newa1 = a1 + d
newb1 = b1
newa2 = a2 + (b1*d)/2
newa3 = a3 + (a2*d)/2 - (a1*b1*d)/12 + (b1*d^2)/12
newb3 = b3 - (b1^2*d)/12
newa4 = a4 - (a2*b1*d)/12 + (b3*d)/2 - (b1^2*d^2)/24
newb4 = b4
newa5 = a5 - (a2^2*d)/12 + (a4*d)/2 + (a3*b1*d)/12 + (a1^2*b1^2*d)/360 - 
   (a1*b3*d)/12 - (a2*b1*d^2)/24 + (a1*b1^2*d^2)/360 + (b3*d^2)/12 - 
   (b1^2*d^3)/120
newb5 = b5 + (a1*b1^3*d)/720 + (b1*b3*d)/12 + (b4*d)/2 - (b1^3*d^2)/360
newc5 = c5 + (a1*b1^3*d)/360 - (b1*b3*d)/6 + (b1^3*d^2)/120
newd5 = (b1^4*d)/720 + d5
newa6 = a6 + (a4*b1*d)/18 + (a1*a2*b1^2*d)/720 + (a2*b3*d)/36 - 
   (a1*b4*d)/12 + (b5*d)/2 - (a2*b1^2*d^2)/360 + (a1*b1^3*d^2)/1440 + 
   (b1*b3*d^2)/24 + (b4*d^2)/12 - (b1^3*d^3)/720
newb6 = b6 - (a4*b1*d)/12 + (a1*a2*b1^2*d)/360 - (a2*b3*d)/12 + (c5*d)/2 + 
   (a2*b1^2*d^2)/120 + (a1*b1^3*d^2)/720 - (b1*b3*d^2)/12 + (b1^3*d^3)/240
newc6 = c6 + (a2*b1^3*d)/720 + (b1*b4*d)/12 + (b1^4*d^2)/1440 + (d*d5)/2
newd6 = -(b1*b4*d)/6 + d6
newe6 = e6
newa7 = a7 - (a2*a4*d)/6 + (a1*a2^2*b1*d)/240 + (a5*b1*d)/12 - 
   (a1*a3*b1^2*d)/180 - (a1^3*b1^3*d)/7560 + (a3*b3*d)/12 + 
   (a1^2*b1*b3*d)/180 + (b6*d)/2 - (a1*c5*d)/12 + (a2^2*b1*d^2)/180 - 
   (a4*b1*d^2)/24 + (a1*a2*b1^2*d^2)/720 - (a3*b1^2*d^2)/360 - 
   (a1^2*b1^3*d^2)/5040 - (a2*b3*d^2)/24 + (a1*b1*b3*d^2)/180 + (c5*d^2)/12 + 
   (a2*b1^2*d^3)/240 + (a1*b1^3*d^3)/10080 - (b1*b3*d^3)/60 + (b1^3*d^4)/1120
newb7 = b7 + (a2*a4*d)/12 + (a6*d)/2 - (a1*a2^2*b1*d)/1080 - (a5*b1*d)/36 + 
   (7*a1*a3*b1^2*d)/2160 - (a1^3*b1^3*d)/90720 - (a3*b3*d)/18 - 
   (a1^2*b1*b3*d)/360 - (a1*b5*d)/12 - (a2^2*b1*d^2)/360 + (a4*b1*d^2)/36 + 
   (a1*a2*b1^2*d^2)/1440 + (a3*b1^2*d^2)/360 - (a1^2*b1^3*d^2)/7560 + 
   (a2*b3*d^2)/72 - (a1*b1*b3*d^2)/360 - (a1*b4*d^2)/24 + (b5*d^2)/12 - 
   (a2*b1^2*d^3)/720 + (a1*b1^3*d^3)/15120 + (b1*b3*d^3)/120 - (b1^3*d^4)/3024
newc7 = c7 + (a3*b1^3*d)/720 + (a1^2*b1^4*d)/30240 - (b3^2*d)/12 + 
   (a2*b4*d)/12 - (b1*c5*d)/12 + (c6*d)/2 + (a2*b1^3*d^2)/1440 - 
   (a1*b1^4*d^2)/5040 + (b1^2*b3*d^2)/72 + (b1*b4*d^2)/24 - (b1^4*d^3)/3360 - 
   (a1*d*d5)/12 + (d^2*d5)/12
newd7 = (a2^2*b1^2*d)/720 - (a3*b1^3*d)/360 - (a1^2*b1^4*d)/6048 - 
   (a1*b1^2*b3*d)/720 + (b3^2*d)/6 - (a2*b4*d)/4 + (b1*b5*d)/12 + 
   (b1*c5*d)/6 + (a1*b1^4*d^2)/3360 - (b1^2*b3*d^2)/40 - (b1*b4*d^2)/12 + 
   (b1^4*d^3)/1260 + (d*d6)/2 + d7
newe7 = -(a2^2*b1^2*d)/720 + (a3*b1^3*d)/360 - (a1^2*b1^4*d)/90720 - 
   (a1*b1^2*b3*d)/540 - (b3^2*d)/36 + (a2*b4*d)/6 - (b1*b5*d)/6 - 
   (a1*b1^4*d^2)/6048 - (b1^2*b3*d^2)/180 + (b1^4*d^3)/10080 + e7
newf7 = (a2^2*b1^2*d)/720 - (a3*b1^3*d)/360 - (a1^2*b1^4*d)/7560 + 
   (a1*b1^2*b3*d)/120 - (b3^2*d)/12 - (b1*c5*d)/6 - (a1*b1^4*d^2)/1680 + 
   (b1^2*b3*d^2)/40 - (b1^4*d^3)/1120 + f7
newg7 = -(a1*b1^5*d)/30240 - (b1^3*b3*d)/720 + (b1^5*d^2)/10080 + 
   (b1*d*d5)/12 + (d*e6)/2 + g7
newh7 = (a1*b1^5*d)/30240 - (b1^5*d^2)/10080 - (b1*d*d5)/6 + h7
newi7 = -(a1*b1^5*d)/6048 + (b1^3*b3*d)/360 - (b1^5*d^2)/5040 + i7
newj7 = -(b1^6*d)/30240 + j7
