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= 0.00 , h=0.125 deriv= 0.00 x= 1.00 pwr= 0 err= 0.00 , h=0.125 deriv= 1.00 x= 1.00 pwr= 1 err=-.125 , h=0.125 deriv= 2.00 x= 1.00 pwr= 2 err=-.391 , h=0.125 deriv= 3.00 x= 1.00 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= 0.00 , h=0.125 deriv= 0.00 x= 1.12 pwr= 0 err= 0.00 , h=0.125 deriv= 1.00 x= 1.12 pwr= 1 err=0.125 , h=0.125 deriv= 2.25 x= 1.12 pwr= 2 err=0.406 , h=0.125 deriv= 3.80 x= 1.12 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= 0.00 , h=0.125 deriv= 1.00 x= 1.00 pwr= 1 err= 0.00 , h=0.125 deriv= 2.00 x= 1.00 pwr= 2 err=0.312E-01, h=0.125 deriv= 3.00 x= 1.00 pwr= 3 err=0.137 , h=0.125 deriv= 4.00 x= 1.00 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= 0.00 , h=0.125 deriv= 1.00 x= 1.12 pwr= 1 err= 0.00 , h=0.125 deriv= 2.25 x= 1.12 pwr= 2 err=-.156E-01, h=0.125 deriv= 3.80 x= 1.12 pwr= 3 err=-.703E-01, h=0.125 deriv= 5.70 x= 1.12 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= 0.00 , h=0.125 deriv= 1.00 x= 1.25 pwr= 1 err= 0.00 , h=0.125 deriv= 2.50 x= 1.25 pwr= 2 err=0.312E-01, h=0.125 deriv= 4.69 x= 1.25 pwr= 3 err=0.145 , h=0.125 deriv= 7.81 x= 1.25 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= 0.00 , h=0.125 deriv= 2.00 x= 1.00 pwr= 2 err= 0.00 , h=0.125 deriv= 3.00 x= 1.00 pwr= 3 err=-.117E-01, h=0.125 deriv= 4.00 x= 1.00 pwr= 4 err=-.674E-01, h=0.125 deriv= 5.00 x= 1.00 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= 0.00 , h=0.125 deriv= 2.25 x= 1.12 pwr= 2 err= 0.00 , h=0.125 deriv= 3.80 x= 1.12 pwr= 3 err=0.391E-02, h=0.125 deriv= 5.70 x= 1.12 pwr= 4 err=0.229E-01, h=0.125 deriv= 8.01 x= 1.12 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= 0.00 , h=0.125 deriv= 2.50 x= 1.25 pwr= 2 err= 0.00 , h=0.125 deriv= 4.69 x= 1.25 pwr= 3 err=-.391E-02, h=0.125 deriv= 7.81 x= 1.25 pwr= 4 err=-.234E-01, h=0.125 deriv= 12.2 x= 1.25 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= 0.00 , h=0.125 deriv= 2.75 x= 1.38 pwr= 2 err= 0.00 , h=0.125 deriv= 5.67 x= 1.38 pwr= 3 err=0.117E-01, h=0.125 deriv= 10.4 x= 1.38 pwr= 4 err=0.718E-01, h=0.125 deriv= 17.9 x= 1.38 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= 0.00 , h=0.125 deriv= 3.00 x= 1.00 pwr= 3 err= 0.00 , h=0.125 deriv= 4.00 x= 1.00 pwr= 4 err=0.586E-02, h=0.125 deriv= 5.00 x= 1.00 pwr= 5 err=0.425E-01, h=0.125 deriv= 6.00 x= 1.00 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= 0.00 , h=0.125 deriv= 3.80 x= 1.12 pwr= 3 err= 0.00 , h=0.125 deriv= 5.70 x= 1.12 pwr= 4 err=-.146E-02, h=0.125 deriv= 8.01 x= 1.12 pwr= 5 err=-.108E-01, h=0.125 deriv= 10.8 x= 1.12 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= 0.00 , h=0.125 deriv= 4.69 x= 1.25 pwr= 3 err= 0.00 , h=0.125 deriv= 7.81 x= 1.25 pwr= 4 err=0.977E-03, h=0.125 deriv= 12.2 x= 1.25 pwr= 5 err=0.732E-02, h=0.125 deriv= 18.3 x= 1.25 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= 0.00 , h=0.125 deriv= 5.67 x= 1.38 pwr= 3 err= 0.00 , h=0.125 deriv= 10.4 x= 1.38 pwr= 4 err=-.146E-02, h=0.125 deriv= 17.9 x= 1.38 pwr= 5 err=-.112E-01, h=0.125 deriv= 29.5 x= 1.38 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= 0.00 , h=0.125 deriv= 6.75 x= 1.50 pwr= 3 err= 0.00 , h=0.125 deriv= 13.5 x= 1.50 pwr= 4 err=0.586E-02, h=0.125 deriv= 25.3 x= 1.50 pwr= 5 err=0.454E-01, h=0.125 deriv= 45.6 x= 1.50 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= 0.00 , h=0.125 deriv= 4.00 x= 1.00 pwr= 4 err= 0.00 , h=0.125 deriv= 5.00 x= 1.00 pwr= 5 err=-.366E-02, h=0.125 deriv= 6.00 x= 1.00 pwr= 6 err=-.325E-01, h=0.125 deriv= 7.00 x= 1.00 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= 0.00 , h=0.125 deriv= 5.70 x= 1.12 pwr= 4 err= 0.00 , h=0.125 deriv= 8.01 x= 1.12 pwr= 5 err=0.732E-03, h=0.125 deriv= 10.8 x= 1.12 pwr= 6 err=0.659E-02, h=0.125 deriv= 14.2 x= 1.12 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= 0.00 , h=0.125 deriv= 7.81 x= 1.25 pwr= 4 err= 0.00 , h=0.125 deriv= 12.2 x= 1.25 pwr= 5 err=-.366E-03, h=0.125 deriv= 18.3 x= 1.25 pwr= 6 err=-.334E-02, h=0.125 deriv= 26.7 x= 1.25 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= 0.00 , h=0.125 deriv= 10.4 x= 1.38 pwr= 4 err= 0.00 , h=0.125 deriv= 17.9 x= 1.38 pwr= 5 err=0.366E-03, h=0.125 deriv= 29.5 x= 1.38 pwr= 6 err=0.339E-02, h=0.125 deriv= 47.3 x= 1.38 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= 0.00 , h=0.125 deriv= 13.5 x= 1.50 pwr= 4 err= 0.00 , h=0.125 deriv= 25.3 x= 1.50 pwr= 5 err=-.732E-03, h=0.125 deriv= 45.6 x= 1.50 pwr= 6 err=-.687E-02, h=0.125 deriv= 79.7 x= 1.50 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= 0.00 , h=0.125 deriv= 17.2 x= 1.62 pwr= 4 err= 0.00 , h=0.125 deriv= 34.9 x= 1.62 pwr= 5 err=0.366E-02, h=0.125 deriv= 68.0 x= 1.62 pwr= 6 err=0.348E-01, h=0.125 deriv= 129. x= 1.62 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= 0.00 , h=0.125 deriv= 5.00 x= 1.00 pwr= 5 err= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 6 err=0.275E-02, h=0.125 deriv= 7.00 x= 1.00 pwr= 7 err=0.292E-01, h=0.125 deriv= 8.00 x= 1.00 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= 0.00 , h=0.125 deriv= 8.01 x= 1.12 pwr= 5 err= 0.00 , h=0.125 deriv= 10.8 x= 1.12 pwr= 6 err=-.458E-03, h=0.125 deriv= 14.2 x= 1.12 pwr= 7 err=-.492E-02, h=0.125 deriv= 18.2 x= 1.12 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= 0.00 , h=0.125 deriv= 12.2 x= 1.25 pwr= 5 err= 0.00 , h=0.125 deriv= 18.3 x= 1.25 pwr= 6 err=0.183E-03, h=0.125 deriv= 26.7 x= 1.25 pwr= 7 err=0.199E-02, h=0.125 deriv= 38.1 x= 1.25 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= 0.00 , h=0.125 deriv= 17.9 x= 1.38 pwr= 5 err= 0.00 , h=0.125 deriv= 29.5 x= 1.38 pwr= 6 err=-.137E-03, h=0.125 deriv= 47.3 x= 1.38 pwr= 7 err=-.151E-02, h=0.125 deriv= 74.3 x= 1.38 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= 0.00 , h=0.125 deriv= 25.3 x= 1.50 pwr= 5 err= 0.00 , h=0.125 deriv= 45.6 x= 1.50 pwr= 6 err=0.183E-03, h=0.125 deriv= 79.7 x= 1.50 pwr= 7 err=0.204E-02, h=0.125 deriv= 137. x= 1.50 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= 0.00 , h=0.125 deriv= 34.9 x= 1.62 pwr= 5 err= 0.00 , h=0.125 deriv= 68.0 x= 1.62 pwr= 6 err=-.458E-03, h=0.125 deriv= 129. x= 1.62 pwr= 7 err=-.515E-02, h=0.125 deriv= 239. x= 1.62 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= 0.00 , h=0.125 deriv= 46.9 x= 1.75 pwr= 5 err= 0.00 , h=0.125 deriv= 98.5 x= 1.75 pwr= 6 err=0.275E-02, h=0.125 deriv= 201. x= 1.75 pwr= 7 err=0.312E-01, h=0.125 deriv= 402. x= 1.75 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= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 6 err= 0.00 , h=0.125 deriv= 7.00 x= 1.00 pwr= 7 err=-.240E-02, h=0.125 deriv= 8.00 x= 1.00 pwr= 8 err=-.300E-01, h=0.125 deriv= 9.00 x= 1.00 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= 0.00 , h=0.125 deriv= 10.8 x= 1.12 pwr= 6 err= 0.00 , h=0.125 deriv= 14.2 x= 1.12 pwr= 7 err=0.343E-03, h=0.125 deriv= 18.2 x= 1.12 pwr= 8 err=0.433E-02, h=0.125 deriv= 23.1 x= 1.12 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= 0.00 , h=0.125 deriv= 18.3 x= 1.25 pwr= 6 err= 0.00 , h=0.125 deriv= 26.7 x= 1.25 pwr= 7 err=-.114E-03, h=0.125 deriv= 38.1 x= 1.25 pwr= 8 err=-.146E-02, h=0.125 deriv= 53.6 x= 1.25 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= 0.00 , h=0.125 deriv= 29.5 x= 1.38 pwr= 6 err= 0.00 , h=0.125 deriv= 47.3 x= 1.38 pwr= 7 err=0.687E-04, h=0.125 deriv= 74.3 x= 1.38 pwr= 8 err=0.884E-03, h=0.125 deriv= 115. x= 1.38 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= 0.00 , h=0.125 deriv= 45.6 x= 1.50 pwr= 6 err= 0.00 , h=0.125 deriv= 79.7 x= 1.50 pwr= 7 err=-.687E-04, h=0.125 deriv= 137. x= 1.50 pwr= 8 err=-.893E-03, h=0.125 deriv= 231. x= 1.50 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= 0.00 , h=0.125 deriv= 68.0 x= 1.62 pwr= 6 err= 0.00 , h=0.125 deriv= 129. x= 1.62 pwr= 7 err=0.114E-03, h=0.125 deriv= 239. x= 1.62 pwr= 8 err=0.150E-02, h=0.125 deriv= 438. x= 1.62 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= 0.00 , h=0.125 deriv= 98.5 x= 1.75 pwr= 6 err= 0.00 , h=0.125 deriv= 201. x= 1.75 pwr= 7 err=-.343E-03, h=0.125 deriv= 402. x= 1.75 pwr= 8 err=-.455E-02, h=0.125 deriv= 792. x= 1.75 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= 0.00 , h=0.125 deriv= 139. x= 1.88 pwr= 6 err= 0.00 , h=0.125 deriv= 304. x= 1.88 pwr= 7 err=0.240E-02, h=0.125 deriv= 652. x= 1.88 pwr= 8 err=0.321E-01, h=0.125 deriv=0.137E+04 x= 1.88 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= 0.00 , h=0.125 deriv= 7.00 x= 1.00 pwr= 7 err= 0.00 , h=0.125 deriv= 8.00 x= 1.00 pwr= 8 err=0.240E-02, h=0.125 deriv= 9.00 x= 1.00 pwr= 9 err=0.348E-01, h=0.125 deriv= 10.0 x= 1.00 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= 0.00 , h=0.125 deriv= 14.2 x= 1.12 pwr= 7 err= 0.00 , h=0.125 deriv= 18.2 x= 1.12 pwr= 8 err=-.300E-03, h=0.125 deriv= 23.1 x= 1.12 pwr= 9 err=-.439E-02, h=0.125 deriv= 28.9 x= 1.12 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= 0.00 , h=0.125 deriv= 26.7 x= 1.25 pwr= 7 err= 0.00 , h=0.125 deriv= 38.1 x= 1.25 pwr= 8 err=0.858E-04, h=0.125 deriv= 53.6 x= 1.25 pwr= 9 err=0.127E-02, h=0.125 deriv= 74.5 x= 1.25 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= 0.00 , h=0.125 deriv= 47.3 x= 1.38 pwr= 7 err= 0.00 , h=0.125 deriv= 74.3 x= 1.38 pwr= 8 err=-.429E-04, h=0.125 deriv= 115. x= 1.38 pwr= 9 err=-.638E-03, h=0.125 deriv= 176. x= 1.38 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= 0.00 , h=0.125 deriv= 79.7 x= 1.50 pwr= 7 err= 0.00 , h=0.125 deriv= 137. x= 1.50 pwr= 8 err=0.343E-04, h=0.125 deriv= 231. x= 1.50 pwr= 9 err=0.515E-03, h=0.125 deriv= 384. x= 1.50 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= 0.00 , h=0.125 deriv= 129. x= 1.62 pwr= 7 err= 0.00 , h=0.125 deriv= 239. x= 1.62 pwr= 8 err=-.429E-04, h=0.125 deriv= 438. x= 1.62 pwr= 9 err=-.649E-03, h=0.125 deriv= 790. x= 1.62 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= 0.00 , h=0.125 deriv= 201. x= 1.75 pwr= 7 err= 0.00 , h=0.125 deriv= 402. x= 1.75 pwr= 8 err=0.858E-04, h=0.125 deriv= 792. x= 1.75 pwr= 9 err=0.131E-02, h=0.125 deriv=0.154E+04 x= 1.75 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= 0.00 , h=0.125 deriv= 304. x= 1.88 pwr= 7 err= 0.00 , h=0.125 deriv= 652. x= 1.88 pwr= 8 err=-.300E-03, h=0.125 deriv=0.137E+04 x= 1.88 pwr= 9 err=-.462E-02, h=0.125 deriv=0.286E+04 x= 1.88 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= 0.00 , h=0.125 deriv= 448. x= 2.00 pwr= 7 err= 0.00 , h=0.125 deriv=0.102E+04 x= 2.00 pwr= 8 err=0.240E-02, h=0.125 deriv=0.230E+04 x= 2.00 pwr= 9 err=0.373E-01, h=0.125 deriv=0.512E+04 x= 2.00 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= 0.00 , h=0.125 deriv= 8.00 x= 1.00 pwr= 8 err= 0.00 , h=0.125 deriv= 9.00 x= 1.00 pwr= 9 err=-.270E-02, h=0.125 deriv= 10.0 x= 1.00 pwr=10 err=-.449E-01, h=0.125 deriv= 11.0 x= 1.00 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= 0.00 , h=0.125 deriv= 18.2 x= 1.12 pwr= 8 err= 0.00 , h=0.125 deriv= 23.1 x= 1.12 pwr= 9 err=0.300E-03, h=0.125 deriv= 28.9 x= 1.12 pwr=10 err=0.503E-02, h=0.125 deriv= 35.7 x= 1.12 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= 0.00 , h=0.125 deriv= 38.1 x= 1.25 pwr= 8 err= 0.00 , h=0.125 deriv= 53.6 x= 1.25 pwr= 9 err=-.751E-04, h=0.125 deriv= 74.5 x= 1.25 pwr=10 err=-.127E-02, h=0.125 deriv= 102. x= 1.25 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= 0.00 , h=0.125 deriv= 74.3 x= 1.38 pwr= 8 err= 0.00 , h=0.125 deriv= 115. x= 1.38 pwr= 9 err=0.322E-04, h=0.125 deriv= 176. x= 1.38 pwr=10 err=0.547E-03, h=0.125 deriv= 266. x= 1.38 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= 0.00 , h=0.125 deriv= 137. x= 1.50 pwr= 8 err= 0.00 , h=0.125 deriv= 231. x= 1.50 pwr= 9 err=-.215E-04, h=0.125 deriv= 384. x= 1.50 pwr=10 err=-.367E-03, h=0.125 deriv= 634. x= 1.50 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= 0.00 , h=0.125 deriv= 239. x= 1.62 pwr= 8 err= 0.00 , h=0.125 deriv= 438. x= 1.62 pwr= 9 err=0.215E-04, h=0.125 deriv= 790. x= 1.62 pwr=10 err=0.370E-03, h=0.125 deriv=0.141E+04 x= 1.62 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= 0.00 , h=0.125 deriv= 402. x= 1.75 pwr= 8 err= 0.00 , h=0.125 deriv= 792. x= 1.75 pwr= 9 err=-.322E-04, h=0.125 deriv=0.154E+04 x= 1.75 pwr=10 err=-.559E-03, h=0.125 deriv=0.296E+04 x= 1.75 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= 0.00 , h=0.125 deriv= 652. x= 1.88 pwr= 8 err= 0.00 , h=0.125 deriv=0.137E+04 x= 1.88 pwr= 9 err=0.751E-04, h=0.125 deriv=0.286E+04 x= 1.88 pwr=10 err=0.131E-02, h=0.125 deriv=0.591E+04 x= 1.88 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= 0.00 , h=0.125 deriv=0.102E+04 x= 2.00 pwr= 8 err= 0.00 , h=0.125 deriv=0.230E+04 x= 2.00 pwr= 9 err=-.300E-03, h=0.125 deriv=0.512E+04 x= 2.00 pwr=10 err=-.529E-02, h=0.125 deriv=0.113E+05 x= 2.00 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= 0.00 , h=0.125 deriv=0.157E+04 x= 2.12 pwr= 8 err= 0.00 , h=0.125 deriv=0.374E+04 x= 2.12 pwr= 9 err=0.270E-02, h=0.125 deriv=0.884E+04 x= 2.12 pwr=10 err=0.480E-01, h=0.125 deriv=0.207E+05 x= 2.12 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= 0.00 , h=0.125 deriv= 0.00 x= 1.00 pwr= 1 err= 0.00 , h=0.125 deriv= 2.00 x= 1.00 pwr= 2 err=-.750 , h=0.125 deriv= 6.00 x= 1.00 pwr= 3 err=-3.22 , h=0.125 deriv= 12.0 x= 1.00 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= 0.00 , h=0.125 deriv= 0.00 x= 1.12 pwr= 1 err= 0.00 , h=0.125 deriv= 2.00 x= 1.12 pwr= 2 err= 0.00 , h=0.125 deriv= 6.75 x= 1.12 pwr= 3 err=-.312E-01, h=0.125 deriv= 15.2 x= 1.12 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= 0.00 , h=0.125 deriv= 0.00 x= 1.25 pwr= 1 err= 0.00 , h=0.125 deriv= 2.00 x= 1.25 pwr= 2 err=0.750 , h=0.125 deriv= 7.50 x= 1.25 pwr= 3 err= 3.53 , h=0.125 deriv= 18.8 x= 1.25 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= 0.00 , h=0.125 deriv= 2.00 x= 1.00 pwr= 2 err= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 3 err=0.344 , h=0.125 deriv= 12.0 x= 1.00 pwr= 4 err= 1.95 , h=0.125 deriv= 20.0 x= 1.00 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= 0.00 , h=0.125 deriv= 2.00 x= 1.12 pwr= 2 err= 0.00 , h=0.125 deriv= 6.75 x= 1.12 pwr= 3 err=-.312E-01, h=0.125 deriv= 15.2 x= 1.12 pwr= 4 err=-.176 , h=0.125 deriv= 28.5 x= 1.12 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= 0.00 , h=0.125 deriv= 2.00 x= 1.25 pwr= 2 err= 0.00 , h=0.125 deriv= 7.50 x= 1.25 pwr= 3 err=-.312E-01, h=0.125 deriv= 18.8 x= 1.25 pwr= 4 err=-.195 , h=0.125 deriv= 39.1 x= 1.25 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= 0.00 , h=0.125 deriv= 2.00 x= 1.38 pwr= 2 err= 0.00 , h=0.125 deriv= 8.25 x= 1.38 pwr= 3 err=0.344 , h=0.125 deriv= 22.7 x= 1.38 pwr= 4 err= 2.13 , h=0.125 deriv= 52.0 x= 1.38 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= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 3 err= 0.00 , h=0.125 deriv= 12.0 x= 1.00 pwr= 4 err=-.195 , h=0.125 deriv= 20.0 x= 1.00 pwr= 5 err=-1.40 , h=0.125 deriv= 30.0 x= 1.00 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= 0.00 , h=0.125 deriv= 6.75 x= 1.12 pwr= 3 err= 0.00 , h=0.125 deriv= 15.2 x= 1.12 pwr= 4 err=0.195E-01, h=0.125 deriv= 28.5 x= 1.12 pwr= 5 err=0.141 , h=0.125 deriv= 48.1 x= 1.12 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= 0.00 , h=0.125 deriv= 7.50 x= 1.25 pwr= 3 err= 0.00 , h=0.125 deriv= 18.8 x= 1.25 pwr= 4 err= 0.00 , h=0.125 deriv= 39.1 x= 1.25 pwr= 5 err=0.195E-02, h=0.125 deriv= 73.2 x= 1.25 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= 0.00 , h=0.125 deriv= 8.25 x= 1.38 pwr= 3 err= 0.00 , h=0.125 deriv= 22.7 x= 1.38 pwr= 4 err=-.195E-01, h=0.125 deriv= 52.0 x= 1.38 pwr= 5 err=-.152 , h=0.125 deriv= 107. x= 1.38 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= 0.00 , h=0.125 deriv= 9.00 x= 1.50 pwr= 3 err= 0.00 , h=0.125 deriv= 27.0 x= 1.50 pwr= 4 err=0.195 , h=0.125 deriv= 67.5 x= 1.50 pwr= 5 err= 1.53 , h=0.125 deriv= 152. x= 1.50 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= 0.00 , h=0.125 deriv= 12.0 x= 1.00 pwr= 4 err= 0.00 , h=0.125 deriv= 20.0 x= 1.00 pwr= 5 err=0.134 , h=0.125 deriv= 30.0 x= 1.00 pwr= 6 err= 1.18 , h=0.125 deriv= 42.0 x= 1.00 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= 0.00 , h=0.125 deriv= 15.2 x= 1.12 pwr= 4 err= 0.00 , h=0.125 deriv= 28.5 x= 1.12 pwr= 5 err=-.127E-01, h=0.125 deriv= 48.1 x= 1.12 pwr= 6 err=-.113 , h=0.125 deriv= 75.7 x= 1.12 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= 0.00 , h=0.125 deriv= 18.8 x= 1.25 pwr= 4 err= 0.00 , h=0.125 deriv= 39.1 x= 1.25 pwr= 5 err=0.195E-02, h=0.125 deriv= 73.2 x= 1.25 pwr= 6 err=0.171E-01, h=0.125 deriv= 128. x= 1.25 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= 0.00 , h=0.125 deriv= 22.7 x= 1.38 pwr= 4 err= 0.00 , h=0.125 deriv= 52.0 x= 1.38 pwr= 5 err=0.195E-02, h=0.125 deriv= 107. x= 1.38 pwr= 6 err=0.188E-01, h=0.125 deriv= 206. x= 1.38 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= 0.00 , h=0.125 deriv= 27.0 x= 1.50 pwr= 4 err= 0.00 , h=0.125 deriv= 67.5 x= 1.50 pwr= 5 err=-.127E-01, h=0.125 deriv= 152. x= 1.50 pwr= 6 err=-.120 , h=0.125 deriv= 319. x= 1.50 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= 0.00 , h=0.125 deriv= 31.7 x= 1.62 pwr= 4 err= 0.00 , h=0.125 deriv= 85.8 x= 1.62 pwr= 5 err=0.134 , h=0.125 deriv= 209. x= 1.62 pwr= 6 err= 1.28 , h=0.125 deriv= 476. x= 1.62 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= 0.00 , h=0.125 deriv= 20.0 x= 1.00 pwr= 5 err= 0.00 , h=0.125 deriv= 30.0 x= 1.00 pwr= 6 err=-.108 , h=0.125 deriv= 42.0 x= 1.00 pwr= 7 err=-1.14 , h=0.125 deriv= 56.0 x= 1.00 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= 0.00 , h=0.125 deriv= 28.5 x= 1.12 pwr= 5 err= 0.00 , h=0.125 deriv= 48.1 x= 1.12 pwr= 6 err=0.940E-02, h=0.125 deriv= 75.7 x= 1.12 pwr= 7 err=0.100 , h=0.125 deriv= 114. x= 1.12 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= 0.00 , h=0.125 deriv= 39.1 x= 1.25 pwr= 5 err= 0.00 , h=0.125 deriv= 73.2 x= 1.25 pwr= 6 err=-.171E-02, h=0.125 deriv= 128. x= 1.25 pwr= 7 err=-.182E-01, h=0.125 deriv= 214. x= 1.25 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= 0.00 , h=0.125 deriv= 52.0 x= 1.38 pwr= 5 err= 0.00 , h=0.125 deriv= 107. x= 1.38 pwr= 6 err= 0.00 , h=0.125 deriv= 206. x= 1.38 pwr= 7 err=-.275E-03, h=0.125 deriv= 378. x= 1.38 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= 0.00 , h=0.125 deriv= 67.5 x= 1.50 pwr= 5 err= 0.00 , h=0.125 deriv= 152. x= 1.50 pwr= 6 err=0.171E-02, h=0.125 deriv= 319. x= 1.50 pwr= 7 err=0.194E-01, h=0.125 deriv= 638. x= 1.50 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= 0.00 , h=0.125 deriv= 85.8 x= 1.62 pwr= 5 err= 0.00 , h=0.125 deriv= 209. x= 1.62 pwr= 6 err=-.940E-02, h=0.125 deriv= 476. x= 1.62 pwr= 7 err=-.107 , h=0.125 deriv=0.103E+04 x= 1.62 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= 0.00 , h=0.125 deriv= 107. x= 1.75 pwr= 5 err= 0.00 , h=0.125 deriv= 281. x= 1.75 pwr= 6 err=0.108 , h=0.125 deriv= 689. x= 1.75 pwr= 7 err= 1.23 , h=0.125 deriv=0.161E+04 x= 1.75 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= 0.00 , h=0.125 deriv= 30.0 x= 1.00 pwr= 6 err= 0.00 , h=0.125 deriv= 42.0 x= 1.00 pwr= 7 err=0.997E-01, h=0.125 deriv= 56.0 x= 1.00 pwr= 8 err= 1.24 , h=0.125 deriv= 72.0 x= 1.00 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= 0.00 , h=0.125 deriv= 48.1 x= 1.12 pwr= 6 err= 0.00 , h=0.125 deriv= 75.7 x= 1.12 pwr= 7 err=-.797E-02, h=0.125 deriv= 114. x= 1.12 pwr= 8 err=-.999E-01, h=0.125 deriv= 164. x= 1.12 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= 0.00 , h=0.125 deriv= 73.2 x= 1.25 pwr= 6 err= 0.00 , h=0.125 deriv= 128. x= 1.25 pwr= 7 err=0.143E-02, h=0.125 deriv= 214. x= 1.25 pwr= 8 err=0.181E-01, h=0.125 deriv= 343. x= 1.25 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= 0.00 , h=0.125 deriv= 107. x= 1.38 pwr= 6 err= 0.00 , h=0.125 deriv= 206. x= 1.38 pwr= 7 err=-.275E-03, h=0.125 deriv= 378. x= 1.38 pwr= 8 err=-.340E-02, h=0.125 deriv= 669. x= 1.38 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= 0.00 , h=0.125 deriv= 152. x= 1.50 pwr= 6 err= 0.00 , h=0.125 deriv= 319. x= 1.50 pwr= 7 err=-.275E-03, h=0.125 deriv= 638. x= 1.50 pwr= 8 err=-.371E-02, h=0.125 deriv=0.123E+04 x= 1.50 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= 0.00 , h=0.125 deriv= 209. x= 1.62 pwr= 6 err= 0.00 , h=0.125 deriv= 476. x= 1.62 pwr= 7 err=0.143E-02, h=0.125 deriv=0.103E+04 x= 1.62 pwr= 8 err=0.191E-01, h=0.125 deriv=0.215E+04 x= 1.62 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= 0.00 , h=0.125 deriv= 281. x= 1.75 pwr= 6 err= 0.00 , h=0.125 deriv= 689. x= 1.75 pwr= 7 err=-.797E-02, h=0.125 deriv=0.161E+04 x= 1.75 pwr= 8 err=-.106 , h=0.125 deriv=0.362E+04 x= 1.75 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= 0.00 , h=0.125 deriv= 371. x= 1.88 pwr= 6 err= 0.00 , h=0.125 deriv= 973. x= 1.88 pwr= 7 err=0.997E-01, h=0.125 deriv=0.243E+04 x= 1.88 pwr= 8 err= 1.34 , h=0.125 deriv=0.587E+04 x= 1.88 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= 0.00 , h=0.125 deriv= 0.00 x= 1.00 pwr= 2 err= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 3 err=-4.50 , h=0.125 deriv= 24.0 x= 1.00 pwr= 4 err=-24.8 , h=0.125 deriv= 60.0 x= 1.00 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= 0.00 , h=0.125 deriv= 0.00 x= 1.12 pwr= 2 err= 0.00 , h=0.125 deriv= 6.00 x= 1.12 pwr= 3 err=-1.50 , h=0.125 deriv= 27.0 x= 1.12 pwr= 4 err=-8.91 , h=0.125 deriv= 75.9 x= 1.12 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= 0.00 , h=0.125 deriv= 0.00 x= 1.25 pwr= 2 err= 0.00 , h=0.125 deriv= 6.00 x= 1.25 pwr= 3 err= 1.50 , h=0.125 deriv= 30.0 x= 1.25 pwr= 4 err= 8.91 , h=0.125 deriv= 93.8 x= 1.25 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= 0.00 , h=0.125 deriv= 0.00 x= 1.38 pwr= 2 err= 0.00 , h=0.125 deriv= 6.00 x= 1.38 pwr= 3 err= 4.50 , h=0.125 deriv= 33.0 x= 1.38 pwr= 4 err= 28.6 , h=0.125 deriv= 113. x= 1.38 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= 0.00 , h=0.125 deriv= 6.00 x= 1.00 pwr= 3 err= 0.00 , h=0.125 deriv= 24.0 x= 1.00 pwr= 4 err= 3.28 , h=0.125 deriv= 60.0 x= 1.00 pwr= 5 err= 23.2 , h=0.125 deriv= 120. x= 1.00 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= 0.00 , h=0.125 deriv= 6.00 x= 1.12 pwr= 3 err= 0.00 , h=0.125 deriv= 27.0 x= 1.12 pwr= 4 err=0.469 , h=0.125 deriv= 75.9 x= 1.12 pwr= 5 err= 3.52 , h=0.125 deriv= 171. x= 1.12 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= 0.00 , h=0.125 deriv= 6.00 x= 1.25 pwr= 3 err= 0.00 , h=0.125 deriv= 30.0 x= 1.25 pwr= 4 err=-.469 , h=0.125 deriv= 93.8 x= 1.25 pwr= 5 err=-3.52 , h=0.125 deriv= 234. x= 1.25 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= 0.00 , h=0.125 deriv= 6.00 x= 1.38 pwr= 3 err= 0.00 , h=0.125 deriv= 33.0 x= 1.38 pwr= 4 err=0.469 , h=0.125 deriv= 113. x= 1.38 pwr= 5 err= 3.52 , h=0.125 deriv= 312. x= 1.38 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= 0.00 , h=0.125 deriv= 6.00 x= 1.50 pwr= 3 err= 0.00 , h=0.125 deriv= 36.0 x= 1.50 pwr= 4 err= 3.28 , h=0.125 deriv= 135. x= 1.50 pwr= 5 err= 26.0 , h=0.125 deriv= 405. x= 1.50 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= 0.00 , h=0.125 deriv= 24.0 x= 1.00 pwr= 4 err= 0.00 , h=0.125 deriv= 60.0 x= 1.00 pwr= 5 err=-2.64 , h=0.125 deriv= 120. x= 1.00 pwr= 6 err=-23.0 , h=0.125 deriv= 210. x= 1.00 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= 0.00 , h=0.125 deriv= 27.0 x= 1.12 pwr= 4 err= 0.00 , h=0.125 deriv= 75.9 x= 1.12 pwr= 5 err=-.176 , h=0.125 deriv= 171. x= 1.12 pwr= 6 err=-1.62 , h=0.125 deriv= 336. x= 1.12 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= 0.00 , h=0.125 deriv= 30.0 x= 1.25 pwr= 4 err= 0.00 , h=0.125 deriv= 93.8 x= 1.25 pwr= 5 err=0.176 , h=0.125 deriv= 234. x= 1.25 pwr= 6 err= 1.61 , h=0.125 deriv= 513. x= 1.25 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= 0.00 , h=0.125 deriv= 33.0 x= 1.38 pwr= 4 err= 0.00 , h=0.125 deriv= 113. x= 1.38 pwr= 5 err=-.176 , h=0.125 deriv= 312. x= 1.38 pwr= 6 err=-1.62 , h=0.125 deriv= 751. x= 1.38 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= 0.00 , h=0.125 deriv= 36.0 x= 1.50 pwr= 4 err= 0.00 , h=0.125 deriv= 135. x= 1.50 pwr= 5 err=0.176 , h=0.125 deriv= 405. x= 1.50 pwr= 6 err= 1.61 , h=0.125 deriv=0.106E+04 x= 1.50 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= 0.00 , h=0.125 deriv= 39.0 x= 1.62 pwr= 4 err= 0.00 , h=0.125 deriv= 158. x= 1.62 pwr= 5 err= 2.64 , h=0.125 deriv= 515. x= 1.62 pwr= 6 err= 25.5 , h=0.125 deriv=0.146E+04 x= 1.62 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= 0.00 , h=0.625E-01 deriv= 0.00 x= 1.00 pwr= 3 err= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.00 pwr= 4 err=-15.0 , h=0.625E-01 deriv= 120. x= 1.00 pwr= 5 err=-96.1 , h=0.625E-01 deriv= 360. x= 1.00 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= 0.00 , h=0.625E-01 deriv= 0.00 x= 1.06 pwr= 3 err= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.06 pwr= 4 err=-7.50 , h=0.625E-01 deriv= 128. x= 1.06 pwr= 5 err=-49.7 , h=0.625E-01 deriv= 406. x= 1.06 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= 0.00 , h=0.625E-01 deriv= 0.00 x= 1.12 pwr= 3 err= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.12 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 135. x= 1.12 pwr= 5 err=-.469 , h=0.625E-01 deriv= 456. x= 1.12 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= 0.00 , h=0.625E-01 deriv= 0.00 x= 1.19 pwr= 3 err= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.19 pwr= 4 err= 7.50 , h=0.625E-01 deriv= 142. x= 1.19 pwr= 5 err= 51.6 , h=0.625E-01 deriv= 508. x= 1.19 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= 0.00 , h=0.625E-01 deriv= 0.00 x= 1.25 pwr= 3 err= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.25 pwr= 4 err= 15.0 , h=0.625E-01 deriv= 150. x= 1.25 pwr= 5 err= 106. , h=0.625E-01 deriv= 562. x= 1.25 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.00 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 120. x= 1.00 pwr= 5 err= 7.97 , h=0.625E-01 deriv= 360. x= 1.00 pwr= 6 err= 61.9 , h=0.625E-01 deriv= 840. x= 1.00 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.06 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 128. x= 1.06 pwr= 5 err= 2.34 , h=0.625E-01 deriv= 406. x= 1.06 pwr= 6 err= 18.7 , h=0.625E-01 deriv=0.101E+04 x= 1.06 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.12 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 135. x= 1.12 pwr= 5 err=-.469 , h=0.625E-01 deriv= 456. x= 1.12 pwr= 6 err=-3.69 , h=0.625E-01 deriv=0.120E+04 x= 1.12 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.19 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 142. x= 1.19 pwr= 5 err=-.469 , h=0.625E-01 deriv= 508. x= 1.19 pwr= 6 err=-3.90 , h=0.625E-01 deriv=0.141E+04 x= 1.19 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.25 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 150. x= 1.25 pwr= 5 err= 2.34 , h=0.625E-01 deriv= 562. x= 1.25 pwr= 6 err= 19.3 , h=0.625E-01 deriv=0.164E+04 x= 1.25 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= 0.00 , h=0.625E-01 deriv= 24.0 x= 1.31 pwr= 4 err= 0.00 , h=0.625E-01 deriv= 158. x= 1.31 pwr= 5 err= 7.97 , h=0.625E-01 deriv= 620. x= 1.31 pwr= 6 err= 67.1 , h=0.625E-01 deriv=0.190E+04 x= 1.31 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.00 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.00 pwr= 5 err=-56.2 , h=0.312E-01 deriv= 720. x= 1.00 pwr= 6 err=-410. , h=0.312E-01 deriv=0.252E+04 x= 1.00 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.03 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.03 pwr= 5 err=-33.8 , h=0.312E-01 deriv= 742. x= 1.03 pwr= 6 err=-250. , h=0.312E-01 deriv=0.268E+04 x= 1.03 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.06 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.06 pwr= 5 err=-11.2 , h=0.312E-01 deriv= 765. x= 1.06 pwr= 6 err=-85.3 , h=0.312E-01 deriv=0.284E+04 x= 1.06 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.09 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.09 pwr= 5 err= 11.2 , h=0.312E-01 deriv= 788. x= 1.09 pwr= 6 err= 84.5 , h=0.312E-01 deriv=0.301E+04 x= 1.09 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.12 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.12 pwr= 5 err= 33.8 , h=0.312E-01 deriv= 810. x= 1.12 pwr= 6 err= 259. , h=0.312E-01 deriv=0.319E+04 x= 1.12 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= 0.00 , h=0.312E-01 deriv= 0.00 x= 1.16 pwr= 4 err= 0.00 , h=0.312E-01 deriv= 120. x= 1.16 pwr= 5 err= 56.2 , h=0.312E-01 deriv= 832. x= 1.16 pwr= 6 err= 439. , h=0.312E-01 deriv=0.337E+04 x= 1.16 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.00 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 720. x= 1.00 pwr= 6 err= 20.5 , h=0.312E-01 deriv=0.252E+04 x= 1.00 pwr= 7 err= 175. , h=0.312E-01 deriv=0.672E+04 x= 1.00 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.03 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 742. x= 1.03 pwr= 6 err= 8.20 , h=0.312E-01 deriv=0.268E+04 x= 1.03 pwr= 7 err= 70.8 , h=0.312E-01 deriv=0.737E+04 x= 1.03 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.06 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 765. x= 1.06 pwr= 6 err=0.820 , h=0.312E-01 deriv=0.284E+04 x= 1.06 pwr= 7 err= 7.28 , h=0.312E-01 deriv=0.806E+04 x= 1.06 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.09 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 788. x= 1.09 pwr= 6 err=-1.64 , h=0.312E-01 deriv=0.301E+04 x= 1.09 pwr= 7 err=-14.4 , h=0.312E-01 deriv=0.879E+04 x= 1.09 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.12 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 810. x= 1.12 pwr= 6 err=0.820 , h=0.312E-01 deriv=0.319E+04 x= 1.12 pwr= 7 err= 7.08 , h=0.312E-01 deriv=0.957E+04 x= 1.12 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.16 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 832. x= 1.16 pwr= 6 err= 8.20 , h=0.312E-01 deriv=0.337E+04 x= 1.16 pwr= 7 err= 72.8 , h=0.312E-01 deriv=0.104E+05 x= 1.16 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= 0.00 , h=0.312E-01 deriv= 120. x= 1.19 pwr= 5 err= 0.00 , h=0.312E-01 deriv= 855. x= 1.19 pwr= 6 err= 20.5 , h=0.312E-01 deriv=0.355E+04 x= 1.19 pwr= 7 err= 184. , h=0.312E-01 deriv=0.113E+05 x= 1.19 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.00 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.00 pwr= 6 err=-236. , h=0.156E-01 deriv=0.504E+04 x= 1.00 pwr= 7 err=-.194E+04, h=0.156E-01 deriv=0.202E+05 x= 1.00 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.02 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.02 pwr= 6 err=-158. , h=0.156E-01 deriv=0.512E+04 x= 1.02 pwr= 7 err=-.130E+04, h=0.156E-01 deriv=0.208E+05 x= 1.02 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.03 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.03 pwr= 6 err=-78.8 , h=0.156E-01 deriv=0.520E+04 x= 1.03 pwr= 7 err=-657. , h=0.156E-01 deriv=0.214E+05 x= 1.03 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.05 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.05 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.528E+04 x= 1.05 pwr= 7 err=-2.46 , h=0.156E-01 deriv=0.221E+05 x= 1.05 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.06 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.06 pwr= 6 err= 78.8 , h=0.156E-01 deriv=0.536E+04 x= 1.06 pwr= 7 err= 662. , h=0.156E-01 deriv=0.228E+05 x= 1.06 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.08 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.08 pwr= 6 err= 158. , h=0.156E-01 deriv=0.543E+04 x= 1.08 pwr= 7 err=0.134E+04, h=0.156E-01 deriv=0.234E+05 x= 1.08 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= 0.00 , h=0.156E-01 deriv= 0.00 x= 1.09 pwr= 5 err= 0.00 , h=0.156E-01 deriv= 720. x= 1.09 pwr= 6 err= 236. , h=0.156E-01 deriv=0.551E+04 x= 1.09 pwr= 7 err=0.202E+04, h=0.156E-01 deriv=0.241E+05 x= 1.09 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.00 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.504E+04 x= 1.00 pwr= 7 err= 56.6 , h=0.156E-01 deriv=0.202E+05 x= 1.00 pwr= 8 err= 529. , h=0.156E-01 deriv=0.605E+05 x= 1.00 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.02 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.512E+04 x= 1.02 pwr= 7 err= 27.1 , h=0.156E-01 deriv=0.208E+05 x= 1.02 pwr= 8 err= 254. , h=0.156E-01 deriv=0.634E+05 x= 1.02 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.03 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.520E+04 x= 1.03 pwr= 7 err= 7.38 , h=0.156E-01 deriv=0.214E+05 x= 1.03 pwr= 8 err= 69.9 , h=0.156E-01 deriv=0.663E+05 x= 1.03 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.05 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.528E+04 x= 1.05 pwr= 7 err=-2.46 , h=0.156E-01 deriv=0.221E+05 x= 1.05 pwr= 8 err=-23.2 , h=0.156E-01 deriv=0.694E+05 x= 1.05 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.06 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.536E+04 x= 1.06 pwr= 7 err=-2.46 , h=0.156E-01 deriv=0.228E+05 x= 1.06 pwr= 8 err=-23.5 , h=0.156E-01 deriv=0.725E+05 x= 1.06 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.08 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.543E+04 x= 1.08 pwr= 7 err= 7.38 , h=0.156E-01 deriv=0.234E+05 x= 1.08 pwr= 8 err= 70.3 , h=0.156E-01 deriv=0.758E+05 x= 1.08 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.09 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.551E+04 x= 1.09 pwr= 7 err= 27.1 , h=0.156E-01 deriv=0.241E+05 x= 1.09 pwr= 8 err= 260. , h=0.156E-01 deriv=0.791E+05 x= 1.09 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= 0.00 , h=0.156E-01 deriv= 720. x= 1.11 pwr= 6 err= 0.00 , h=0.156E-01 deriv=0.559E+04 x= 1.11 pwr= 7 err= 56.6 , h=0.156E-01 deriv=0.248E+05 x= 1.11 pwr= 8 err= 546. , h=0.156E-01 deriv=0.826E+05 x= 1.11 pwr= 9 many formulas checked against Abramowitz and Stegun, Handbook of Mathematical Functions Table 25.2