1 ] + -1764 * f(x[ 2 ] + 3675 * f(x[ 3 ] + -4900 * f(x[ 4 ] + 4410 * f(x[ 5 ] + -2940 * f(x[ 6 ] + 1089 * f(x[ 7 ] ) + O(h^ 7 )f^( 8 )(z) err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.875 , pwr= 6 err= 12.125 , h= 0.125 , deriv= 13.125 , x= 1.875 , pwr= 7 err= 14.0 , h= 0.125 , deriv= 15.0 , x= 1.875 , pwr= 8 err= 10.5 , h= 0.0625 , deriv= 11.5 , x= 1.4375 , pwr= 8 err= 15.875 , h= 0.125 , deriv= 16.875 , x= 1.875 , pwr= 9 err= 11.9375 , h= 0.0625 , deriv= 12.9375 , x= 1.4375 , pwr= 9 computing order= 1 , npoints= 9 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 840 h^ 1 )( -2283 * f(x[ 0 ]) + 6720 * f(x[ 1 ] + -11760 * f(x[ 2 ] + 15680 * f(x[ 3 ] + -14700 * f(x[ 4 ] + 9408 * f(x[ 5 ] + -3920 * f(x[ 6 ] + 960 * f(x[ 7 ] + -105 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 6.0 , h= 0.125 , deriv= 7.0 , x= 1.0 , pwr= 7 err= 7.0 , h= 0.125 , deriv= 8.0 , x= 1.0 , pwr= 8 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.0 , pwr= 9 err= 8.0 , h= 0.0625 , deriv= 9.0 , x= 1.0 , pwr= 9 err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.0 , pwr= 10 err= 9.0 , h= 0.0625 , deriv= 10.0 , x= 1.0 , pwr= 10 computing order= 1 , npoints= 9 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 840 h^ 1 )( -105 * f(x[ 0 ]) + -1338 * f(x[ 1 ] + 2940 * f(x[ 2 ] + -2940 * f(x[ 3 ] + 2450 * f(x[ 4 ] + -1470 * f(x[ 5 ] + 588 * f(x[ 6 ] + -140 * f(x[ 7 ] + 15 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 6.875 , h= 0.125 , deriv= 7.875 , x= 1.125 , pwr= 7 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.125 , pwr= 8 err= 9.125 , h= 0.125 , deriv= 10.125 , x= 1.125 , pwr= 9 err= 8.5625 , h= 0.0625 , deriv= 9.5625 , x= 1.0625 , pwr= 9 err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.125 , pwr= 10 err= 9.625 , h= 0.0625 , deriv= 10.625 , x= 1.0625 , pwr= 10 computing order= 1 , npoints= 9 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 840 h^ 1 )( 15 * f(x[ 0 ]) + -240 * f(x[ 1 ] + -798 * f(x[ 2 ] + 1680 * f(x[ 3 ] + -1050 * f(x[ 4 ] + 560 * f(x[ 5 ] + -210 * f(x[ 6 ] + 48 * f(x[ 7 ] + -5 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 7.75 , h= 0.125 , deriv= 8.75 , x= 1.25 , pwr= 7 err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.25 , pwr= 8 err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.25 , pwr= 9 err= 9.125 , h= 0.0625 , deriv= 10.125 , x= 1.125 , pwr= 9 err= 11.5 , h= 0.125 , deriv= 12.5 , x= 1.25 , pwr= 10 err= 10.25 , h= 0.0625 , deriv= 11.25 , x= 1.125 , pwr= 10 computing order= 1 , npoints= 9 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 840 h^ 1 )( -5 * f(x[ 0 ]) + 60 * f(x[ 1 ] + -420 * f(x[ 2 ] + -378 * f(x[ 3 ] + 1050 * f(x[ 4 ] + -420 * f(x[ 5 ] + 140 * f(x[ 6 ] + -30 * f(x[ 7 ] + 3 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 8.625 , h= 0.125 , deriv= 9.625 , x= 1.375 , pwr= 7 err= 10.0 , h= 0.125 , deriv= 11.0 , x= 1.375 , pwr= 8 err= 11.375 , h= 0.125 , deriv= 12.375 , x= 1.375 , pwr= 9 err= 9.6875 , h= 0.0625 , deriv= 10.6875 , x= 1.1875 , pwr= 9 err= 12.75 , h= 0.125 , deriv= 13.75 , x= 1.375 , pwr= 10 err= 10.875 , h= 0.0625 , deriv= 11.875 , x= 1.1875 , pwr= 10 computing order= 1 , npoints= 9 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 840 h^ 1 )( 3 * f(x[ 0 ]) + -32 * f(x[ 1 ] + 168 * f(x[ 2 ] + -672 * f(x[ 3 ] + 0 * f(x[ 4 ] + 672 * f(x[ 5 ] + -168 * f(x[ 6 ] + 32 * f(x[ 7 ] + -3 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 9.5 , h= 0.125 , deriv= 10.5 , x= 1.5 , pwr= 7 err= 11.0 , h= 0.125 , deriv= 12.0 , x= 1.5 , pwr= 8 err= 12.5 , h= 0.125 , deriv= 13.5 , x= 1.5 , pwr= 9 err= 10.25 , h= 0.0625 , deriv= 11.25 , x= 1.25 , pwr= 9 err= 14.0 , h= 0.125 , deriv= 15.0 , x= 1.5 , pwr= 10 err= 11.5 , h= 0.0625 , deriv= 12.5 , x= 1.25 , pwr= 10 computing order= 1 , npoints= 9 , at term= 5 f^( 1 )(x[ 5 ])=(1/ 840 h^ 1 )( -3 * f(x[ 0 ]) + 30 * f(x[ 1 ] + -140 * f(x[ 2 ] + 420 * f(x[ 3 ] + -1050 * f(x[ 4 ] + 378 * f(x[ 5 ] + 420 * f(x[ 6 ] + -60 * f(x[ 7 ] + 5 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 10.375 , h= 0.125 , deriv= 11.375 , x= 1.625 , pwr= 7 err= 12.0 , h= 0.125 , deriv= 13.0 , x= 1.625 , pwr= 8 err= 13.625 , h= 0.125 , deriv= 14.625 , x= 1.625 , pwr= 9 err= 10.8125 , h= 0.0625 , deriv= 11.8125 , x= 1.3125 , pwr= 9 err= 15.25 , h= 0.125 , deriv= 16.25 , x= 1.625 , pwr= 10 err= 12.125 , h= 0.0625 , deriv= 13.125 , x= 1.3125 , pwr= 10 computing order= 1 , npoints= 9 , at term= 6 f^( 1 )(x[ 6 ])=(1/ 840 h^ 1 )( 5 * f(x[ 0 ]) + -48 * f(x[ 1 ] + 210 * f(x[ 2 ] + -560 * f(x[ 3 ] + 1050 * f(x[ 4 ] + -1680 * f(x[ 5 ] + 798 * f(x[ 6 ] + 240 * f(x[ 7 ] + -15 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 11.25 , h= 0.125 , deriv= 12.25 , x= 1.75 , pwr= 7 err= 13.0 , h= 0.125 , deriv= 14.0 , x= 1.75 , pwr= 8 err= 14.75 , h= 0.125 , deriv= 15.75 , x= 1.75 , pwr= 9 err= 11.375 , h= 0.0625 , deriv= 12.375 , x= 1.375 , pwr= 9 err= 16.5 , h= 0.125 , deriv= 17.5 , x= 1.75 , pwr= 10 err= 12.75 , h= 0.0625 , deriv= 13.75 , x= 1.375 , pwr= 10 computing order= 1 , npoints= 9 , at term= 7 f^( 1 )(x[ 7 ])=(1/ 840 h^ 1 )( -15 * f(x[ 0 ]) + 140 * f(x[ 1 ] + -588 * f(x[ 2 ] + 1470 * f(x[ 3 ] + -2450 * f(x[ 4 ] + 2940 * f(x[ 5 ] + -2940 * f(x[ 6 ] + 1338 * f(x[ 7 ] + 105 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 12.125 , h= 0.125 , deriv= 13.125 , x= 1.875 , pwr= 7 err= 14.0 , h= 0.125 , deriv= 15.0 , x= 1.875 , pwr= 8 err= 15.875 , h= 0.125 , deriv= 16.875 , x= 1.875 , pwr= 9 err= 11.9375 , h= 0.0625 , deriv= 12.9375 , x= 1.4375 , pwr= 9 err= 17.75 , h= 0.125 , deriv= 18.75 , x= 1.875 , pwr= 10 err= 13.375 , h= 0.0625 , deriv= 14.375 , x= 1.4375 , pwr= 10 computing order= 1 , npoints= 9 , at term= 8 f^( 1 )(x[ 8 ])=(1/ 840 h^ 1 )( 105 * f(x[ 0 ]) + -960 * f(x[ 1 ] + 3920 * f(x[ 2 ] + -9408 * f(x[ 3 ] + 14700 * f(x[ 4 ] + -15680 * f(x[ 5 ] + 11760 * f(x[ 6 ] + -6720 * f(x[ 7 ] + 2283 * f(x[ 8 ] ) + O(h^ 8 )f^( 9 )(z) err= 13.0 , h= 0.125 , deriv= 14.0 , x= 2.0 , pwr= 7 err= 15.0 , h= 0.125 , deriv= 16.0 , x= 2.0 , pwr= 8 err= 17.0 , h= 0.125 , deriv= 18.0 , x= 2.0 , pwr= 9 err= 12.5 , h= 0.0625 , deriv= 13.5 , x= 1.5 , pwr= 9 err= 19.0 , h= 0.125 , deriv= 20.0 , x= 2.0 , pwr= 10 err= 14.0 , h= 0.0625 , deriv= 15.0 , x= 1.5 , pwr= 10 computing order= 1 , npoints= 10 , at term= 0 f^( 1 )(x[ 0 ])=(1/ 2520 h^ 1 )( -7129 * f(x[ 0 ]) + 22680 * f(x[ 1 ] + -45360 * f(x[ 2 ] + 70560 * f(x[ 3 ] + -79380 * f(x[ 4 ] + 63504 * f(x[ 5 ] + -35280 * f(x[ 6 ] + 12960 * f(x[ 7 ] + -2835 * f(x[ 8 ] + 280 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 7.0 , h= 0.125 , deriv= 8.0 , x= 1.0 , pwr= 8 err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.0 , pwr= 9 err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.0 , pwr= 10 err= 9.0 , h= 0.0625 , deriv= 10.0 , x= 1.0 , pwr= 10 err= 10.0 , h= 0.125 , deriv= 11.0 , x= 1.0 , pwr= 11 err= 10.0 , h= 0.0625 , deriv= 11.0 , x= 1.0 , pwr= 11 computing order= 1 , npoints= 10 , at term= 1 f^( 1 )(x[ 1 ])=(1/ 2520 h^ 1 )( -280 * f(x[ 0 ]) + -4329 * f(x[ 1 ] + 10080 * f(x[ 2 ] + -11760 * f(x[ 3 ] + 11760 * f(x[ 4 ] + -8820 * f(x[ 5 ] + 4704 * f(x[ 6 ] + -1680 * f(x[ 7 ] + 360 * f(x[ 8 ] + -35 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 8.0 , h= 0.125 , deriv= 9.0 , x= 1.125 , pwr= 8 err= 9.125 , h= 0.125 , deriv= 10.125 , x= 1.125 , pwr= 9 err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.125 , pwr= 10 err= 9.625 , h= 0.0625 , deriv= 10.625 , x= 1.0625 , pwr= 10 err= 11.375 , h= 0.125 , deriv= 12.375 , x= 1.125 , pwr= 11 err= 10.6875 , h= 0.0625 , deriv= 11.6875 , x= 1.0625 , pwr= 11 computing order= 1 , npoints= 10 , at term= 2 f^( 1 )(x[ 2 ])=(1/ 2520 h^ 1 )( 35 * f(x[ 0 ]) + -630 * f(x[ 1 ] + -2754 * f(x[ 2 ] + 5880 * f(x[ 3 ] + -4410 * f(x[ 4 ] + 2940 * f(x[ 5 ] + -1470 * f(x[ 6 ] + 504 * f(x[ 7 ] + -105 * f(x[ 8 ] + 10 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 9.0 , h= 0.125 , deriv= 10.0 , x= 1.25 , pwr= 8 err= 10.25 , h= 0.125 , deriv= 11.25 , x= 1.25 , pwr= 9 err= 11.5 , h= 0.125 , deriv= 12.5 , x= 1.25 , pwr= 10 err= 10.25 , h= 0.0625 , deriv= 11.25 , x= 1.125 , pwr= 10 err= 12.75 , h= 0.125 , deriv= 13.75 , x= 1.25 , pwr= 11 err= 11.375 , h= 0.0625 , deriv= 12.375 , x= 1.125 , pwr= 11 computing order= 1 , npoints= 10 , at term= 3 f^( 1 )(x[ 3 ])=(1/ 2520 h^ 1 )( -10 * f(x[ 0 ]) + 135 * f(x[ 1 ] + -1080 * f(x[ 2 ] + -1554 * f(x[ 3 ] + 3780 * f(x[ 4 ] + -1890 * f(x[ 5 ] + 840 * f(x[ 6 ] + -270 * f(x[ 7 ] + 54 * f(x[ 8 ] + -5 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 10.0 , h= 0.125 , deriv= 11.0 , x= 1.375 , pwr= 8 err= 11.375 , h= 0.125 , deriv= 12.375 , x= 1.375 , pwr= 9 err= 12.75 , h= 0.125 , deriv= 13.75 , x= 1.375 , pwr= 10 err= 10.875 , h= 0.0625 , deriv= 11.875 , x= 1.1875 , pwr= 10 err= 14.125 , h= 0.125 , deriv= 15.125 , x= 1.375 , pwr= 11 err= 12.0625 , h= 0.0625 , deriv= 13.0625 , x= 1.1875 , pwr= 11 computing order= 1 , npoints= 10 , at term= 4 f^( 1 )(x[ 4 ])=(1/ 2520 h^ 1 )( 5 * f(x[ 0 ]) + -60 * f(x[ 1 ] + 360 * f(x[ 2 ] + -1680 * f(x[ 3 ] + -504 * f(x[ 4 ] + 2520 * f(x[ 5 ] + -840 * f(x[ 6 ] + 240 * f(x[ 7 ] + -45 * f(x[ 8 ] + 4 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 11.0 , h= 0.125 , deriv= 12.0 , x= 1.5 , pwr= 8 err= 12.5 , h= 0.125 , deriv= 13.5 , x= 1.5 , pwr= 9 err= 14.0 , h= 0.125 , deriv= 15.0 , x= 1.5 , pwr= 10 err= 11.5 , h= 0.0625 , deriv= 12.5 , x= 1.25 , pwr= 10 err= 15.5 , h= 0.125 , deriv= 16.5 , x= 1.5 , pwr= 11 err= 12.75 , h= 0.0625 , deriv= 13.75 , x= 1.25 , pwr= 11 computing order= 1 , npoints= 10 , at term= 5 f^( 1 )(x[ 5 ])=(1/ 2520 h^ 1 )( -4 * f(x[ 0 ]) + 45 * f(x[ 1 ] + -240 * f(x[ 2 ] + 840 * f(x[ 3 ] + -2520 * f(x[ 4 ] + 504 * f(x[ 5 ] + 1680 * f(x[ 6 ] + -360 * f(x[ 7 ] + 60 * f(x[ 8 ] + -5 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 12.0 , h= 0.125 , deriv= 13.0 , x= 1.625 , pwr= 8 err= 13.625 , h= 0.125 , deriv= 14.625 , x= 1.625 , pwr= 9 err= 15.25 , h= 0.125 , deriv= 16.25 , x= 1.625 , pwr= 10 err= 12.125 , h= 0.0625 , deriv= 13.125 , x= 1.3125 , pwr= 10 err= 16.875 , h= 0.125 , deriv= 17.875 , x= 1.625 , pwr= 11 err= 13.4375 , h= 0.0625 , deriv= 14.4375 , x= 1.3125 , pwr= 11 computing order= 1 , npoints= 10 , at term= 6 f^( 1 )(x[ 6 ])=(1/ 2520 h^ 1 )( 5 * f(x[ 0 ]) + -54 * f(x[ 1 ] + 270 * f(x[ 2 ] + -840 * f(x[ 3 ] + 1890 * f(x[ 4 ] + -3780 * f(x[ 5 ] + 1554 * f(x[ 6 ] + 1080 * f(x[ 7 ] + -135 * f(x[ 8 ] + 10 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 13.0 , h= 0.125 , deriv= 14.0 , x= 1.75 , pwr= 8 err= 14.75 , h= 0.125 , deriv= 15.75 , x= 1.75 , pwr= 9 err= 16.5 , h= 0.125 , deriv= 17.5 , x= 1.75 , pwr= 10 err= 12.75 , h= 0.0625 , deriv= 13.75 , x= 1.375 , pwr= 10 err= 18.25 , h= 0.125 , deriv= 19.25 , x= 1.75 , pwr= 11 err= 14.125 , h= 0.0625 , deriv= 15.125 , x= 1.375 , pwr= 11 computing order= 1 , npoints= 10 , at term= 7 f^( 1 )(x[ 7 ])=(1/ 2520 h^ 1 )( -10 * f(x[ 0 ]) + 105 * f(x[ 1 ] + -504 * f(x[ 2 ] + 1470 * f(x[ 3 ] + -2940 * f(x[ 4 ] + 4410 * f(x[ 5 ] + -5880 * f(x[ 6 ] + 2754 * f(x[ 7 ] + 630 * f(x[ 8 ] + -35 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 14.0 , h= 0.125 , deriv= 15.0 , x= 1.875 , pwr= 8 err= 15.875 , h= 0.125 , deriv= 16.875 , x= 1.875 , pwr= 9 err= 17.75 , h= 0.125 , deriv= 18.75 , x= 1.875 , pwr= 10 err= 13.375 , h= 0.0625 , deriv= 14.375 , x= 1.4375 , pwr= 10 err= 19.625 , h= 0.125 , deriv= 20.625 , x= 1.875 , pwr= 11 err= 14.8125 , h= 0.0625 , deriv= 15.8125 , x= 1.4375 , pwr= 11 computing order= 1 , npoints= 10 , at term= 8 f^( 1 )(x[ 8 ])=(1/ 2520 h^ 1 )( 35 * f(x[ 0 ]) + -360 * f(x[ 1 ] + 1680 * f(x[ 2 ] + -4704 * f(x[ 3 ] + 8820 * f(x[ 4 ] + -11760 * f(x[ 5 ] + 11760 * f(x[ 6 ] + -10080 * f(x[ 7 ] + 4329 * f(x[ 8 ] + 280 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 15.0 , h= 0.125 , deriv= 16.0 , x= 2.0 , pwr= 8 err= 17.0 , h= 0.125 , deriv= 18.0 , x= 2.0 , pwr= 9 err= 19.0 , h= 0.125 , deriv= 20.0 , x= 2.0 , pwr= 10 err= 14.0 , h= 0.0625 , deriv= 15.0 , x= 1.5 , pwr= 10 err= 21.0 , h= 0.125 , deriv= 22.0 , x= 2.0 , pwr= 11 err= 15.5 , h= 0.0625 , deriv= 16.5 , x= 1.5 , pwr= 11 computing order= 1 , npoints= 10 , at term= 9 f^( 1 )(x[ 9 ])=(1/ 2520 h^ 1 )( -280 * f(x[ 0 ]) + 2835 * f(x[ 1 ] + -12960 * f(x[ 2 ] + 35280 * f(x[ 3 ] + -63504 * f(x[ 4 ] + 79380 * f(x[ 5 ] + -70560 * f(x[ 6 ] + 45360 * f(x[ 7 ] + -22680 * f(x[ 8 ] + 7129 * f(x[ 9 ] ) + O(h^ 9 )f^( 10 )(z) err= 16.0 , h= 0.125 , deriv= 17.0 , x= 2.125 , pwr= 8 err= 18.125 , h= 0.125 , deriv= 19.125 , x= 2.125 , pwr= 9 err= 20.25 , h= 0.125 , deriv= 21.25 , x= 2.125 , pwr= 10 err= 14.625 , h= 0.0625 , deriv= 15.625 , x= 1.5625 , pwr= 10 err= 22.375 , h= 0.125 , deriv= 23.375 , x= 2.125 , pwr= 11 err= 16.1875 , h= 0.0625 , deriv= 17.1875 , x= 1.5625 , pwr= 11 computing order= 2 , npoints= 3 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 1 h^ 2 )( 1 * f(x[ 0 ]) + -2 * f(x[ 1 ] + 1 * f(x[ 2 ] ) + O(h^ 1 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.0 , pwr= 1 err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 6.0 , h= 0.0625 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 12.0 , h= 0.125 , deriv= 12.0 , x= 1.0 , pwr= 4 err= 12.0 , h= 0.0625 , deriv= 12.0 , x= 1.0 , pwr= 4 computing order= 2 , npoints= 3 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 1 h^ 2 )( 1 * f(x[ 0 ]) + -2 * f(x[ 1 ] + 1 * f(x[ 2 ] ) + O(h^ 1 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.125 , pwr= 1 err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.125 , pwr= 2 err= 6.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 3 err= 6.375 , h= 0.0625 , deriv= 6.375 , x= 1.0625 , pwr= 3 err= 13.5 , h= 0.125 , deriv= 13.5 , x= 1.125 , pwr= 4 err= 12.75 , h= 0.0625 , deriv= 12.75 , x= 1.0625 , pwr= 4 computing order= 2 , npoints= 3 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 1 h^ 2 )( 1 * f(x[ 0 ]) + -2 * f(x[ 1 ] + 1 * f(x[ 2 ] ) + O(h^ 1 )f^( 3 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.25 , pwr= 1 err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.25 , pwr= 2 err= 7.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 3 err= 6.75 , h= 0.0625 , deriv= 6.75 , x= 1.125 , pwr= 3 err= 15.0 , h= 0.125 , deriv= 15.0 , x= 1.25 , pwr= 4 err= 13.5 , h= 0.0625 , deriv= 13.5 , x= 1.125 , pwr= 4 computing order= 2 , npoints= 4 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 1 h^ 2 )( 2 * f(x[ 0 ]) + -5 * f(x[ 1 ] + 4 * f(x[ 2 ] + -1 * f(x[ 3 ] ) + O(h^ 2 )f^( 4 )(z) err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.0 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 12.0 , h= 0.125 , deriv= 12.0 , x= 1.0 , pwr= 4 err= 12.0 , h= 0.0625 , deriv= 12.0 , x= 1.0 , pwr= 4 err= 20.0 , h= 0.125 , deriv= 20.0 , x= 1.0 , pwr= 5 err= 20.0 , h= 0.0625 , deriv= 20.0 , x= 1.0 , pwr= 5 computing order= 2 , npoints= 4 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 1 h^ 2 )( 1 * f(x[ 0 ]) + -2 * f(x[ 1 ] + 1 * f(x[ 2 ] + 0 * f(x[ 3 ] ) + O(h^ 2 )f^( 4 )(z) err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.125 , pwr= 2 err= 6.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 3 err= 13.5 , h= 0.125 , deriv= 13.5 , x= 1.125 , pwr= 4 err= 12.75 , h= 0.0625 , deriv= 12.75 , x= 1.0625 , pwr= 4 err= 22.5 , h= 0.125 , deriv= 22.5 , x= 1.125 , pwr= 5 err= 21.25 , h= 0.0625 , deriv= 21.25 , x= 1.0625 , pwr= 5 computing order= 2 , npoints= 4 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 1 h^ 2 )( 0 * f(x[ 0 ]) + 1 * f(x[ 1 ] + -2 * f(x[ 2 ] + 1 * f(x[ 3 ] ) + O(h^ 2 )f^( 4 )(z) err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.25 , pwr= 2 err= 7.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 3 err= 15.0 , h= 0.125 , deriv= 15.0 , x= 1.25 , pwr= 4 err= 13.5 , h= 0.0625 , deriv= 13.5 , x= 1.125 , pwr= 4 err= 25.0 , h= 0.125 , deriv= 25.0 , x= 1.25 , pwr= 5 err= 22.5 , h= 0.0625 , deriv= 22.5 , x= 1.125 , pwr= 5 computing order= 2 , npoints= 4 , at term= 3 f^( 2 )(x[ 3 ])=(1/ 1 h^ 2 )( -1 * f(x[ 0 ]) + 4 * f(x[ 1 ] + -5 * f(x[ 2 ] + 2 * f(x[ 3 ] ) + O(h^ 2 )f^( 4 )(z) err= 2.0 , h= 0.125 , deriv= 2.0 , x= 1.375 , pwr= 2 err= 8.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 3 err= 16.5 , h= 0.125 , deriv= 16.5 , x= 1.375 , pwr= 4 err= 14.25 , h= 0.0625 , deriv= 14.25 , x= 1.1875 , pwr= 4 err= 27.5 , h= 0.125 , deriv= 27.5 , x= 1.375 , pwr= 5 err= 23.75 , h= 0.0625 , deriv= 23.75 , x= 1.1875 , pwr= 5 computing order= 2 , npoints= 5 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 12 h^ 2 )( 35 * f(x[ 0 ]) + -104 * f(x[ 1 ] + 114 * f(x[ 2 ] + -56 * f(x[ 3 ] + 11 * f(x[ 4 ] ) + O(h^ 3 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 12.0 , h= 0.125 , deriv= 12.0 , x= 1.0 , pwr= 4 err= 20.0 , h= 0.125 , deriv= 20.0 , x= 1.0 , pwr= 5 err= 20.0 , h= 0.0625 , deriv= 20.0 , x= 1.0 , pwr= 5 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.0 , pwr= 6 err= 30.0 , h= 0.0625 , deriv= 30.0 , x= 1.0 , pwr= 6 computing order= 2 , npoints= 5 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 12 h^ 2 )( 11 * f(x[ 0 ]) + -20 * f(x[ 1 ] + 6 * f(x[ 2 ] + 4 * f(x[ 3 ] + -1 * f(x[ 4 ] ) + O(h^ 3 )f^( 5 )(z) err= 6.75 , h= 0.125 , deriv= 6.75 , x= 1.125 , pwr= 3 err= 13.5 , h= 0.125 , deriv= 13.5 , x= 1.125 , pwr= 4 err= 22.5 , h= 0.125 , deriv= 22.5 , x= 1.125 , pwr= 5 err= 21.25 , h= 0.0625 , deriv= 21.25 , x= 1.0625 , pwr= 5 err= 33.75 , h= 0.125 , deriv= 33.75 , x= 1.125 , pwr= 6 err= 31.875 , h= 0.0625 , deriv= 31.875 , x= 1.0625 , pwr= 6 computing order= 2 , npoints= 5 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 12 h^ 2 )( -1 * f(x[ 0 ]) + 16 * f(x[ 1 ] + -30 * f(x[ 2 ] + 16 * f(x[ 3 ] + -1 * f(x[ 4 ] ) + O(h^ 3 )f^( 5 )(z) err= 7.5 , h= 0.125 , deriv= 7.5 , x= 1.25 , pwr= 3 err= 15.0 , h= 0.125 , deriv= 15.0 , x= 1.25 , pwr= 4 err= 25.0 , h= 0.125 , deriv= 25.0 , x= 1.25 , pwr= 5 err= 22.5 , h= 0.0625 , deriv= 22.5 , x= 1.125 , pwr= 5 err= 37.5 , h= 0.125 , deriv= 37.5 , x= 1.25 , pwr= 6 err= 33.75 , h= 0.0625 , deriv= 33.75 , x= 1.125 , pwr= 6 computing order= 2 , npoints= 5 , at term= 3 f^( 2 )(x[ 3 ])=(1/ 12 h^ 2 )( -1 * f(x[ 0 ]) + 4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -20 * f(x[ 3 ] + 11 * f(x[ 4 ] ) + O(h^ 3 )f^( 5 )(z) err= 8.25 , h= 0.125 , deriv= 8.25 , x= 1.375 , pwr= 3 err= 16.5 , h= 0.125 , deriv= 16.5 , x= 1.375 , pwr= 4 err= 27.5 , h= 0.125 , deriv= 27.5 , x= 1.375 , pwr= 5 err= 23.75 , h= 0.0625 , deriv= 23.75 , x= 1.1875 , pwr= 5 err= 41.25 , h= 0.125 , deriv= 41.25 , x= 1.375 , pwr= 6 err= 35.625 , h= 0.0625 , deriv= 35.625 , x= 1.1875 , pwr= 6 computing order= 2 , npoints= 5 , at term= 4 f^( 2 )(x[ 4 ])=(1/ 12 h^ 2 )( 11 * f(x[ 0 ]) + -56 * f(x[ 1 ] + 114 * f(x[ 2 ] + -104 * f(x[ 3 ] + 35 * f(x[ 4 ] ) + O(h^ 3 )f^( 5 )(z) err= 9.0 , h= 0.125 , deriv= 9.0 , x= 1.5 , pwr= 3 err= 18.0 , h= 0.125 , deriv= 18.0 , x= 1.5 , pwr= 4 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.5 , pwr= 5 err= 25.0 , h= 0.0625 , deriv= 25.0 , x= 1.25 , pwr= 5 err= 45.0 , h= 0.125 , deriv= 45.0 , x= 1.5 , pwr= 6 err= 37.5 , h= 0.0625 , deriv= 37.5 , x= 1.25 , pwr= 6 computing order= 2 , npoints= 6 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 12 h^ 2 )( 45 * f(x[ 0 ]) + -154 * f(x[ 1 ] + 214 * f(x[ 2 ] + -156 * f(x[ 3 ] + 61 * f(x[ 4 ] + -10 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 12.0 , h= 0.125 , deriv= 12.0 , x= 1.0 , pwr= 4 err= 20.0 , h= 0.125 , deriv= 20.0 , x= 1.0 , pwr= 5 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.0 , pwr= 6 err= 30.0 , h= 0.0625 , deriv= 30.0 , x= 1.0 , pwr= 6 err= 42.0 , h= 0.125 , deriv= 42.0 , x= 1.0 , pwr= 7 err= 42.0 , h= 0.0625 , deriv= 42.0 , x= 1.0 , pwr= 7 computing order= 2 , npoints= 6 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 12 h^ 2 )( 10 * f(x[ 0 ]) + -15 * f(x[ 1 ] + -4 * f(x[ 2 ] + 14 * f(x[ 3 ] + -6 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 13.5 , h= 0.125 , deriv= 13.5 , x= 1.125 , pwr= 4 err= 22.5 , h= 0.125 , deriv= 22.5 , x= 1.125 , pwr= 5 err= 33.75 , h= 0.125 , deriv= 33.75 , x= 1.125 , pwr= 6 err= 31.875 , h= 0.0625 , deriv= 31.875 , x= 1.0625 , pwr= 6 err= 47.25 , h= 0.125 , deriv= 47.25 , x= 1.125 , pwr= 7 err= 44.625 , h= 0.0625 , deriv= 44.625 , x= 1.0625 , pwr= 7 computing order= 2 , npoints= 6 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 12 h^ 2 )( -1 * f(x[ 0 ]) + 16 * f(x[ 1 ] + -30 * f(x[ 2 ] + 16 * f(x[ 3 ] + -1 * f(x[ 4 ] + 0 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 15.0 , h= 0.125 , deriv= 15.0 , x= 1.25 , pwr= 4 err= 25.0 , h= 0.125 , deriv= 25.0 , x= 1.25 , pwr= 5 err= 37.5 , h= 0.125 , deriv= 37.5 , x= 1.25 , pwr= 6 err= 33.75 , h= 0.0625 , deriv= 33.75 , x= 1.125 , pwr= 6 err= 52.5 , h= 0.125 , deriv= 52.5 , x= 1.25 , pwr= 7 err= 47.25 , h= 0.0625 , deriv= 47.25 , x= 1.125 , pwr= 7 computing order= 2 , npoints= 6 , at term= 3 f^( 2 )(x[ 3 ])=(1/ 12 h^ 2 )( 0 * f(x[ 0 ]) + -1 * f(x[ 1 ] + 16 * f(x[ 2 ] + -30 * f(x[ 3 ] + 16 * f(x[ 4 ] + -1 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 16.5 , h= 0.125 , deriv= 16.5 , x= 1.375 , pwr= 4 err= 27.5 , h= 0.125 , deriv= 27.5 , x= 1.375 , pwr= 5 err= 41.25 , h= 0.125 , deriv= 41.25 , x= 1.375 , pwr= 6 err= 35.625 , h= 0.0625 , deriv= 35.625 , x= 1.1875 , pwr= 6 err= 57.75 , h= 0.125 , deriv= 57.75 , x= 1.375 , pwr= 7 err= 49.875 , h= 0.0625 , deriv= 49.875 , x= 1.1875 , pwr= 7 computing order= 2 , npoints= 6 , at term= 4 f^( 2 )(x[ 4 ])=(1/ 12 h^ 2 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 14 * f(x[ 2 ] + -4 * f(x[ 3 ] + -15 * f(x[ 4 ] + 10 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 18.0 , h= 0.125 , deriv= 18.0 , x= 1.5 , pwr= 4 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.5 , pwr= 5 err= 45.0 , h= 0.125 , deriv= 45.0 , x= 1.5 , pwr= 6 err= 37.5 , h= 0.0625 , deriv= 37.5 , x= 1.25 , pwr= 6 err= 63.0 , h= 0.125 , deriv= 63.0 , x= 1.5 , pwr= 7 err= 52.5 , h= 0.0625 , deriv= 52.5 , x= 1.25 , pwr= 7 computing order= 2 , npoints= 6 , at term= 5 f^( 2 )(x[ 5 ])=(1/ 12 h^ 2 )( -10 * f(x[ 0 ]) + 61 * f(x[ 1 ] + -156 * f(x[ 2 ] + 214 * f(x[ 3 ] + -154 * f(x[ 4 ] + 45 * f(x[ 5 ] ) + O(h^ 4 )f^( 6 )(z) err= 19.5 , h= 0.125 , deriv= 19.5 , x= 1.625 , pwr= 4 err= 32.5 , h= 0.125 , deriv= 32.5 , x= 1.625 , pwr= 5 err= 48.75 , h= 0.125 , deriv= 48.75 , x= 1.625 , pwr= 6 err= 39.375 , h= 0.0625 , deriv= 39.375 , x= 1.3125 , pwr= 6 err= 68.25 , h= 0.125 , deriv= 68.25 , x= 1.625 , pwr= 7 err= 55.125 , h= 0.0625 , deriv= 55.125 , x= 1.3125 , pwr= 7 computing order= 2 , npoints= 7 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 180 h^ 2 )( 812 * f(x[ 0 ]) + -3132 * f(x[ 1 ] + 5265 * f(x[ 2 ] + -5080 * f(x[ 3 ] + 2970 * f(x[ 4 ] + -972 * f(x[ 5 ] + 137 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 20.0 , h= 0.125 , deriv= 20.0 , x= 1.0 , pwr= 5 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.0 , pwr= 6 err= 42.0 , h= 0.125 , deriv= 42.0 , x= 1.0 , pwr= 7 err= 42.0 , h= 0.0625 , deriv= 42.0 , x= 1.0 , pwr= 7 err= 56.0 , h= 0.125 , deriv= 56.0 , x= 1.0 , pwr= 8 err= 56.0 , h= 0.0625 , deriv= 56.0 , x= 1.0 , pwr= 8 computing order= 2 , npoints= 7 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 180 h^ 2 )( 137 * f(x[ 0 ]) + -147 * f(x[ 1 ] + -255 * f(x[ 2 ] + 470 * f(x[ 3 ] + -285 * f(x[ 4 ] + 93 * f(x[ 5 ] + -13 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 22.5 , h= 0.125 , deriv= 22.5 , x= 1.125 , pwr= 5 err= 33.75 , h= 0.125 , deriv= 33.75 , x= 1.125 , pwr= 6 err= 47.25 , h= 0.125 , deriv= 47.25 , x= 1.125 , pwr= 7 err= 44.625 , h= 0.0625 , deriv= 44.625 , x= 1.0625 , pwr= 7 err= 63.0 , h= 0.125 , deriv= 63.0 , x= 1.125 , pwr= 8 err= 59.5 , h= 0.0625 , deriv= 59.5 , x= 1.0625 , pwr= 8 computing order= 2 , npoints= 7 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 180 h^ 2 )( -13 * f(x[ 0 ]) + 228 * f(x[ 1 ] + -420 * f(x[ 2 ] + 200 * f(x[ 3 ] + 15 * f(x[ 4 ] + -12 * f(x[ 5 ] + 2 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 25.0 , h= 0.125 , deriv= 25.0 , x= 1.25 , pwr= 5 err= 37.5 , h= 0.125 , deriv= 37.5 , x= 1.25 , pwr= 6 err= 52.5 , h= 0.125 , deriv= 52.5 , x= 1.25 , pwr= 7 err= 47.25 , h= 0.0625 , deriv= 47.25 , x= 1.125 , pwr= 7 err= 70.0 , h= 0.125 , deriv= 70.0 , x= 1.25 , pwr= 8 err= 63.0 , h= 0.0625 , deriv= 63.0 , x= 1.125 , pwr= 8 computing order= 2 , npoints= 7 , at term= 3 f^( 2 )(x[ 3 ])=(1/ 180 h^ 2 )( 2 * f(x[ 0 ]) + -27 * f(x[ 1 ] + 270 * f(x[ 2 ] + -490 * f(x[ 3 ] + 270 * f(x[ 4 ] + -27 * f(x[ 5 ] + 2 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 27.5 , h= 0.125 , deriv= 27.5 , x= 1.375 , pwr= 5 err= 41.25 , h= 0.125 , deriv= 41.25 , x= 1.375 , pwr= 6 err= 57.75 , h= 0.125 , deriv= 57.75 , x= 1.375 , pwr= 7 err= 49.875 , h= 0.0625 , deriv= 49.875 , x= 1.1875 , pwr= 7 err= 77.0 , h= 0.125 , deriv= 77.0 , x= 1.375 , pwr= 8 err= 66.5 , h= 0.0625 , deriv= 66.5 , x= 1.1875 , pwr= 8 computing order= 2 , npoints= 7 , at term= 4 f^( 2 )(x[ 4 ])=(1/ 180 h^ 2 )( 2 * f(x[ 0 ]) + -12 * f(x[ 1 ] + 15 * f(x[ 2 ] + 200 * f(x[ 3 ] + -420 * f(x[ 4 ] + 228 * f(x[ 5 ] + -13 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.5 , pwr= 5 err= 45.0 , h= 0.125 , deriv= 45.0 , x= 1.5 , pwr= 6 err= 63.0 , h= 0.125 , deriv= 63.0 , x= 1.5 , pwr= 7 err= 52.5 , h= 0.0625 , deriv= 52.5 , x= 1.25 , pwr= 7 err= 84.0 , h= 0.125 , deriv= 84.0 , x= 1.5 , pwr= 8 err= 70.0 , h= 0.0625 , deriv= 70.0 , x= 1.25 , pwr= 8 computing order= 2 , npoints= 7 , at term= 5 f^( 2 )(x[ 5 ])=(1/ 180 h^ 2 )( -13 * f(x[ 0 ]) + 93 * f(x[ 1 ] + -285 * f(x[ 2 ] + 470 * f(x[ 3 ] + -255 * f(x[ 4 ] + -147 * f(x[ 5 ] + 137 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 32.5 , h= 0.125 , deriv= 32.5 , x= 1.625 , pwr= 5 err= 48.75 , h= 0.125 , deriv= 48.75 , x= 1.625 , pwr= 6 err= 68.25 , h= 0.125 , deriv= 68.25 , x= 1.625 , pwr= 7 err= 55.125 , h= 0.0625 , deriv= 55.125 , x= 1.3125 , pwr= 7 err= 91.0 , h= 0.125 , deriv= 91.0 , x= 1.625 , pwr= 8 err= 73.5 , h= 0.0625 , deriv= 73.5 , x= 1.3125 , pwr= 8 computing order= 2 , npoints= 7 , at term= 6 f^( 2 )(x[ 6 ])=(1/ 180 h^ 2 )( 137 * f(x[ 0 ]) + -972 * f(x[ 1 ] + 2970 * f(x[ 2 ] + -5080 * f(x[ 3 ] + 5265 * f(x[ 4 ] + -3132 * f(x[ 5 ] + 812 * f(x[ 6 ] ) + O(h^ 5 )f^( 7 )(z) err= 35.0 , h= 0.125 , deriv= 35.0 , x= 1.75 , pwr= 5 err= 52.5 , h= 0.125 , deriv= 52.5 , x= 1.75 , pwr= 6 err= 73.5 , h= 0.125 , deriv= 73.5 , x= 1.75 , pwr= 7 err= 57.75 , h= 0.0625 , deriv= 57.75 , x= 1.375 , pwr= 7 err= 98.0 , h= 0.125 , deriv= 98.0 , x= 1.75 , pwr= 8 err= 77.0 , h= 0.0625 , deriv= 77.0 , x= 1.375 , pwr= 8 computing order= 2 , npoints= 8 , at term= 0 f^( 2 )(x[ 0 ])=(1/ 180 h^ 2 )( 938 * f(x[ 0 ]) + -4014 * f(x[ 1 ] + 7911 * f(x[ 2 ] + -9490 * f(x[ 3 ] + 7380 * f(x[ 4 ] + -3618 * f(x[ 5 ] + 1019 * f(x[ 6 ] + -126 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.0 , pwr= 6 err= 42.0 , h= 0.125 , deriv= 42.0 , x= 1.0 , pwr= 7 err= 56.0 , h= 0.125 , deriv= 56.0 , x= 1.0 , pwr= 8 err= 56.0 , h= 0.0625 , deriv= 56.0 , x= 1.0 , pwr= 8 err= 72.0 , h= 0.125 , deriv= 72.0 , x= 1.0 , pwr= 9 err= 72.0 , h= 0.0625 , deriv= 72.0 , x= 1.0 , pwr= 9 computing order= 2 , npoints= 8 , at term= 1 f^( 2 )(x[ 1 ])=(1/ 180 h^ 2 )( 126 * f(x[ 0 ]) + -70 * f(x[ 1 ] + -486 * f(x[ 2 ] + 855 * f(x[ 3 ] + -670 * f(x[ 4 ] + 324 * f(x[ 5 ] + -90 * f(x[ 6 ] + 11 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 33.75 , h= 0.125 , deriv= 33.75 , x= 1.125 , pwr= 6 err= 47.25 , h= 0.125 , deriv= 47.25 , x= 1.125 , pwr= 7 err= 63.0 , h= 0.125 , deriv= 63.0 , x= 1.125 , pwr= 8 err= 59.5 , h= 0.0625 , deriv= 59.5 , x= 1.0625 , pwr= 8 err= 81.0 , h= 0.125 , deriv= 81.0 , x= 1.125 , pwr= 9 err= 76.5 , h= 0.0625 , deriv= 76.5 , x= 1.0625 , pwr= 9 computing order= 2 , npoints= 8 , at term= 2 f^( 2 )(x[ 2 ])=(1/ 180 h^ 2 )( -11 * f(x[ 0 ]) + 214 * f(x[ 1 ] + -378 * f(x[ 2 ] + 130 * f(x[ 3 ] + 85 * f(x[ 4 ] + -54 * f(x[ 5 ] + 16 * f(x[ 6 ] + -2 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 37.5 , h= 0.125 , deriv= 37.5 , x= 1.25 , pwr= 6 err= 52.5 , h= 0.125 , deriv= 52.5 , x= 1.25 , pwr= 7 err= 70.0 , h= 0.125 , deriv= 70.0 , x= 1.25 , pwr= 8 err= 63.0 , h= 0.0625 , deriv= 63.0 , x= 1.125 , pwr= 8 err= 90.0 , h= 0.125 , deriv= 90.0 , x= 1.25 , pwr= 9 err= 81.0 , h= 0.0625 , deriv= 81.0 , x= 1.125 , pwr= 9 computing order= 2 , npoints= 8 , at term= 3 f^( 2 )(x[ 3 ])=(1/ 180 h^ 2 )( 2 * f(x[ 0 ]) + -27 * f(x[ 1 ] + 270 * f(x[ 2 ] + -490 * f(x[ 3 ] + 270 * f(x[ 4 ] + -27 * f(x[ 5 ] + 2 * f(x[ 6 ] + 0 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 41.25 , h= 0.125 , deriv= 41.25 , x= 1.375 , pwr= 6 err= 57.75 , h= 0.125 , deriv= 57.75 , x= 1.375 , pwr= 7 err= 77.0 , h= 0.125 , deriv= 77.0 , x= 1.375 , pwr= 8 err= 66.5 , h= 0.0625 , deriv= 66.5 , x= 1.1875 , pwr= 8 err= 99.0 , h= 0.125 , deriv= 99.0 , x= 1.375 , pwr= 9 err= 85.5 , h= 0.0625 , deriv= 85.5 , x= 1.1875 , pwr= 9 computing order= 2 , npoints= 8 , at term= 4 f^( 2 )(x[ 4 ])=(1/ 180 h^ 2 )( 0 * f(x[ 0 ]) + 2 * f(x[ 1 ] + -27 * f(x[ 2 ] + 270 * f(x[ 3 ] + -490 * f(x[ 4 ] + 270 * f(x[ 5 ] + -27 * f(x[ 6 ] + 2 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 45.0 , h= 0.125 , deriv= 45.0 , x= 1.5 , pwr= 6 err= 63.0 , h= 0.125 , deriv= 63.0 , x= 1.5 , pwr= 7 err= 84.0 , h= 0.125 , deriv= 84.0 , x= 1.5 , pwr= 8 err= 70.0 , h= 0.0625 , deriv= 70.0 , x= 1.25 , pwr= 8 err= 108.0 , h= 0.125 , deriv= 108.0 , x= 1.5 , pwr= 9 err= 90.0 , h= 0.0625 , deriv= 90.0 , x= 1.25 , pwr= 9 computing order= 2 , npoints= 8 , at term= 5 f^( 2 )(x[ 5 ])=(1/ 180 h^ 2 )( -2 * f(x[ 0 ]) + 16 * f(x[ 1 ] + -54 * f(x[ 2 ] + 85 * f(x[ 3 ] + 130 * f(x[ 4 ] + -378 * f(x[ 5 ] + 214 * f(x[ 6 ] + -11 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 48.75 , h= 0.125 , deriv= 48.75 , x= 1.625 , pwr= 6 err= 68.25 , h= 0.125 , deriv= 68.25 , x= 1.625 , pwr= 7 err= 91.0 , h= 0.125 , deriv= 91.0 , x= 1.625 , pwr= 8 err= 73.5 , h= 0.0625 , deriv= 73.5 , x= 1.3125 , pwr= 8 err= 117.0 , h= 0.125 , deriv= 117.0 , x= 1.625 , pwr= 9 err= 94.5 , h= 0.0625 , deriv= 94.5 , x= 1.3125 , pwr= 9 computing order= 2 , npoints= 8 , at term= 6 f^( 2 )(x[ 6 ])=(1/ 180 h^ 2 )( 11 * f(x[ 0 ]) + -90 * f(x[ 1 ] + 324 * f(x[ 2 ] + -670 * f(x[ 3 ] + 855 * f(x[ 4 ] + -486 * f(x[ 5 ] + -70 * f(x[ 6 ] + 126 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 52.5 , h= 0.125 , deriv= 52.5 , x= 1.75 , pwr= 6 err= 73.5 , h= 0.125 , deriv= 73.5 , x= 1.75 , pwr= 7 err= 98.0 , h= 0.125 , deriv= 98.0 , x= 1.75 , pwr= 8 err= 77.0 , h= 0.0625 , deriv= 77.0 , x= 1.375 , pwr= 8 err= 126.0 , h= 0.125 , deriv= 126.0 , x= 1.75 , pwr= 9 err= 99.0 , h= 0.0625 , deriv= 99.0 , x= 1.375 , pwr= 9 computing order= 2 , npoints= 8 , at term= 7 f^( 2 )(x[ 7 ])=(1/ 180 h^ 2 )( -126 * f(x[ 0 ]) + 1019 * f(x[ 1 ] + -3618 * f(x[ 2 ] + 7380 * f(x[ 3 ] + -9490 * f(x[ 4 ] + 7911 * f(x[ 5 ] + -4014 * f(x[ 6 ] + 938 * f(x[ 7 ] ) + O(h^ 6 )f^( 8 )(z) err= 56.25 , h= 0.125 , deriv= 56.25 , x= 1.875 , pwr= 6 err= 78.75 , h= 0.125 , deriv= 78.75 , x= 1.875 , pwr= 7 err= 105.0 , h= 0.125 , deriv= 105.0 , x= 1.875 , pwr= 8 err= 80.5 , h= 0.0625 , deriv= 80.5 , x= 1.4375 , pwr= 8 err= 135.0 , h= 0.125 , deriv= 135.0 , x= 1.875 , pwr= 9 err= 103.5 , h= 0.0625 , deriv= 103.5 , x= 1.4375 , pwr= 9 computing order= 3 , npoints= 4 , at term= 0 f^( 3 )(x[ 0 ])=(1/ 1 h^ 3 )( -1 * f(x[ 0 ]) + 3 * f(x[ 1 ] + -3 * f(x[ 2 ] + 1 * f(x[ 3 ] ) + O(h^ 1 )f^( 4 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.0 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 24.0 , h= 0.125 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 60.0 , h= 0.125 , deriv= 60.0 , x= 1.0 , pwr= 5 err= 60.0 , h= 0.0625 , deriv= 60.0 , x= 1.0 , pwr= 5 computing order= 3 , npoints= 4 , at term= 1 f^( 3 )(x[ 1 ])=(1/ 1 h^ 3 )( -1 * f(x[ 0 ]) + 3 * f(x[ 1 ] + -3 * f(x[ 2 ] + 1 * f(x[ 3 ] ) + O(h^ 1 )f^( 4 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.125 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.125 , pwr= 3 err= 27.0 , h= 0.125 , deriv= 27.0 , x= 1.125 , pwr= 4 err= 25.5 , h= 0.0625 , deriv= 25.5 , x= 1.0625 , pwr= 4 err= 67.5 , h= 0.125 , deriv= 67.5 , x= 1.125 , pwr= 5 err= 63.75 , h= 0.0625 , deriv= 63.75 , x= 1.0625 , pwr= 5 computing order= 3 , npoints= 4 , at term= 2 f^( 3 )(x[ 2 ])=(1/ 1 h^ 3 )( -1 * f(x[ 0 ]) + 3 * f(x[ 1 ] + -3 * f(x[ 2 ] + 1 * f(x[ 3 ] ) + O(h^ 1 )f^( 4 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.25 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.25 , pwr= 3 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.25 , pwr= 4 err= 27.0 , h= 0.0625 , deriv= 27.0 , x= 1.125 , pwr= 4 err= 75.0 , h= 0.125 , deriv= 75.0 , x= 1.25 , pwr= 5 err= 67.5 , h= 0.0625 , deriv= 67.5 , x= 1.125 , pwr= 5 computing order= 3 , npoints= 4 , at term= 3 f^( 3 )(x[ 3 ])=(1/ 1 h^ 3 )( -1 * f(x[ 0 ]) + 3 * f(x[ 1 ] + -3 * f(x[ 2 ] + 1 * f(x[ 3 ] ) + O(h^ 1 )f^( 4 )(z) err= 0.0 , h= 0.125 , deriv= 0.0 , x= 1.375 , pwr= 2 err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.375 , pwr= 3 err= 33.0 , h= 0.125 , deriv= 33.0 , x= 1.375 , pwr= 4 err= 28.5 , h= 0.0625 , deriv= 28.5 , x= 1.1875 , pwr= 4 err= 82.5 , h= 0.125 , deriv= 82.5 , x= 1.375 , pwr= 5 err= 71.25 , h= 0.0625 , deriv= 71.25 , x= 1.1875 , pwr= 5 computing order= 3 , npoints= 5 , at term= 0 f^( 3 )(x[ 0 ])=(1/ 2 h^ 3 )( -5 * f(x[ 0 ]) + 18 * f(x[ 1 ] + -24 * f(x[ 2 ] + 14 * f(x[ 3 ] + -3 * f(x[ 4 ] ) + O(h^ 2 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.0 , pwr= 3 err= 24.0 , h= 0.125 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 60.0 , h= 0.125 , deriv= 60.0 , x= 1.0 , pwr= 5 err= 60.0 , h= 0.0625 , deriv= 60.0 , x= 1.0 , pwr= 5 err= 120.0 , h= 0.125 , deriv= 120.0 , x= 1.0 , pwr= 6 err= 120.0 , h= 0.0625 , deriv= 120.0 , x= 1.0 , pwr= 6 computing order= 3 , npoints= 5 , at term= 1 f^( 3 )(x[ 1 ])=(1/ 2 h^ 3 )( -3 * f(x[ 0 ]) + 10 * f(x[ 1 ] + -12 * f(x[ 2 ] + 6 * f(x[ 3 ] + -1 * f(x[ 4 ] ) + O(h^ 2 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.125 , pwr= 3 err= 27.0 , h= 0.125 , deriv= 27.0 , x= 1.125 , pwr= 4 err= 67.5 , h= 0.125 , deriv= 67.5 , x= 1.125 , pwr= 5 err= 63.75 , h= 0.0625 , deriv= 63.75 , x= 1.0625 , pwr= 5 err= 135.0 , h= 0.125 , deriv= 135.0 , x= 1.125 , pwr= 6 err= 127.5 , h= 0.0625 , deriv= 127.5 , x= 1.0625 , pwr= 6 computing order= 3 , npoints= 5 , at term= 2 f^( 3 )(x[ 2 ])=(1/ 2 h^ 3 )( -1 * f(x[ 0 ]) + 2 * f(x[ 1 ] + 0 * f(x[ 2 ] + -2 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 2 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.25 , pwr= 3 err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.25 , pwr= 4 err= 75.0 , h= 0.125 , deriv= 75.0 , x= 1.25 , pwr= 5 err= 67.5 , h= 0.0625 , deriv= 67.5 , x= 1.125 , pwr= 5 err= 150.0 , h= 0.125 , deriv= 150.0 , x= 1.25 , pwr= 6 err= 135.0 , h= 0.0625 , deriv= 135.0 , x= 1.125 , pwr= 6 computing order= 3 , npoints= 5 , at term= 3 f^( 3 )(x[ 3 ])=(1/ 2 h^ 3 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 12 * f(x[ 2 ] + -10 * f(x[ 3 ] + 3 * f(x[ 4 ] ) + O(h^ 2 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.375 , pwr= 3 err= 33.0 , h= 0.125 , deriv= 33.0 , x= 1.375 , pwr= 4 err= 82.5 , h= 0.125 , deriv= 82.5 , x= 1.375 , pwr= 5 err= 71.25 , h= 0.0625 , deriv= 71.25 , x= 1.1875 , pwr= 5 err= 165.0 , h= 0.125 , deriv= 165.0 , x= 1.375 , pwr= 6 err= 142.5 , h= 0.0625 , deriv= 142.5 , x= 1.1875 , pwr= 6 computing order= 3 , npoints= 5 , at term= 4 f^( 3 )(x[ 4 ])=(1/ 2 h^ 3 )( 3 * f(x[ 0 ]) + -14 * f(x[ 1 ] + 24 * f(x[ 2 ] + -18 * f(x[ 3 ] + 5 * f(x[ 4 ] ) + O(h^ 2 )f^( 5 )(z) err= 6.0 , h= 0.125 , deriv= 6.0 , x= 1.5 , pwr= 3 err= 36.0 , h= 0.125 , deriv= 36.0 , x= 1.5 , pwr= 4 err= 90.0 , h= 0.125 , deriv= 90.0 , x= 1.5 , pwr= 5 err= 75.0 , h= 0.0625 , deriv= 75.0 , x= 1.25 , pwr= 5 err= 180.0 , h= 0.125 , deriv= 180.0 , x= 1.5 , pwr= 6 err= 150.0 , h= 0.0625 , deriv= 150.0 , x= 1.25 , pwr= 6 computing order= 3 , npoints= 6 , at term= 0 f^( 3 )(x[ 0 ])=(1/ 4 h^ 3 )( -17 * f(x[ 0 ]) + 71 * f(x[ 1 ] + -118 * f(x[ 2 ] + 98 * f(x[ 3 ] + -41 * f(x[ 4 ] + 7 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 24.0 , h= 0.125 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 60.0 , h= 0.125 , deriv= 60.0 , x= 1.0 , pwr= 5 err= 120.0 , h= 0.125 , deriv= 120.0 , x= 1.0 , pwr= 6 err= 120.0 , h= 0.0625 , deriv= 120.0 , x= 1.0 , pwr= 6 err= 210.0 , h= 0.125 , deriv= 210.0 , x= 1.0 , pwr= 7 err= 210.0 , h= 0.0625 , deriv= 210.0 , x= 1.0 , pwr= 7 computing order= 3 , npoints= 6 , at term= 1 f^( 3 )(x[ 1 ])=(1/ 4 h^ 3 )( -7 * f(x[ 0 ]) + 25 * f(x[ 1 ] + -34 * f(x[ 2 ] + 22 * f(x[ 3 ] + -7 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 27.0 , h= 0.125 , deriv= 27.0 , x= 1.125 , pwr= 4 err= 67.5 , h= 0.125 , deriv= 67.5 , x= 1.125 , pwr= 5 err= 135.0 , h= 0.125 , deriv= 135.0 , x= 1.125 , pwr= 6 err= 127.5 , h= 0.0625 , deriv= 127.5 , x= 1.0625 , pwr= 6 err= 236.25 , h= 0.125 , deriv= 236.25 , x= 1.125 , pwr= 7 err= 223.125 , h= 0.0625 , deriv= 223.125 , x= 1.0625 , pwr= 7 computing order= 3 , npoints= 6 , at term= 2 f^( 3 )(x[ 2 ])=(1/ 4 h^ 3 )( -1 * f(x[ 0 ]) + -1 * f(x[ 1 ] + 10 * f(x[ 2 ] + -14 * f(x[ 3 ] + 7 * f(x[ 4 ] + -1 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 30.0 , h= 0.125 , deriv= 30.0 , x= 1.25 , pwr= 4 err= 75.0 , h= 0.125 , deriv= 75.0 , x= 1.25 , pwr= 5 err= 150.0 , h= 0.125 , deriv= 150.0 , x= 1.25 , pwr= 6 err= 135.0 , h= 0.0625 , deriv= 135.0 , x= 1.125 , pwr= 6 err= 262.5 , h= 0.125 , deriv= 262.5 , x= 1.25 , pwr= 7 err= 236.25 , h= 0.0625 , deriv= 236.25 , x= 1.125 , pwr= 7 computing order= 3 , npoints= 6 , at term= 3 f^( 3 )(x[ 3 ])=(1/ 4 h^ 3 )( 1 * f(x[ 0 ]) + -7 * f(x[ 1 ] + 14 * f(x[ 2 ] + -10 * f(x[ 3 ] + 1 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 33.0 , h= 0.125 , deriv= 33.0 , x= 1.375 , pwr= 4 err= 82.5 , h= 0.125 , deriv= 82.5 , x= 1.375 , pwr= 5 err= 165.0 , h= 0.125 , deriv= 165.0 , x= 1.375 , pwr= 6 err= 142.5 , h= 0.0625 , deriv= 142.5 , x= 1.1875 , pwr= 6 err= 288.75 , h= 0.125 , deriv= 288.75 , x= 1.375 , pwr= 7 err= 249.375 , h= 0.0625 , deriv= 249.375 , x= 1.1875 , pwr= 7 computing order= 3 , npoints= 6 , at term= 4 f^( 3 )(x[ 4 ])=(1/ 4 h^ 3 )( -1 * f(x[ 0 ]) + 7 * f(x[ 1 ] + -22 * f(x[ 2 ] + 34 * f(x[ 3 ] + -25 * f(x[ 4 ] + 7 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 36.0 , h= 0.125 , deriv= 36.0 , x= 1.5 , pwr= 4 err= 90.0 , h= 0.125 , deriv= 90.0 , x= 1.5 , pwr= 5 err= 180.0 , h= 0.125 , deriv= 180.0 , x= 1.5 , pwr= 6 err= 150.0 , h= 0.0625 , deriv= 150.0 , x= 1.25 , pwr= 6 err= 315.0 , h= 0.125 , deriv= 315.0 , x= 1.5 , pwr= 7 err= 262.5 , h= 0.0625 , deriv= 262.5 , x= 1.25 , pwr= 7 computing order= 3 , npoints= 6 , at term= 5 f^( 3 )(x[ 5 ])=(1/ 4 h^ 3 )( -7 * f(x[ 0 ]) + 41 * f(x[ 1 ] + -98 * f(x[ 2 ] + 118 * f(x[ 3 ] + -71 * f(x[ 4 ] + 17 * f(x[ 5 ] ) + O(h^ 3 )f^( 6 )(z) err= 39.0 , h= 0.125 , deriv= 39.0 , x= 1.625 , pwr= 4 err= 97.5 , h= 0.125 , deriv= 97.5 , x= 1.625 , pwr= 5 err= 195.0 , h= 0.125 , deriv= 195.0 , x= 1.625 , pwr= 6 err= 157.5 , h= 0.0625 , deriv= 157.5 , x= 1.3125 , pwr= 6 err= 341.25 , h= 0.125 , deriv= 341.25 , x= 1.625 , pwr= 7 err= 275.625 , h= 0.0625 , deriv= 275.625 , x= 1.3125 , pwr= 7 computing order= 4 , npoints= 5 , at term= 0 f^( 4 )(x[ 0 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 1 )f^( 5 )(z) err= 0.0 , h= 0.0625 , deriv= 0.0 , x= 1.0 , pwr= 3 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 120.0 , h= 0.0625 , deriv= 120.0 , x= 1.0 , pwr= 5 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.0 , pwr= 5 err= 360.0 , h= 0.0625 , deriv= 360.0 , x= 1.0 , pwr= 6 err= 360.0 , h= 0.03125 , deriv= 360.0 , x= 1.0 , pwr= 6 err= 360.0 , h= 0.015625 , deriv= 360.0 , x= 1.0 , pwr= 6 computing order= 4 , npoints= 5 , at term= 1 f^( 4 )(x[ 1 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 1 )f^( 5 )(z) err= 0.0 , h= 0.0625 , deriv= 0.0 , x= 1.0625 , pwr= 3 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.0625 , pwr= 4 err= 127.5 , h= 0.0625 , deriv= 127.5 , x= 1.0625 , pwr= 5 err= 123.75 , h= 0.03125 , deriv= 123.75 , x= 1.03125 , pwr= 5 err= 382.5 , h= 0.0625 , deriv= 382.5 , x= 1.0625 , pwr= 6 err= 371.25 , h= 0.03125 , deriv= 371.25 , x= 1.03125 , pwr= 6 err= 365.625 , h= 0.015625 , deriv= 365.625 , x= 1.015625 , pwr= 6 computing order= 4 , npoints= 5 , at term= 2 f^( 4 )(x[ 2 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 1 )f^( 5 )(z) err= 0.0 , h= 0.0625 , deriv= 0.0 , x= 1.125 , pwr= 3 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.125 , pwr= 4 err= 135.0 , h= 0.0625 , deriv= 135.0 , x= 1.125 , pwr= 5 err= 127.5 , h= 0.03125 , deriv= 127.5 , x= 1.0625 , pwr= 5 err= 405.0 , h= 0.0625 , deriv= 405.0 , x= 1.125 , pwr= 6 err= 382.5 , h= 0.03125 , deriv= 382.5 , x= 1.0625 , pwr= 6 err= 371.25 , h= 0.015625 , deriv= 371.25 , x= 1.03125 , pwr= 6 computing order= 4 , npoints= 5 , at term= 3 f^( 4 )(x[ 3 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 1 )f^( 5 )(z) err= 0.0 , h= 0.0625 , deriv= 0.0 , x= 1.1875 , pwr= 3 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.1875 , pwr= 4 err= 142.5 , h= 0.0625 , deriv= 142.5 , x= 1.1875 , pwr= 5 err= 131.25 , h= 0.03125 , deriv= 131.25 , x= 1.09375 , pwr= 5 err= 427.5 , h= 0.0625 , deriv= 427.5 , x= 1.1875 , pwr= 6 err= 393.75 , h= 0.03125 , deriv= 393.75 , x= 1.09375 , pwr= 6 err= 376.875 , h= 0.015625 , deriv= 376.875 , x= 1.046875 , pwr= 6 computing order= 4 , npoints= 5 , at term= 4 f^( 4 )(x[ 4 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] ) + O(h^ 1 )f^( 5 )(z) err= 0.0 , h= 0.0625 , deriv= 0.0 , x= 1.25 , pwr= 3 err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.25 , pwr= 4 err= 150.0 , h= 0.0625 , deriv= 150.0 , x= 1.25 , pwr= 5 err= 135.0 , h= 0.03125 , deriv= 135.0 , x= 1.125 , pwr= 5 err= 450.0 , h= 0.0625 , deriv= 450.0 , x= 1.25 , pwr= 6 err= 405.0 , h= 0.03125 , deriv= 405.0 , x= 1.125 , pwr= 6 err= 382.5 , h= 0.015625 , deriv= 382.5 , x= 1.0625 , pwr= 6 computing order= 4 , npoints= 6 , at term= 0 f^( 4 )(x[ 0 ])=(1/ 1 h^ 4 )( 3 * f(x[ 0 ]) + -14 * f(x[ 1 ] + 26 * f(x[ 2 ] + -24 * f(x[ 3 ] + 11 * f(x[ 4 ] + -2 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.0 , pwr= 4 err= 120.0 , h= 0.0625 , deriv= 120.0 , x= 1.0 , pwr= 5 err= 360.0 , h= 0.0625 , deriv= 360.0 , x= 1.0 , pwr= 6 err= 360.0 , h= 0.03125 , deriv= 360.0 , x= 1.0 , pwr= 6 err= 840.0 , h= 0.0625 , deriv= 840.0 , x= 1.0 , pwr= 7 err= 840.0 , h= 0.03125 , deriv= 840.0 , x= 1.0 , pwr= 7 err= 840.0 , h= 0.015625 , deriv= 840.0 , x= 1.0 , pwr= 7 computing order= 4 , npoints= 6 , at term= 1 f^( 4 )(x[ 1 ])=(1/ 1 h^ 4 )( 2 * f(x[ 0 ]) + -9 * f(x[ 1 ] + 16 * f(x[ 2 ] + -14 * f(x[ 3 ] + 6 * f(x[ 4 ] + -1 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.0625 , pwr= 4 err= 127.5 , h= 0.0625 , deriv= 127.5 , x= 1.0625 , pwr= 5 err= 382.5 , h= 0.0625 , deriv= 382.5 , x= 1.0625 , pwr= 6 err= 371.25 , h= 0.03125 , deriv= 371.25 , x= 1.03125 , pwr= 6 err= 892.5 , h= 0.0625 , deriv= 892.5 , x= 1.0625 , pwr= 7 err= 866.25 , h= 0.03125 , deriv= 866.25 , x= 1.03125 , pwr= 7 err= 853.125 , h= 0.015625 , deriv= 853.125 , x= 1.015625 , pwr= 7 computing order= 4 , npoints= 6 , at term= 2 f^( 4 )(x[ 2 ])=(1/ 1 h^ 4 )( 1 * f(x[ 0 ]) + -4 * f(x[ 1 ] + 6 * f(x[ 2 ] + -4 * f(x[ 3 ] + 1 * f(x[ 4 ] + 0 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.125 , pwr= 4 err= 135.0 , h= 0.0625 , deriv= 135.0 , x= 1.125 , pwr= 5 err= 405.0 , h= 0.0625 , deriv= 405.0 , x= 1.125 , pwr= 6 err= 382.5 , h= 0.03125 , deriv= 382.5 , x= 1.0625 , pwr= 6 err= 945.0 , h= 0.0625 , deriv= 945.0 , x= 1.125 , pwr= 7 err= 892.5 , h= 0.03125 , deriv= 892.5 , x= 1.0625 , pwr= 7 err= 866.25 , h= 0.015625 , deriv= 866.25 , x= 1.03125 , pwr= 7 computing order= 4 , npoints= 6 , at term= 3 f^( 4 )(x[ 3 ])=(1/ 1 h^ 4 )( 0 * f(x[ 0 ]) + 1 * f(x[ 1 ] + -4 * f(x[ 2 ] + 6 * f(x[ 3 ] + -4 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.1875 , pwr= 4 err= 142.5 , h= 0.0625 , deriv= 142.5 , x= 1.1875 , pwr= 5 err= 427.5 , h= 0.0625 , deriv= 427.5 , x= 1.1875 , pwr= 6 err= 393.75 , h= 0.03125 , deriv= 393.75 , x= 1.09375 , pwr= 6 err= 997.5 , h= 0.0625 , deriv= 997.5 , x= 1.1875 , pwr= 7 err= 918.75 , h= 0.03125 , deriv= 918.75 , x= 1.09375 , pwr= 7 err= 879.375 , h= 0.015625 , deriv= 879.375 , x= 1.046875 , pwr= 7 computing order= 4 , npoints= 6 , at term= 4 f^( 4 )(x[ 4 ])=(1/ 1 h^ 4 )( -1 * f(x[ 0 ]) + 6 * f(x[ 1 ] + -14 * f(x[ 2 ] + 16 * f(x[ 3 ] + -9 * f(x[ 4 ] + 2 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.25 , pwr= 4 err= 150.0 , h= 0.0625 , deriv= 150.0 , x= 1.25 , pwr= 5 err= 450.0 , h= 0.0625 , deriv= 450.0 , x= 1.25 , pwr= 6 err= 405.0 , h= 0.03125 , deriv= 405.0 , x= 1.125 , pwr= 6 err= 1050.0 , h= 0.0625 , deriv= 1050.0 , x= 1.25 , pwr= 7 err= 945.0 , h= 0.03125 , deriv= 945.0 , x= 1.125 , pwr= 7 err= 892.5 , h= 0.015625 , deriv= 892.5 , x= 1.0625 , pwr= 7 computing order= 4 , npoints= 6 , at term= 5 f^( 4 )(x[ 5 ])=(1/ 1 h^ 4 )( -2 * f(x[ 0 ]) + 11 * f(x[ 1 ] + -24 * f(x[ 2 ] + 26 * f(x[ 3 ] + -14 * f(x[ 4 ] + 3 * f(x[ 5 ] ) + O(h^ 2 )f^( 6 )(z) err= 24.0 , h= 0.0625 , deriv= 24.0 , x= 1.3125 , pwr= 4 err= 157.5 , h= 0.0625 , deriv= 157.5 , x= 1.3125 , pwr= 5 err= 472.5 , h= 0.0625 , deriv= 472.5 , x= 1.3125 , pwr= 6 err= 416.25 , h= 0.03125 , deriv= 416.25 , x= 1.15625 , pwr= 6 err= 1102.5 , h= 0.0625 , deriv= 1102.5 , x= 1.3125 , pwr= 7 err= 971.25 , h= 0.03125 , deriv= 971.25 , x= 1.15625 , pwr= 7 err= 905.625 , h= 0.015625 , deriv= 905.625 , x= 1.078125 , pwr= 7 computing order= 5 , npoints= 6 , at term= 0 f^( 5 )(x[ 0 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.0 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.0 , pwr= 5 err= 720.0 , h= 0.03125 , deriv= 720.0 , x= 1.0 , pwr= 6 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.0 , pwr= 6 err= 2520.0 , h= 0.03125 , deriv= 2520.0 , x= 1.0 , pwr= 7 err= 2520.0 , h= 0.015625 , deriv= 2520.0 , x= 1.0 , pwr= 7 err= 2520.0 , h= 0.0078125 , deriv= 2520.0 , x= 1.0 , pwr= 7 computing order= 5 , npoints= 6 , at term= 1 f^( 5 )(x[ 1 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.03125 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.03125 , pwr= 5 err= 742.5 , h= 0.03125 , deriv= 742.5 , x= 1.03125 , pwr= 6 err= 731.25 , h= 0.015625 , deriv= 731.25 , x= 1.015625 , pwr= 6 err= 2598.75 , h= 0.03125 , deriv= 2598.75 , x= 1.03125 , pwr= 7 err= 2559.375 , h= 0.015625 , deriv= 2559.375 , x= 1.015625 , pwr= 7 err= 2539.6875 , h= 0.0078125 , deriv= 2539.6875 , x= 1.0078125 , pwr= 7 computing order= 5 , npoints= 6 , at term= 2 f^( 5 )(x[ 2 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.0625 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.0625 , pwr= 5 err= 765.0 , h= 0.03125 , deriv= 765.0 , x= 1.0625 , pwr= 6 err= 742.5 , h= 0.015625 , deriv= 742.5 , x= 1.03125 , pwr= 6 err= 2677.5 , h= 0.03125 , deriv= 2677.5 , x= 1.0625 , pwr= 7 err= 2598.75 , h= 0.015625 , deriv= 2598.75 , x= 1.03125 , pwr= 7 err= 2559.375 , h= 0.0078125 , deriv= 2559.375 , x= 1.015625 , pwr= 7 computing order= 5 , npoints= 6 , at term= 3 f^( 5 )(x[ 3 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.09375 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.09375 , pwr= 5 err= 787.5 , h= 0.03125 , deriv= 787.5 , x= 1.09375 , pwr= 6 err= 753.75 , h= 0.015625 , deriv= 753.75 , x= 1.046875 , pwr= 6 err= 2756.25 , h= 0.03125 , deriv= 2756.25 , x= 1.09375 , pwr= 7 err= 2638.125 , h= 0.015625 , deriv= 2638.125 , x= 1.046875 , pwr= 7 err= 2579.0625 , h= 0.0078125 , deriv= 2579.0625 , x= 1.0234375 , pwr= 7 computing order= 5 , npoints= 6 , at term= 4 f^( 5 )(x[ 4 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.125 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.125 , pwr= 5 err= 810.0 , h= 0.03125 , deriv= 810.0 , x= 1.125 , pwr= 6 err= 765.0 , h= 0.015625 , deriv= 765.0 , x= 1.0625 , pwr= 6 err= 2835.0 , h= 0.03125 , deriv= 2835.0 , x= 1.125 , pwr= 7 err= 2677.5 , h= 0.015625 , deriv= 2677.5 , x= 1.0625 , pwr= 7 err= 2598.75 , h= 0.0078125 , deriv= 2598.75 , x= 1.03125 , pwr= 7 computing order= 5 , npoints= 6 , at term= 5 f^( 5 )(x[ 5 ])=(1/ 1 h^ 5 )( -1 * f(x[ 0 ]) + 5 * f(x[ 1 ] + -10 * f(x[ 2 ] + 10 * f(x[ 3 ] + -5 * f(x[ 4 ] + 1 * f(x[ 5 ] ) + O(h^ 1 )f^( 6 )(z) err= 0.0 , h= 0.03125 , deriv= 0.0 , x= 1.15625 , pwr= 4 err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.15625 , pwr= 5 err= 832.5 , h= 0.03125 , deriv= 832.5 , x= 1.15625 , pwr= 6 err= 776.25 , h= 0.015625 , deriv= 776.25 , x= 1.078125 , pwr= 6 err= 2913.75 , h= 0.03125 , deriv= 2913.75 , x= 1.15625 , pwr= 7 err= 2716.875 , h= 0.015625 , deriv= 2716.875 , x= 1.078125 , pwr= 7 err= 2618.4375 , h= 0.0078125 , deriv= 2618.4375 , x= 1.0390625 , pwr= 7 computing order= 5 , npoints= 7 , at term= 0 f^( 5 )(x[ 0 ])=(1/ 2 h^ 5 )( -7 * f(x[ 0 ]) + 40 * f(x[ 1 ] + -95 * f(x[ 2 ] + 120 * f(x[ 3 ] + -85 * f(x[ 4 ] + 32 * f(x[ 5 ] + -5 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.0 , pwr= 5 err= 720.0 , h= 0.03125 , deriv= 720.0 , x= 1.0 , pwr= 6 err= 2520.0 , h= 0.03125 , deriv= 2520.0 , x= 1.0 , pwr= 7 err= 2520.0 , h= 0.015625 , deriv= 2520.0 , x= 1.0 , pwr= 7 err= 6720.0 , h= 0.03125 , deriv= 6720.0 , x= 1.0 , pwr= 8 err= 6720.0 , h= 0.015625 , deriv= 6720.0 , x= 1.0 , pwr= 8 err= 6720.0 , h= 0.0078125 , deriv= 6720.0 , x= 1.0 , pwr= 8 computing order= 5 , npoints= 7 , at term= 1 f^( 5 )(x[ 1 ])=(1/ 2 h^ 5 )( -5 * f(x[ 0 ]) + 28 * f(x[ 1 ] + -65 * f(x[ 2 ] + 80 * f(x[ 3 ] + -55 * f(x[ 4 ] + 20 * f(x[ 5 ] + -3 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.03125 , pwr= 5 err= 742.5 , h= 0.03125 , deriv= 742.5 , x= 1.03125 , pwr= 6 err= 2598.75 , h= 0.03125 , deriv= 2598.75 , x= 1.03125 , pwr= 7 err= 2559.375 , h= 0.015625 , deriv= 2559.375 , x= 1.015625 , pwr= 7 err= 6930.0 , h= 0.03125 , deriv= 6930.0 , x= 1.03125 , pwr= 8 err= 6825.0 , h= 0.015625 , deriv= 6825.0 , x= 1.015625 , pwr= 8 err= 6772.5 , h= 0.0078125 , deriv= 6772.5 , x= 1.0078125 , pwr= 8 computing order= 5 , npoints= 7 , at term= 2 f^( 5 )(x[ 2 ])=(1/ 2 h^ 5 )( -3 * f(x[ 0 ]) + 16 * f(x[ 1 ] + -35 * f(x[ 2 ] + 40 * f(x[ 3 ] + -25 * f(x[ 4 ] + 8 * f(x[ 5 ] + -1 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.0625 , pwr= 5 err= 765.0 , h= 0.03125 , deriv= 765.0 , x= 1.0625 , pwr= 6 err= 2677.5 , h= 0.03125 , deriv= 2677.5 , x= 1.0625 , pwr= 7 err= 2598.75 , h= 0.015625 , deriv= 2598.75 , x= 1.03125 , pwr= 7 err= 7140.0 , h= 0.03125 , deriv= 7140.0 , x= 1.0625 , pwr= 8 err= 6930.0 , h= 0.015625 , deriv= 6930.0 , x= 1.03125 , pwr= 8 err= 6825.0 , h= 0.0078125 , deriv= 6825.0 , x= 1.015625 , pwr= 8 computing order= 5 , npoints= 7 , at term= 3 f^( 5 )(x[ 3 ])=(1/ 2 h^ 5 )( -1 * f(x[ 0 ]) + 4 * f(x[ 1 ] + -5 * f(x[ 2 ] + 0 * f(x[ 3 ] + 5 * f(x[ 4 ] + -4 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.09375 , pwr= 5 err= 787.5 , h= 0.03125 , deriv= 787.5 , x= 1.09375 , pwr= 6 err= 2756.25 , h= 0.03125 , deriv= 2756.25 , x= 1.09375 , pwr= 7 err= 2638.125 , h= 0.015625 , deriv= 2638.125 , x= 1.046875 , pwr= 7 err= 7350.0 , h= 0.03125 , deriv= 7350.0 , x= 1.09375 , pwr= 8 err= 7035.0 , h= 0.015625 , deriv= 7035.0 , x= 1.046875 , pwr= 8 err= 6877.5 , h= 0.0078125 , deriv= 6877.5 , x= 1.0234375 , pwr= 8 computing order= 5 , npoints= 7 , at term= 4 f^( 5 )(x[ 4 ])=(1/ 2 h^ 5 )( 1 * f(x[ 0 ]) + -8 * f(x[ 1 ] + 25 * f(x[ 2 ] + -40 * f(x[ 3 ] + 35 * f(x[ 4 ] + -16 * f(x[ 5 ] + 3 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.125 , pwr= 5 err= 810.0 , h= 0.03125 , deriv= 810.0 , x= 1.125 , pwr= 6 err= 2835.0 , h= 0.03125 , deriv= 2835.0 , x= 1.125 , pwr= 7 err= 2677.5 , h= 0.015625 , deriv= 2677.5 , x= 1.0625 , pwr= 7 err= 7560.0 , h= 0.03125 , deriv= 7560.0 , x= 1.125 , pwr= 8 err= 7140.0 , h= 0.015625 , deriv= 7140.0 , x= 1.0625 , pwr= 8 err= 6930.0 , h= 0.0078125 , deriv= 6930.0 , x= 1.03125 , pwr= 8 computing order= 5 , npoints= 7 , at term= 5 f^( 5 )(x[ 5 ])=(1/ 2 h^ 5 )( 3 * f(x[ 0 ]) + -20 * f(x[ 1 ] + 55 * f(x[ 2 ] + -80 * f(x[ 3 ] + 65 * f(x[ 4 ] + -28 * f(x[ 5 ] + 5 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.15625 , pwr= 5 err= 832.5 , h= 0.03125 , deriv= 832.5 , x= 1.15625 , pwr= 6 err= 2913.75 , h= 0.03125 , deriv= 2913.75 , x= 1.15625 , pwr= 7 err= 2716.875 , h= 0.015625 , deriv= 2716.875 , x= 1.078125 , pwr= 7 err= 7770.0 , h= 0.03125 , deriv= 7770.0 , x= 1.15625 , pwr= 8 err= 7245.0 , h= 0.015625 , deriv= 7245.0 , x= 1.078125 , pwr= 8 err= 6982.5 , h= 0.0078125 , deriv= 6982.5 , x= 1.0390625 , pwr= 8 computing order= 5 , npoints= 7 , at term= 6 f^( 5 )(x[ 6 ])=(1/ 2 h^ 5 )( 5 * f(x[ 0 ]) + -32 * f(x[ 1 ] + 85 * f(x[ 2 ] + -120 * f(x[ 3 ] + 95 * f(x[ 4 ] + -40 * f(x[ 5 ] + 7 * f(x[ 6 ] ) + O(h^ 2 )f^( 7 )(z) err= 120.0 , h= 0.03125 , deriv= 120.0 , x= 1.1875 , pwr= 5 err= 855.0 , h= 0.03125 , deriv= 855.0 , x= 1.1875 , pwr= 6 err= 2992.5 , h= 0.03125 , deriv= 2992.5 , x= 1.1875 , pwr= 7 err= 2756.25 , h= 0.015625 , deriv= 2756.25 , x= 1.09375 , pwr= 7 err= 7980.0 , h= 0.03125 , deriv= 7980.0 , x= 1.1875 , pwr= 8 err= 7350.0 , h= 0.015625 , deriv= 7350.0 , x= 1.09375 , pwr= 8 err= 7035.0 , h= 0.0078125 , deriv= 7035.0 , x= 1.046875 , pwr= 8 computing order= 6 , npoints= 7 , at term= 0 f^( 6 )(x[ 0 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.0 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.0 , pwr= 6 err= 5040.0 , h= 0.015625 , deriv= 5040.0 , x= 1.0 , pwr= 7 err= 5040.0 , h= 0.0078125 , deriv= 5040.0 , x= 1.0 , pwr= 7 err= 20160.0 , h= 0.015625 , deriv= 20160.0 , x= 1.0 , pwr= 8 err= 20160.0 , h= 0.0078125 , deriv= 20160.0 , x= 1.0 , pwr= 8 err= 20160.0 , h= 0.00390625 , deriv= 20160.0 , x= 1.0 , pwr= 8 computing order= 6 , npoints= 7 , at term= 1 f^( 6 )(x[ 1 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.015625 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.015625 , pwr= 6 err= 5118.75 , h= 0.015625 , deriv= 5118.75 , x= 1.015625 , pwr= 7 err= 5079.375 , h= 0.0078125 , deriv= 5079.375 , x= 1.0078125 , pwr= 7 err= 20475.0 , h= 0.015625 , deriv= 20475.0 , x= 1.015625 , pwr= 8 err= 20317.5 , h= 0.0078125 , deriv= 20317.5 , x= 1.0078125 , pwr= 8 err= 20238.75 , h= 0.00390625 , deriv= 20238.75 , x= 1.00390625 , pwr= 8 computing order= 6 , npoints= 7 , at term= 2 f^( 6 )(x[ 2 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.03125 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.03125 , pwr= 6 err= 5197.5 , h= 0.015625 , deriv= 5197.5 , x= 1.03125 , pwr= 7 err= 5118.75 , h= 0.0078125 , deriv= 5118.75 , x= 1.015625 , pwr= 7 err= 20790.0 , h= 0.015625 , deriv= 20790.0 , x= 1.03125 , pwr= 8 err= 20475.0 , h= 0.0078125 , deriv= 20475.0 , x= 1.015625 , pwr= 8 err= 20317.5 , h= 0.00390625 , deriv= 20317.5 , x= 1.0078125 , pwr= 8 computing order= 6 , npoints= 7 , at term= 3 f^( 6 )(x[ 3 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.046875 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.046875 , pwr= 6 err= 5276.25 , h= 0.015625 , deriv= 5276.25 , x= 1.046875 , pwr= 7 err= 5158.125 , h= 0.0078125 , deriv= 5158.125 , x= 1.0234375 , pwr= 7 err= 21105.0 , h= 0.015625 , deriv= 21105.0 , x= 1.046875 , pwr= 8 err= 20632.5 , h= 0.0078125 , deriv= 20632.5 , x= 1.0234375 , pwr= 8 err= 20396.25 , h= 0.00390625 , deriv= 20396.25 , x= 1.01171875 , pwr= 8 computing order= 6 , npoints= 7 , at term= 4 f^( 6 )(x[ 4 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.0625 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.0625 , pwr= 6 err= 5355.0 , h= 0.015625 , deriv= 5355.0 , x= 1.0625 , pwr= 7 err= 5197.5 , h= 0.0078125 , deriv= 5197.5 , x= 1.03125 , pwr= 7 err= 21420.0 , h= 0.015625 , deriv= 21420.0 , x= 1.0625 , pwr= 8 err= 20790.0 , h= 0.0078125 , deriv= 20790.0 , x= 1.03125 , pwr= 8 err= 20475.0 , h= 0.00390625 , deriv= 20475.0 , x= 1.015625 , pwr= 8 computing order= 6 , npoints= 7 , at term= 5 f^( 6 )(x[ 5 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.078125 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.078125 , pwr= 6 err= 5433.75 , h= 0.015625 , deriv= 5433.75 , x= 1.078125 , pwr= 7 err= 5236.875 , h= 0.0078125 , deriv= 5236.875 , x= 1.0390625 , pwr= 7 err= 21735.0 , h= 0.015625 , deriv= 21735.0 , x= 1.078125 , pwr= 8 err= 20947.5 , h= 0.0078125 , deriv= 20947.5 , x= 1.0390625 , pwr= 8 err= 20553.75 , h= 0.00390625 , deriv= 20553.75 , x= 1.01953125 , pwr= 8 computing order= 6 , npoints= 7 , at term= 6 f^( 6 )(x[ 6 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] ) + O(h^ 1 )f^( 7 )(z) err= 0.0 , h= 0.015625 , deriv= 0.0 , x= 1.09375 , pwr= 5 err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.09375 , pwr= 6 err= 5512.5 , h= 0.015625 , deriv= 5512.5 , x= 1.09375 , pwr= 7 err= 5276.25 , h= 0.0078125 , deriv= 5276.25 , x= 1.046875 , pwr= 7 err= 22050.0 , h= 0.015625 , deriv= 22050.0 , x= 1.09375 , pwr= 8 err= 21105.0 , h= 0.0078125 , deriv= 21105.0 , x= 1.046875 , pwr= 8 err= 20632.5 , h= 0.00390625 , deriv= 20632.5 , x= 1.0234375 , pwr= 8 computing order= 6 , npoints= 8 , at term= 0 f^( 6 )(x[ 0 ])=(1/ 1 h^ 6 )( 4 * f(x[ 0 ]) + -27 * f(x[ 1 ] + 78 * f(x[ 2 ] + -125 * f(x[ 3 ] + 120 * f(x[ 4 ] + -69 * f(x[ 5 ] + 22 * f(x[ 6 ] + -3 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.0 , pwr= 6 err= 5040.0 , h= 0.015625 , deriv= 5040.0 , x= 1.0 , pwr= 7 err= 20160.0 , h= 0.015625 , deriv= 20160.0 , x= 1.0 , pwr= 8 err= 20160.0 , h= 0.0078125 , deriv= 20160.0 , x= 1.0 , pwr= 8 err= 60480.0 , h= 0.015625 , deriv= 60480.0 , x= 1.0 , pwr= 9 err= 60480.0 , h= 0.0078125 , deriv= 60480.0 , x= 1.0 , pwr= 9 err= 60480.0 , h= 0.00390625 , deriv= 60480.0 , x= 1.0 , pwr= 9 computing order= 6 , npoints= 8 , at term= 1 f^( 6 )(x[ 1 ])=(1/ 1 h^ 6 )( 3 * f(x[ 0 ]) + -20 * f(x[ 1 ] + 57 * f(x[ 2 ] + -90 * f(x[ 3 ] + 85 * f(x[ 4 ] + -48 * f(x[ 5 ] + 15 * f(x[ 6 ] + -2 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.015625 , pwr= 6 err= 5118.75 , h= 0.015625 , deriv= 5118.75 , x= 1.015625 , pwr= 7 err= 20475.0 , h= 0.015625 , deriv= 20475.0 , x= 1.015625 , pwr= 8 err= 20317.5 , h= 0.0078125 , deriv= 20317.5 , x= 1.0078125 , pwr= 8 err= 61425.0 , h= 0.015625 , deriv= 61425.0 , x= 1.015625 , pwr= 9 err= 60952.5 , h= 0.0078125 , deriv= 60952.5 , x= 1.0078125 , pwr= 9 err= 60716.25 , h= 0.00390625 , deriv= 60716.25 , x= 1.00390625 , pwr= 9 computing order= 6 , npoints= 8 , at term= 2 f^( 6 )(x[ 2 ])=(1/ 1 h^ 6 )( 2 * f(x[ 0 ]) + -13 * f(x[ 1 ] + 36 * f(x[ 2 ] + -55 * f(x[ 3 ] + 50 * f(x[ 4 ] + -27 * f(x[ 5 ] + 8 * f(x[ 6 ] + -1 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.03125 , pwr= 6 err= 5197.5 , h= 0.015625 , deriv= 5197.5 , x= 1.03125 , pwr= 7 err= 20790.0 , h= 0.015625 , deriv= 20790.0 , x= 1.03125 , pwr= 8 err= 20475.0 , h= 0.0078125 , deriv= 20475.0 , x= 1.015625 , pwr= 8 err= 62370.0 , h= 0.015625 , deriv= 62370.0 , x= 1.03125 , pwr= 9 err= 61425.0 , h= 0.0078125 , deriv= 61425.0 , x= 1.015625 , pwr= 9 err= 60952.5 , h= 0.00390625 , deriv= 60952.5 , x= 1.0078125 , pwr= 9 computing order= 6 , npoints= 8 , at term= 3 f^( 6 )(x[ 3 ])=(1/ 1 h^ 6 )( 1 * f(x[ 0 ]) + -6 * f(x[ 1 ] + 15 * f(x[ 2 ] + -20 * f(x[ 3 ] + 15 * f(x[ 4 ] + -6 * f(x[ 5 ] + 1 * f(x[ 6 ] + 0 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.046875 , pwr= 6 err= 5276.25 , h= 0.015625 , deriv= 5276.25 , x= 1.046875 , pwr= 7 err= 21105.0 , h= 0.015625 , deriv= 21105.0 , x= 1.046875 , pwr= 8 err= 20632.5 , h= 0.0078125 , deriv= 20632.5 , x= 1.0234375 , pwr= 8 err= 63315.0 , h= 0.015625 , deriv= 63315.0 , x= 1.046875 , pwr= 9 err= 61897.5 , h= 0.0078125 , deriv= 61897.5 , x= 1.0234375 , pwr= 9 err= 61188.75 , h= 0.00390625 , deriv= 61188.75 , x= 1.01171875 , pwr= 9 computing order= 6 , npoints= 8 , at term= 4 f^( 6 )(x[ 4 ])=(1/ 1 h^ 6 )( 0 * f(x[ 0 ]) + 1 * f(x[ 1 ] + -6 * f(x[ 2 ] + 15 * f(x[ 3 ] + -20 * f(x[ 4 ] + 15 * f(x[ 5 ] + -6 * f(x[ 6 ] + 1 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.0625 , pwr= 6 err= 5355.0 , h= 0.015625 , deriv= 5355.0 , x= 1.0625 , pwr= 7 err= 21420.0 , h= 0.015625 , deriv= 21420.0 , x= 1.0625 , pwr= 8 err= 20790.0 , h= 0.0078125 , deriv= 20790.0 , x= 1.03125 , pwr= 8 err= 64260.0 , h= 0.015625 , deriv= 64260.0 , x= 1.0625 , pwr= 9 err= 62370.0 , h= 0.0078125 , deriv= 62370.0 , x= 1.03125 , pwr= 9 err= 61425.0 , h= 0.00390625 , deriv= 61425.0 , x= 1.015625 , pwr= 9 computing order= 6 , npoints= 8 , at term= 5 f^( 6 )(x[ 5 ])=(1/ 1 h^ 6 )( -1 * f(x[ 0 ]) + 8 * f(x[ 1 ] + -27 * f(x[ 2 ] + 50 * f(x[ 3 ] + -55 * f(x[ 4 ] + 36 * f(x[ 5 ] + -13 * f(x[ 6 ] + 2 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.078125 , pwr= 6 err= 5433.75 , h= 0.015625 , deriv= 5433.75 , x= 1.078125 , pwr= 7 err= 21735.0 , h= 0.015625 , deriv= 21735.0 , x= 1.078125 , pwr= 8 err= 20947.5 , h= 0.0078125 , deriv= 20947.5 , x= 1.0390625 , pwr= 8 err= 65205.0 , h= 0.015625 , deriv= 65205.0 , x= 1.078125 , pwr= 9 err= 62842.5 , h= 0.0078125 , deriv= 62842.5 , x= 1.0390625 , pwr= 9 err= 61661.25 , h= 0.00390625 , deriv= 61661.25 , x= 1.01953125 , pwr= 9 computing order= 6 , npoints= 8 , at term= 6 f^( 6 )(x[ 6 ])=(1/ 1 h^ 6 )( -2 * f(x[ 0 ]) + 15 * f(x[ 1 ] + -48 * f(x[ 2 ] + 85 * f(x[ 3 ] + -90 * f(x[ 4 ] + 57 * f(x[ 5 ] + -20 * f(x[ 6 ] + 3 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.09375 , pwr= 6 err= 5512.5 , h= 0.015625 , deriv= 5512.5 , x= 1.09375 , pwr= 7 err= 22050.0 , h= 0.015625 , deriv= 22050.0 , x= 1.09375 , pwr= 8 err= 21105.0 , h= 0.0078125 , deriv= 21105.0 , x= 1.046875 , pwr= 8 err= 66150.0 , h= 0.015625 , deriv= 66150.0 , x= 1.09375 , pwr= 9 err= 63315.0 , h= 0.0078125 , deriv= 63315.0 , x= 1.046875 , pwr= 9 err= 61897.5 , h= 0.00390625 , deriv= 61897.5 , x= 1.0234375 , pwr= 9 computing order= 6 , npoints= 8 , at term= 7 f^( 6 )(x[ 7 ])=(1/ 1 h^ 6 )( -3 * f(x[ 0 ]) + 22 * f(x[ 1 ] + -69 * f(x[ 2 ] + 120 * f(x[ 3 ] + -125 * f(x[ 4 ] + 78 * f(x[ 5 ] + -27 * f(x[ 6 ] + 4 * f(x[ 7 ] ) + O(h^ 2 )f^( 8 )(z) err= 720.0 , h= 0.015625 , deriv= 720.0 , x= 1.109375 , pwr= 6 err= 5591.25 , h= 0.015625 , deriv= 5591.25 , x= 1.109375 , pwr= 7 err= 22365.0 , h= 0.015625 , deriv= 22365.0 , x= 1.109375 , pwr= 8 err= 21262.5 , h= 0.0078125 , deriv= 21262.5 , x= 1.0546875 , pwr= 8 err= 67095.0 , h= 0.015625 , deriv= 67095.0 , x= 1.109375 , pwr= 9 err= 63787.5 , h= 0.0078125 , deriv= 63787.5 , x= 1.0546875 , pwr= 9 err= 62133.75 , h= 0.00390625 , deriv= 62133.75 , x= 1.02734375 , pwr= 9 many formulas checked against Abramowitz and Stegun, Handbook of Mathematical Functions Table 25.2