scaling by the factor "tau".

When scaling the problem by the factor τ, the expression of the z-formula changes. First, the term such as w and v0 are multiplied by On the other hand, terms such as and are multiplied by τ, terms such as and are by   The cr[r] coefficient for modified signed distance is multiplied by .

(-v0 + w + o*(-cr[0] + w^2*(-cr[2] + tp3[9, 9, 9]/6) - 
     (v0^2*tp3[9, 9, 9])/3 + (v0*w*tp3[9, 9, 9])/6) + 
   o^2*(-(v0*cr[0]*tp3[9, 9, 9])/6 + 
     w*(-cr[1] - (cr[0]*tp3[9, 9, 9])/3 + 
       v0^2*(-(tp3[9, 9, al1]*tp3[9, 9, au1])/8 + 
         tp4[9, 9, 9, 9]/24)) + v0^3*(tp3[9, 9, 9]^2/18 + 
       (tp3[9, 9, al1]*tp3[9, 9, au1])/8 - tp4[9, 9, 9, 9]/8) + 
     v0*w^2*(-(cr[2]*tp3[9, 9, 9])/6 - tp3[9, 9, 9]^2/24 + 
       tp4[9, 9, 9, 9]/24) + w^3*(-cr[3] - (cr[2]*tp3[9, 9, 9])/3 - 
       tp3[9, 9, 9]^2/72 + tp4[9, 9, 9, 9]/24)))/tau + 
 tau*(o*(-td[al1, au1] - tp3[9, 9, 9]/6) + 
   o^2*(v0*(td[al1, au2]*td[al2, au1] - (td[al1, au1]*tp3[9, 9, 9])/
        6 + (5*tp3[9, 9, 9]^2)/72 + (tp3[9, 9, al1]*tp3[9, 9, au1])/
        8 - tp4[9, 9, 9, 9]/24) + w*(td[al1, au2]*td[al2, au1] + 
       (td[al1, au1]*tp3[9, 9, 9])/6 + (13*tp3[9, 9, 9]^2)/72 + 
       (tp3[9, 9, al1]*tp3[9, 9, au1])/2 - td[au1, au2]*
        tp3[9, al1, al2] + (tp3[9, al1, au2]*tp3[9, al2, au1])/2 - 
       tp4[9, 9, 9, 9]/8 - tp4[9, 9, al1, au1]/4)))

tau*(o*(-Daa - P999/6) + 
   o^2*((Dab2 - (Daa*P999)/6 + (5*P999^2)/72 - P9999/24 + P99a2/8)*
      v0 + (Dab2 - DabP9ab + (Daa*P999)/6 + (13*P999^2)/72 - 
       P9999/8 + P99a2/2 - P99aa/4 + P9ab2/2)*w)) + 
 (-v0 + w + o*(-c0 - (P999*v0^2)/3 + (P999*v0*w)/6 + 
     (-c2 + P999/6)*w^2) + o^2*(-(c0*P999*v0)/6 + 
     (P999^2/18 - P9999/8 + P99a2/8)*v0^3 + 
     (-c1 - (c0*P999)/3 + (P9999/24 - P99a2/8)*v0^2)*w + 
     (-(c2*P999)/6 - P999^2/24 + P9999/24)*v0*w^2 + 
     (-c3 - (c2*P999)/3 - P999^2/72 + P9999/24)*w^3))/tau