The present worksheet contains the formulaes necessary to calculate the PBE functional, and to generate code that calculate it efficently in different languages (fortran for example).
They are distributed under GPL v2 (http://www.gnu.org/copyleft/gpl.html) as part of the CP2K Project.
Fawzi Mohamed

# PBE

Reference: John P. Perdew, Kieron Burke, Matthias Ernzerhof, Phys. Rev. Letter, vol. 77, n 18, pp. 3865-3868, 28. oct. (1996)
restart;
sost:=eqs -> subs(seq(eqs[nops(eqs)-i],i=1..(nops(eqs)-1)),rhs(eqs[nops(eqs)])):
unk:=eqs -> indets(sost(eqs),symbol):
loc:=eqs -> indets(eqs,symbol) minus unk(eqs):
loc2:=eqs -> indets(map(lhs,eqs),symbol):
e:='e': m:='m': h_bar:='h_bar': a_0:='a_0':myIF:='myIF':
e:=1: m:=1: h_bar:=1: a_0:=h_bar^2 /(m*e^2):
indice:=proc(el,l) local i,ii,elAtt,el_s; i:=-1; ii:=0; el_s:=convert(el,string); for elAtt in l do ii:=ii+1; if evalb(el_s=convert(elAtt,string)) then i:=ii; end if; end do; i; end proc:
indiceDef:=proc(el,l) local i,ii,elAtt; i:=-1; ii:=0; for elAtt in l do ii:=ii+1; if evalb(el=lhs(elAtt)) then i:=ii; end if; end do; i; end proc:
definizioni:= eqs -> map(eq -> if type(eq,equation) then lhs(eq); else 0; end if ,eqs):
sameNameSameDef:=proc(eqs1,eqs2) local commonDef,res,d; commonDef:=convert(definizioni(eqs1),set)intersect convert(definizioni(eqs2),set); res:=true; for d in commonDef do if not evalb(subs(eqs1,d)=subs(eqs2,d)) then; print("def different for "||d); res:=false; end if; end do; res; end proc:
# check same name -> same def apart from eqs at the indexes returned by the function eqs_to_rm checkCompatible:=proc (eqss,eqs_to_rm) local i,j,im_indx,eqd1,eqd2,res,ii,attComp; res:=true; for i from 1 to nops(eqss)-1 do im_indx:=eqs_to_rm(eqss[i]); #print("removed",map(lhs,[eqss[i][im_indx[ii]]$ii=1..nops(im_indx)])); eqd1:=subsop('im_indx[ii]=NULL'$ii=1..nops(im_indx),eqss[i]): for j from i+1 to nops(eqss) do #print("doing (",i,j,")"); im_indx:=eqs_to_rm(eqss[j]); #print("removed",map(lhs,[eqss[j][im_indx[ii]]$ii=1..nops(im_indx)])); eqd2:=subsop('im_indx[ii]=NULL'$ii=1..nops(im_indx),eqss[j]): attComp:=sameNameSameDef(eqd1,eqd2); res:=attComp and res; if not attComp then print("incompatibility between",i,j); end if; end do; end do; res; end proc:
getDef:=proc(symb,eqs) local eq; for eq in eqs do if(lhs(eq)=symb) then return eq; end if; end do; 0; end proc:
eqUses:=(eq1,eq2)->evalb(lhs(eq2) in indets(rhs(eq1),symbol)):
enforceDependencies:=proc(eqs) local dep,eq1,eq2,i,j,ii,eqns; dep:=true; eqns:=eqs; ii:=0; i:=1; while (i<=(nops(eqs)-1) and ii<100000) do dep:=false; j:=i+1; while (j<=nops(eqs) and ii<100000) do if eqUses(eqns[i],eqns[j]) then ii:=ii+1; eqns:=subsop(i=NULL,j=(eqns[j],eqns[i]),eqns); dep:=true; else j:=j+1; end if; end do; if not dep then i:=i+1; end if; end do; eqns; end proc:
combineEqs:=proc(ord) local def,defs,allDefs,allEq; allDefs:=[]: allEq:=[]: for defs in ord do for def in defs do if not lhs(def) in allDefs then allDefs:=[op(allDefs),lhs(def)]; allEq:=[op(allEq),def]; end if; end do; end do; allEq; end proc:
combineDefs:=proc(ord) local def,defs,allDefs; allDefs:=[]: for defs in ord do for def in defs do if not def in allDefs then allDefs:=[op(allDefs),def]; end if; end do; end do; allDefs; end proc:
sostConst:=proc(eqs) local sAtt,sToDo,result; sToDo:=[]; result:=[]; for sAtt in eqs do sAtt:=subs(op(sToDo),sAtt); if type(rhs(sAtt),numeric) then sToDo:=[op(sToDo),sAtt]; end if; if rhs(sAtt)<>0 then result:=[op(result),sAtt]; end if; end do; result; end proc:
calcDerivs:=proc(eqs,arg_names) local cs,r,d,eq,eq2,eq3,i; cs:=CompSeq(locals=loc(eqs),globals=convert(unk(eqs),set)minus convert(arg_names,set), params=arg_names,eqs); r:=convert(cs,procedure); d:=[seq(D[i](r),i=1..nops(arg_names))]; eq:=map(f->op(-1,convert(f,CompSeq)),d); # ensure that the variables are bound in the global namespace eq2:=map(f->evalindets(f,symbol,g->convert(convert(g,string),symbol)),eq); eq3:=[seq(subs(result=convert(cat(lhs(eqs[nops(eqs)]),"_",arg_names[i]),symbol),eq2[i]),i=1..nops(arg_names))]; end proc:
fCostanti:=proc(costanti,eqs) local cs,pr, pEq; pEq:=map(x->getDef(x,eqs),costanti); print(pEq); cs:=CompSeq(globals=costanti,pEq); pr:=convert(cs,procedure); Fortran(pr); end proc:
rmDefs:=proc(lNames,eqs) local my_eqs,nm; my_eqs:=eqs; for nm in lNames do my_eqs:=subsop(indiceDef(nm,my_eqs)=NULL,my_eqs); end do; my_eqs; end proc:
with(CodeGeneration);
Warning, the protected name Matlab has been redefined and unprotected
NiM3LEkiQ0c2IkkoRm9ydHJhbkdGJUkxSW50ZXJtZWRpYXRlQ29kZUdGJUklSmF2YUdGJUkzTGFuZ3VhZ2VEZWZpbml0aW9uR0YlSSdNYXRsYWJHNiRJKnByb3RlY3RlZEdGLEkoX3N5c2xpYkdGJUkmTmFtZXNHRiVJJVNhdmVHRiVJKlRyYW5zbGF0ZUdGJUksVmlzdWFsQmFzaWNHRiU=

## exchange

exhange energy (LDA)
eqx1:=ex_lda=rho*ex_unif*Fx;
NiM+SSVlcXgxRzYiL0knZXhfbGRhR0YlKihJJHJob0dGJSIiIkkoZXhfdW5pZkdGJUYqSSNGeEdGJUYq
Uniform gas exchange:
eqx2:=kf=(3*Pi^2*rho)^(1/3); eqx3:=ex_unif=-3/(4*Pi)*kf;
NiM+SSVlcXgyRzYiL0kja2ZHRiUqJiIiJCMiIiJGKSomSSNQaUdJKnByb3RlY3RlZEdGLiIiI0kkcmhvR0YlRitGKg==
NiM+SSVlcXgzRzYiL0koZXhfdW5pZkdGJSwkKiZJI1BpR0kqcHJvdGVjdGVkR0YrISIiSSNrZkdGJSIiIiMhIiQiIiU=
The enhancement factor Fx is function of just p an z;
eqx4:=p=norm_drho^2/(4*(3*Pi^2)^(2/3)*rho^(8/3)); eqx5:=s=norm_drho/(2*kf*rho);
NiM+SSVlcXg0RzYiL0kicEdGJSwkKipJKm5vcm1fZHJob0dGJSIiIyIiJCMiIiJGLCokSSNQaUdJKnByb3RlY3RlZEdGMUYrIyEiI0YsSSRyaG9HRiUjISIpRiwjRi4iIzc=
NiM+SSVlcXg1RzYiL0kic0dGJSwkKihJKm5vcm1fZHJob0dGJSIiIkkja2ZHRiUhIiJJJHJob0dGJUYtI0YrIiIj
evalb(simplify(subs(eqx4,eqx5,eqx2,s^2=p),symbolic));
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
Fx can be written as
eqx6:=Fx=1+kappa-kappa/(1+mu*s^2/kappa); eqk1:=kappa=0.804; eqpbe8:=beta=0.066725; eqk2:=mu=beta*(Pi^2/3);
NiM+SSVlcXg2RzYiL0kjRnhHRiUsKCIiIkYpSSZrYXBwYUdGJUYpKiZGKkYpLCZGKUYpKihJI211R0YlRilJInNHRiUiIiNGKiEiIkYpRjFGMQ==
NiM+SSVlcWsxRzYiL0kma2FwcGFHRiUkIiQvKSEiJA==
NiM+SSdlcXBiZThHNiIvSSViZXRhR0YlJCImRG4nISIn
NiM+SSVlcWsyRzYiL0kjbXVHRiUsJComSSViZXRhR0YlIiIiSSNQaUdJKnByb3RlY3RlZEdGLSIiIyNGKyIiJA==
eqs_ex_lda := [eqk1,eqpbe8,eqk2,eqx2,eqx3,eqx5, eqx6, eqx1];
NiM+SStlcXNfZXhfbGRhRzYiNyovSSZrYXBwYUdGJSQiJC8pISIkL0klYmV0YUdGJSQiJkRuJyEiJy9JI211R0YlLCQqJkYtIiIiSSNQaUdJKnByb3RlY3RlZEdGNyIiIyNGNSIiJC9JI2tmR0YlKiZGOkY5KiZGNkY4SSRyaG9HRiVGNUY5L0koZXhfdW5pZkdGJSwkKiZGNiEiIkY8RjUjRisiIiUvSSJzR0YlLCQqKEkqbm9ybV9kcmhvR0YlRjVGPEZERj9GRCNGNUY4L0kjRnhHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSdleF9sZGFHRiUqKEY/RjVGQUY1Rk5GNQ==
unk(eqs_ex_lda);
NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2Ikkqbm9ybV9kcmhvR0Yn
loc(eqs_ex_lda);
NiM8Kkkic0c2Ikkma2FwcGFHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0YlSSNtdUdGJUklYmV0YUdGJQ==

## correlation

eqc1:=ec=rho*epsilon_cGGA;
NiM+SSVlcWMxRzYiL0kjZWNHRiUqJkkkcmhvR0YlIiIiSS1lcHNpbG9uX2NHR0FHRiVGKg==
eqc3:=chi=(rhoa-rhob)/rho;
NiM+SSVlcWMzRzYiL0kkY2hpR0YlKiYsJkklcmhvYUdGJSIiIkklcmhvYkdGJSEiIkYrSSRyaG9HRiVGLQ==
eqc7:=rs=(3/(4*Pi*rho))^(1/3);
NiM+SSVlcWM3RzYiL0kjcnNHRiUsJCooIiIkIyIiIkYqIiIlIyIiI0YqKiZJI1BpR0kqcHJvdGVjdGVkR0YyISIiSSRyaG9HRiVGM0YrI0YsRi0=
PBE (alias epsilon_cGGA) from Perdew, Burke, Ernzehof, PRL, vol 77, p 3865 (1996) It has some corrections and discussions.
eqpbe1:=t=norm_drho/(2*phi*k_s*rho);
NiM+SSdlcXBiZTFHNiIvSSJ0R0YlLCQqKkkqbm9ybV9kcmhvR0YlIiIiSSRwaGlHRiUhIiJJJGtfc0dGJUYtSSRyaG9HRiVGLSNGKyIiIw==
eqpbe2:=phi=((1+chi)^(2/3)+(1-chi)^(2/3))/2;
NiM+SSdlcXBiZTJHNiIvSSRwaGlHRiUsJiokLCYiIiJGK0kkY2hpR0YlRisjIiIjIiIkI0YrRi4qJCwmRitGK0YsISIiRi1GMA==
eqpbe3:=k_s=sqrt(4*k_f/(Pi*a_0)); #eqpbe4:=a_0=h_bar^2 /(m*e^2);
NiM+SSdlcXBiZTNHNiIvSSRrX3NHRiUsJCokKiZJJGtfZkdGJSIiIkkjUGlHSSpwcm90ZWN0ZWRHRi4hIiIjRiwiIiNGMQ==
eqpbe5:=H=(e^2/a_0)*gamma_var*phi^3*ln(1+beta/gamma_var*t^2*(1+A*t^2)/(1+A*t^2+A^2*t^4));
NiM+SSdlcXBiZTVHNiIvSSJIR0YlKihJKmdhbW1hX3ZhckdGJSIiIkkkcGhpR0YlIiIkLUkjbG5HNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjLCZGKkYqKixJJWJldGFHRiVGKkYpISIiSSJ0R0YlIiIjLCZGKkYqKiZJIkFHRiVGKkY3RjhGKkYqLChGKkYqRjpGKiomRjtGOEY3IiIlRipGNkYqRio=
eqpbe6:=A=beta/gamma_var*(exp(-epsilon_c_unif/(gamma_var*phi^3*e^2/a_0))-1)^(-1);
NiM+SSdlcXBiZTZHNiIvSSJBR0YlKihJJWJldGFHRiUiIiJJKmdhbW1hX3ZhckdGJSEiIiwmLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjFJKF9zeXNsaWJHRiU2IywkKihJL2Vwc2lsb25fY191bmlmR0YlRipGK0YsSSRwaGlHRiUhIiRGLEYqRixGKkYs
eqpbe7:=epsilon_cGGA=epsilon_c_unif+H;
NiM+SSdlcXBiZTdHNiIvSS1lcHNpbG9uX2NHR0FHRiUsJkkvZXBzaWxvbl9jX3VuaWZHRiUiIiJJIkhHRiVGKg==
eqpbe9:=gamma_var=(1-ln(2))/Pi^2;evalf(rhs(eqpbe9));
NiM+SSdlcXBiZTlHNiIvSSpnYW1tYV92YXJHRiUqJiwmIiIiRiotSSNsbkc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YlNiMiIiMhIiJGKkkjUGlHRi4hIiM=
NiMkIisnM3AhNEohIzY=
eqpbe10:=k_f=(3*Pi^2*rho)^(1/3);
NiM+SShlcXBiZTEwRzYiL0kka19mR0YlKiYiIiQjIiIiRikqJkkjUGlHSSpwcm90ZWN0ZWRHRi4iIiNJJHJob0dGJUYrRio=
eqs_pbec1 := [eqpbe8,eqpbe9,eqc3, eqpbe2, eqpbe10, eqpbe3, eqpbe1, eqpbe6, eqpbe5,eqpbe7,eqc1];
unk(eqs_pbec1);
NiM8KEklcmhvYkc2IkklcmhvYUdGJUkvZXBzaWxvbl9jX3VuaWZHRiVJI1BpR0kqcHJvdGVjdGVkR0YpSSRyaG9HRiVJKm5vcm1fZHJob0dGJQ==
Uniform gas correlation from Perdew,Wang; PRB vol 45, p 13244, 1992
equc1:=epsilon_c_unif=e_c_u_0+alpha_c*f/f_ii_0*(1-chi^4)+(e_c_u_1-e_c_u_0)*f*chi^4;
NiM+SSZlcXVjMUc2Ii9JL2Vwc2lsb25fY191bmlmR0YlLChJKGVfY191XzBHRiUiIiIqKkkoYWxwaGFfY0dGJUYqSSJmR0YlRipJJ2ZfaWlfMEdGJSEiIiwmRipGKiokSSRjaGlHRiUiIiVGL0YqRioqKCwmSShlX2NfdV8xR0YlRipGKUYvRipGLUYqRjJGM0Yq
equc2:=f=((1+chi)^(4/3)+(1-chi)^(4/3)-2)/(2^(4/3)-2);
NiM+SSZlcXVjMkc2Ii9JImZHRiUqJiwoKiQsJiIiIkYsSSRjaGlHRiVGLCMiIiUiIiRGLCokLCZGLEYsRi0hIiJGLkYsISIjRixGLCwmKiQiIiMjRixGMEY3RjRGLEYz
equc3:=f_ii_0=subs(chi=0,diff(subs(equc2,f),chi,chi)); evalf(rhs(equc3));
NiM+SSZlcXVjM0c2Ii9JJ2ZfaWlfMEdGJSwkKiQsJiokIiIjIyIiIiIiJEYsISIjRi4hIiIjIiIpIiIq
NiMkIitMNCMqNDwhIio=
G_uc:=-2*A*(1+alpha_1*rs)*ln(1+1/(2*A*(beta_1*rs^(1/2)+beta_2*rs+beta_3*rs^(3/2)+beta_4*rs^(p+1))));
NiM+SSVHX3VjRzYiLCQqKEkiQUdGJSIiIiwmRilGKSomSShhbHBoYV8xR0YlRilJI3JzR0YlRilGKUYpLUkjbG5HNiRJKnByb3RlY3RlZEdGMUkoX3N5c2xpYkdGJTYjLCZGKUYpKiZGKCEiIiwqKiZJJ2JldGFfMUdGJUYpRi0jRikiIiNGKSomSSdiZXRhXzJHRiVGKUYtRilGKSomSSdiZXRhXzNHRiVGKUYtIyIiJEY7RikqJkknYmV0YV80R0YlRikpRi0sJkkicEdGJUYpRilGKUYpRilGNkY6RikhIiM=
equc4c:=[p_1=1.0,A_1=0.031091,alpha_1_1=0.21370,beta_1_1=7.5957,beta_2_1=3.5876,beta_3_1=1.6382, beta_4_1=0.49294]; equc4:={p=p_1,A=A_1,alpha_1=alpha_1_1,beta_1=beta_1_1,beta_2=beta_2_1,beta_3=beta_3_1, beta_4=beta_4_1}; equc5:=e_c_u_0=subs(equc4,G_uc);
NiM+SSdlcXVjNGNHNiI3KS9JJHBfMUdGJSQiIzUhIiIvSSRBXzFHRiUkIiYiNEohIicvSSphbHBoYV8xXzFHRiUkIiZxOCMhIiYvSSliZXRhXzFfMUdGJSQiJmRmKCEiJS9JKWJldGFfMl8xR0YlJCImd2UkRjovSSliZXRhXzNfMUdGJSQiJiNRO0Y6L0kpYmV0YV80XzFHRiUkIiYlSFxGNQ==
NiM+SSZlcXVjNEc2IjwpL0knYmV0YV80R0YlSSliZXRhXzRfMUdGJS9JIkFHRiVJJEFfMUdGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfMUdGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzFHRiUvSSdiZXRhXzNHRiVJKWJldGFfM18xR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfMUdGJS9JInBHRiVJJHBfMUdGJQ==
NiM+SSZlcXVjNUc2Ii9JKGVfY191XzBHRiUsJCooSSRBXzFHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8xR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8xR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8xR0YlRitGL0YrRisqJkkpYmV0YV8zXzFHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzFHRiVGKylGLywmSSRwXzFHRiVGK0YrRitGK0YrRjhGPEYrISIj
equc6c:=[p_2=1.0,A_2=0.015545,alpha_1_2=0.20548,beta_1_2=14.1189,beta_2_2=6.1977,beta_3_2=3.3662, beta_4_2=0.62517]; equc6:={p=p_2,A=A_2,alpha_1=alpha_1_2,beta_1=beta_1_2,beta_2=beta_2_2,beta_3=beta_3_2, beta_4=beta_4_2}; equc7:=e_c_u_1=subs(equc6,G_uc);
NiM+SSdlcXVjNmNHNiI3KS9JJHBfMkdGJSQiIzUhIiIvSSRBXzJHRiUkIiZYYiIhIicvSSphbHBoYV8xXzJHRiUkIiZbMCMhIiYvSSliZXRhXzFfMkdGJSQiJyo9VCIhIiUvSSliZXRhXzJfMkdGJSQiJng+J0Y6L0kpYmV0YV8zXzJHRiUkIiZpTyRGOi9JKWJldGFfNF8yR0YlJCImPEQnRjU=
NiM+SSZlcXVjNkc2IjwpL0kiQUdGJUkkQV8yR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfMkdGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfMkdGJS9JInBHRiVJJHBfMkdGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzJHRiUvSSdiZXRhXzRHRiVJKWJldGFfNF8yR0YlL0knYmV0YV8zR0YlSSliZXRhXzNfMkdGJQ==
NiM+SSZlcXVjN0c2Ii9JKGVfY191XzFHRiUsJCooSSRBXzJHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8yR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8yR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8yR0YlRitGL0YrRisqJkkpYmV0YV8zXzJHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzJHRiVGKylGLywmSSRwXzJHRiVGK0YrRitGK0YrRjhGPEYrISIj
equc8c:=[p_3=1.0,A_3=0.016887,alpha_1_3=0.11125,beta_1_3=10.357,beta_2_3=3.6231,beta_3_3=0.88026, beta_4_3=0.49671]; equc8:={p=p_3,A=A_3,alpha_1=alpha_1_3,beta_1=beta_1_3,beta_2=beta_2_3,beta_3=beta_3_3, beta_4=beta_4_3}; equc9:=alpha_c=-subs(equc8,G_uc);
NiM+SSdlcXVjOGNHNiI3KS9JJHBfM0dGJSQiIzUhIiIvSSRBXzNHRiUkIiYoKW8iISInL0kqYWxwaGFfMV8zR0YlJCImRDYiISImL0kpYmV0YV8xXzNHRiUkIiZkLiIhIiQvSSliZXRhXzJfM0dGJSQiJkppJCEiJS9JKWJldGFfM18zR0YlJCImRSEpKUY1L0kpYmV0YV80XzNHRiUkIiZyJ1xGNQ==
NiM+SSZlcXVjOEc2IjwpL0kicEdGJUkkcF8zR0YlL0kiQUdGJUkkQV8zR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfM0dGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzNHRiUvSSdiZXRhXzNHRiVJKWJldGFfM18zR0YlL0knYmV0YV80R0YlSSliZXRhXzRfM0dGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfM0dGJQ==
NiM+SSZlcXVjOUc2Ii9JKGFscGhhX2NHRiUsJCooSSRBXzNHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8zR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8zR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8zR0YlRitGL0YrRisqJkkpYmV0YV8zXzNHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzNHRiVGKylGLywmSSRwXzNHRiVGK0YrRitGK0YrRjhGPEYrRj0=
eqs_e_c_unif:=[op(equc4c),op(equc6c),op(equc8c),eqc3,eqc7,equc5,equc7,equc9,equc3,equc2,equc1];
unk(eqs_e_c_unif);
NiM8JkklcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJJHJob0dGJQ==
loc(eqs_e_c_unif)intersect loc(eqs_pbec1);
NiM8I0kkY2hpRzYi
eqs_pbec1_ind:=subsop(3=NULL,eqs_pbec1): loc(eqs_e_c_unif)intersect loc(eqs_pbec1_ind);
NiM8Ig==
eqs_pbec2:=[eqs_e_c_unif[i]$i=1..nops(eqs_e_c_unif),eqs_pbec1_ind[i]$i=1..nops(eqs_pbec1_ind)];
unk(eqs_pbec2);
NiM8J0klcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJJHJob0dGJUkqbm9ybV9kcmhvR0Yl
loc(eqs_pbec2);

## costanti

costanti:=[kappa, beta,mu,gamma_var, p_1,A_1,alpha_1_1,beta_1_1,beta_2_1,beta_3_1,beta_4_1, p_2,A_2,alpha_1_2,beta_1_2,beta_2_2,beta_3_2,beta_4_2, p_3,A_3,alpha_1_3,beta_1_3,beta_2_3,beta_3_3,beta_4_3,scale_ec,scale_ex]:
NiM+SSljb3N0YW50aUc2Ijc9SSZrYXBwYUdGJUklYmV0YUdGJUkjbXVHRiVJKmdhbW1hX3ZhckdGJUkkcF8xR0YlSSRBXzFHRiVJKmFscGhhXzFfMUdGJUkpYmV0YV8xXzFHRiVJKWJldGFfMl8xR0YlSSliZXRhXzNfMUdGJUkpYmV0YV80XzFHRiVJJHBfMkdGJUkkQV8yR0YlSSphbHBoYV8xXzJHRiVJKWJldGFfMV8yR0YlSSliZXRhXzJfMkdGJUkpYmV0YV8zXzJHRiVJKWJldGFfNF8yR0YlSSRwXzNHRiVJJEFfM0dGJUkqYWxwaGFfMV8zR0YlSSliZXRhXzFfM0dGJUkpYmV0YV8yXzNHRiVJKWJldGFfM18zR0YlSSliZXRhXzRfM0dGJUkpc2NhbGVfZWNHRiVJKXNjYWxlX2V4R0Yl

### Fortran

fCostanti(costanti,eqs_lsd);
doubleprecision function pr () doubleprecision kappa doubleprecision beta doubleprecision mu doubleprecision gamma_var doubleprecision p_1 doubleprecision A_1 doubleprecision alpha_1_1 doubleprecision beta_1_1 doubleprecision beta_2_1 doubleprecision beta_3_1 doubleprecision beta_4_1 doubleprecision p_2 doubleprecision A_2 doubleprecision alpha_1_2 doubleprecision beta_1_2 doubleprecision beta_2_2 doubleprecision beta_3_2 doubleprecision beta_4_2 doubleprecision p_3 doubleprecision A_3 doubleprecision alpha_1_3 doubleprecision beta_1_3 doubleprecision beta_2_3 doubleprecision beta_3_3 doubleprecision beta_4_3 doubleprecision scale_ec doubleprecision scale_ex common kappa, beta, mu, gamma_var, p_1, A_1, alpha_1_1, beta_1_1 #, beta_2_1, beta_3_1, beta_4_1, p_2, A_2, alpha_1_2, beta_1_2, bet #a_2_2, beta_3_2, beta_4_2, p_3, A_3, alpha_1_3, beta_1_3, beta_2_3 #, beta_3_3, beta_4_3, scale_ec, scale_ex kappa = 0.804D0 beta = 0.66725D-1 mu = beta * 0.3141592654D1 ** 2 / 0.3D1 gamma_var = (0.1D1 - log(0.2D1)) / 0.3141592654D1 ** 2 p_1 = 0.10D1 A_1 = 0.31091D-1 alpha_1_1 = 0.21370D0 beta_1_1 = 0.75957D1 beta_2_1 = 0.35876D1 beta_3_1 = 0.16382D1 beta_4_1 = 0.49294D0 p_2 = 0.10D1 A_2 = 0.15545D-1 alpha_1_2 = 0.20548D0 beta_1_2 = 0.141189D2 beta_2_2 = 0.61977D1 beta_3_2 = 0.33662D1 beta_4_2 = 0.62517D0 p_3 = 0.10D1 A_3 = 0.16887D-1 alpha_1_3 = 0.11125D0 beta_1_3 = 0.10357D2 beta_2_3 = 0.36231D1 beta_3_3 = 0.88026D0 beta_4_3 = 0.49671D0 scale_ec = 0.1D1 scale_ex = 0.1D1 pr = scale_ex return end

## Tests

loc(eqs_pbec2)intersect loc(eqs_ex_lda);
NiM8I0klYmV0YUc2Ig==
sameNameSameDef(eqs_pbec2,eqs_ex_lda);
Error, (in sameNameSameDef) invalid input: subs received [{alpha_1_1 = .21370, beta_1_1 = 7.5957, beta_2_1 = 3.5876, p_1 = 1.0, A_1 = 0.31091e-1, beta_3_1 = 1.6382, beta_4_1 = .49294}, {p_2 = 1.0, A_2 = 0.15545e-1, alpha_1_2 = .20548, beta_1_2 = 14.1189, beta_3_2 = 3.3662, beta_4_2 = .62517, beta_2_2 = 6.1977}, {beta_2_3 = 3.6231, beta_3_3 = .88026, A_3 = 0.16887e-1, p_3 = 1.0, beta_4_3 = .49671, alpha_1_3 = .11125, beta_1_3 = 10.357}, chi = (rhoa-rhob)/rho, rs = 1/4*3^(1/3)*4^(2/3)*(1/(Pi*rho))^(1/3), e_c_u_0 = -2*A_1*(1+alpha_1_1*rs)*ln(1+1/2/(A_1*(beta_1_1*rs^(1/2)+beta_2_1*rs+beta_3_1*rs^(3/2)+beta_4_1*rs^(p_1+1)))), e_c_u_1 = -2*A_2*(1+alpha_1_2*rs)*ln(1+1/2/(A_2*(beta_1_2*rs^(1/2)+beta_2_2*rs+beta_3_2*rs^(3/2)+beta_4_2*rs^(p_2+1)))), alpha_c = 2*A_3*(1+alpha_1_3*rs)*ln(1+1/2/(A_3*(beta_1_3*rs^(1/2)+beta_2_3*rs+beta_3_3*rs^(3/2)+beta_4_3*rs^(p_3+1)))), f_ii_0 = 8/9/(2*2^(1/3)-2), f = ((1+chi)^(4/3)+(1-chi)^(4/3)-2)/(2*2^(1/3)-2), epsilon_c_unif = e_c_u_0+alpha_c*f*(1-chi^4)/f_ii_0+(e_c_u_1-e_c_u_0)*f*chi^4, beta = 0.66725e-1, gamma_var = (1-ln(2))/Pi^2, phi = 1/2*(1+chi)^(2/3)+1/2*(1-chi)^(2/3), k_f = 3^(1/3)*(Pi^2*rho)^(1/3), k_s = 2*(k_f/Pi)^(1/2), t = 1/2*norm_drho/(phi*k_s*rho), A = beta/(gamma_var*(exp(-epsilon_c_unif/(gamma_var*phi^3))-1)), H = gamma_var*phi^3*ln(1+beta*t^2*(1+A*t^2)/(gamma_var*(1+A*t^2+A^2*t^4))), epsilon_cGGA = epsilon_c_unif+H, ec = rho*epsilon_cGGA], which is not valid for its 1st argument
eqs_fxc:=combineEqs([eqs_pbec2,eqs_ex_lda,[Fxc=Fx+epsilon_cGGA/ex_unif]]): unk(eqs_fxc);
NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kqbm9ybV9kcmhvR0Yn
eqs_fxc1:=subsop(indiceDef(s,eqs_fxc)=NULL,indiceDef(chi,eqs_fxc)=NULL,indiceDef(rs,eqs_fxc)=NULL,eqs_fxc): unk(eqs_fxc1);
NiM8KEkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJJHJob0dGJ0kqbm9ybV9kcmhvR0YnSSRjaGlHRidJI3JzR0Yn
v_rho:=solve(getDef(rs,eqs_fxc),rho);
NiM+SSZ2X3Job0c2IiwkKiZJI3JzR0YlISIkSSNQaUdJKnByb3RlY3RlZEdGKyEiIiMiIiQiIiU=
getDef(chi,eqs_fxc);
NiMvSSRjaGlHNiIqJiwmSSVyaG9hR0YlIiIiSSVyaG9iR0YlISIiRilJJHJob0dGJUYr
v_ndrho:=solve(subs(getDef(kf,eqs_fxc),getDef(s,eqs_fxc)),norm_drho);
NiM+SSh2X25kcmhvRzYiLCQqKkkic0dGJSIiIiomSSNQaUdJKnByb3RlY3RlZEdGLCIiI0kkcmhvR0YlRikjRikiIiRGLkYpRjBGL0Yt
eqs_fxc2:=[rho=v_rho,norm_drho=v_ndrho,chi=0,op(eqs_fxc1)]: unk(eqs_fxc2);
NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJI3JzR0Yn
cs_eqs_fxc:=CompSeq(locals=loc(eqs_fxc2), globals=[Pi],params=[rs,s],eqs_fxc2): r_eqs_fxc:=convert(cs_eqs_fxc,procedure):
plot([r_eqs_fxc(0.,s),r_eqs_fxc(2.,s),r_eqs_fxc(10.,s),r_eqs_fxc(1.0e4,s),r_eqs_fxc(1.0e3,s)],s=0..3,y=1..2);
eqs_fxc_p:=combineEqs([eqs_pbec2,subs(rho=2*rho,norm_drho=2*norm_drho,eqs_ex_lda), [Fxc=Fx*2^(1/3)+2^(1/3)*epsilon_cGGA/ex_unif]]): unk(eqs_fxc_p);
NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kqbm9ybV9kcmhvR0Yn
eqs_fxc1_p:=subsop(indiceDef(s,eqs_fxc_p)=NULL,indiceDef(chi,eqs_fxc_p)=NULL,indiceDef(rs,eqs_fxc_p)=NULL,eqs_fxc_p): unk(eqs_fxc1_p);
NiM8KEkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJJHJob0dGJ0kqbm9ybV9kcmhvR0YnSSRjaGlHRidJI3JzR0Yn
v_rho_p:=solve(getDef(rs,eqs_fxc_p),rho);
NiM+SSh2X3Job19wRzYiLCQqJkkjcnNHRiUhIiRJI1BpR0kqcHJvdGVjdGVkR0YrISIiIyIiJCIiJQ==
getDef(chi,eqs_fxc_p);
NiMvSSRjaGlHNiIqJiwmSSVyaG9hR0YlIiIiSSVyaG9iR0YlISIiRilJJHJob0dGJUYr
v_ndrho_p:=solve(subs(getDef(kf,eqs_fxc_p),getDef(s,eqs_fxc_p)),norm_drho);
NiM+SSp2X25kcmhvX3BHNiIsJCosSSJzR0YlIiIiKiZJI1BpR0kqcHJvdGVjdGVkR0YsIiIjSSRyaG9HRiVGKSNGKSIiJEYuRilGMEYvRi1GL0Yt
eqs_fxc2_p:=[rho=v_rho_p,norm_drho=v_ndrho_p,chi=1,op(eqs_fxc1_p)]: unk(eqs_fxc2_p);
NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJI3JzR0Yn
cs_eqs_fxc_p:=CompSeq(locals=loc(eqs_fxc2_p), globals=[Pi],params=[rs,s],eqs_fxc2_p): r_eqs_fxc_p:=convert(cs_eqs_fxc_p,procedure):
plot([r_eqs_fxc_p(0.,s),r_eqs_fxc_p(2.,s),r_eqs_fxc_p(10.,s),r_eqs_fxc_p(10000.,s),r_eqs_fxc_p(200000.,s)], s=0..3,y=1..2);

### Compare with old QS PBE

eqsPbex:=[kappa = 0.804,cx_vwn_e=-3/4*(3/Pi)^(1/3) ,f13=1/3 ,r2kf = 1/2*(3*Pi^2)^(-f13) ,mu = 0.2195149727645171 ,rho13 = rho^f13 ,rho43 = rho13*rho ,s = r2kf*drho/rho43 ,p = 1/(1 + mu*s*s/kappa) ,fx = 1 + kappa*(1 - p) ,dfx = 2*mu*s*p*p ,ex = cx_vwn_e*rho43*fx ,vx = cx_vwn_v*rho13*(fx - s*dfx) ,vxg = cx_vwn_e*r2kf*dfx/drho,energy=ex];
unk(eqsPbex);
NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJJWRyaG9HNiJJJHJob0dGJw==
cs_eqsPbex:=CompSeq(locals=convert(loc(eqsPbex),list), globals=[Pi],params=[rho,drho],eqsPbex): r_eqsPbex:=convert(cs_eqsPbex,procedure):
eqs_ex_lda;
NiM3Ki9JJmthcHBhRzYiJCIkLykhIiQvSSViZXRhR0YmJCImRG4nISInL0kjbXVHRiYsJComRisiIiJJI1BpR0kqcHJvdGVjdGVkR0Y1IiIjI0YzIiIkL0kja2ZHRiYqJkY4RjcqJkY0RjZJJHJob0dGJkYzRjcvSShleF91bmlmR0YmLCQqJkY0ISIiRjpGMyNGKSIiJS9JInNHRiYsJCooSSpub3JtX2RyaG9HRiZGM0Y6RkJGPUZCI0YzRjYvSSNGeEdGJiwoRjNGM0YlRjMqJkYlRjMsJkYzRjMqKEYwRjNGRkY2RiVGQkYzRkJGQi9JJ2V4X2xkYUdGJiooRj1GM0Y/RjNGTEYz
cs_eqsPbex2:=CompSeq(locals=convert(loc(eqs_ex_lda),list), globals=[Pi],params=[rho,norm_drho],eqs_ex_lda): r_eqsPbex2:=convert(cs_eqsPbex2,procedure):
contourplot3d(r_eqsPbex-r_eqsPbex2,0.1..1,-1..1);
mu=sost([op(eqs_ex_lda),my_m=mu]),mu2=sost([op(eqsPbex),my_m=mu]);
NiQvSSNtdUc2IiwkKiRJI1BpR0kqcHJvdGVjdGVkR0YpIiIjJCIrbm07Q0EhIzYvSSRtdTJHRiUkIjFyXmtGKFxePiMhIzs=
evalf(rhs(%[1])-rhs(%[2])),evalf((rhs(%[1])-rhs(%[2]))/rhs(%[1]));
NiQkIiYmeTkhIzUkIisqSGVfdCchIzo=
This uses VWN correlation instead of the (correct) PW92
eqsPbec:=[f43=4/3 ,f13=1/3 ,f76=7/6 ,r2ks=1/4*(3/Pi)^(-1/6) ,ap = 0.0621814 ,bp = 3.72744 ,cp = 12.9352 ,xp = -0.10498 ,beta_pbe=0.66725e-1 ,gamma_pbe=(1-log(2))/Pi^2 ,rsfac = (f43*Pi)^(-f13) ,x2 = rsfac*rho^(-f13) ,x = sqrt(x2) ,xp2 = xp*xp ,xmxp = x - xp ,xmxp2 = xmxp*xmxp ,pp = x*x + bp*x + cp ,qp = sqrt(4*cp - bp*bp) , ecp = 1/2*ap*(log(x2/xmxp2) - ((xp2 + cp)*log(pp/xmxp2) + 2*bp*(xp2 - cp)*arctan(qp/(2*x + bp))/qp)/ (xp2 + bp*xp + cp)) ,decp = 1/2*f13*ap*((1 + bp/xmxp)*x2/pp - 1) ,ec = ecp*rho ,vc = ecp + decp ,e_var = ec/rho ,rhom76 = rho^(-f76) ,t = r2ks*drho*rhom76 ,t2 = t*t ,expe = exp(-e_var/gamma_pbe) ,bog = beta_pbe/gamma_pbe ,a = bog/(expe - 1) ,at2 = a*t2 ,q = 1/(1 + at2 + at2*at2) ,q2 = q*q ,p = 1 + bog*t2*(1 + at2)*q ,h = gamma_pbe*log(p) ,dpdt = 2*bog*t*(1 + 2*at2)*q2 ,dtdr = -f76*t/rho ,dpda = -bog*at2*t2*t2*(2 + at2)*q2 ,dade = a*a*expe/beta_pbe ,dedr = (vc - e_var)/rho ,dpdr = dpdt*dtdr + dpda*dade*dedr ,dhdr = gamma_pbe*dpdr/p ,dtddr = t/drho^2 ,dhddr = gamma_pbe*dpdt*dtddr/p ,ec = ec + rho*h ,vc = vc + h + rho*dhdr ,vcg = rho*dhddr,energy=ec];
cs_eqsPbec:=CompSeq(locals=convert(loc(eqsPbec),list), globals=[Pi],params=[rho,drho],eqsPbec): r_eqsPbec:=convert(cs_eqsPbec,procedure):
unk(eqs_pbec2);
NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJKm5vcm1fZHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kkcmhvR0Yn
eqs_pbec2_lda:=[rhoa=rho/2,rhob=rho/2,op(eqs_pbec2)];
cs_eqsPbec2:=CompSeq(locals=convert(loc(eqs_pbec2_lda),list), gobals=[Pi],params=[rho,norm_drho],eqs_pbec2_lda): r_eqsPbec2:=convert(cs_eqsPbec2,procedure):
with(plots);
Warning, the name changecoords has been redefined
convert(proc(r) local t; global Pi; t:=Pi*r^2; end proc,CompSeq);
NiMtSShDb21wU2VxRzYiNiYvSSdsb2NhbHNHRiU3I0kidEdGJS9JKGdsb2JhbHNHRiU3I0kjUGlHSSpwcm90ZWN0ZWRHRi8vSSdwYXJhbXNHRiU3I0kickdGJTcjL0YqKiZGLiIiIkYzIiIj
convert(CompSeq(locals=[t],params=[r],[t=r^2]),procedure);
NiNmKjYjSSJyRzYiNiNJInRHRiZGJkYmPjgkKiQ5JCIiI0YmRiZGJg==
contourplot3d(r_eqsPbec-r_eqsPbec2,0.1..1,-1..1);
contourplot3d(r_eqsPbec,0.1..1,-1..1);

# LDA

loc(eqs_ex_lda)intersect loc(eqs_pbec2);
NiM8I0klYmV0YUc2Ig==
sameNameSameDef(eqs_pbec2,eqs_ex_lda);
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
eqs_lda:=combineEqs([subs(rhoa=rho/2,rhob=rho/2,eqs_pbec2),eqs_ex_lda,[exc=ex_lda+ec]]): unk(eqs_lda);
NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJKm5vcm1fZHJob0c2IkkkcmhvR0Yn
arg_lda_names:=[rho,norm_drho];
NiM+SS5hcmdfbGRhX25hbWVzRzYiNyRJJHJob0dGJUkqbm9ybV9kcmhvR0Yl
deriv_lda1:=calcDerivs(eqs_lda,arg_lda_names): deriv_lda2:=[seq(op(calcDerivs(deriv_lda1[i],[rho])),i=1..2),op(calcDerivs(deriv_lda1[2],[norm_drho]))]: deriv_lda3:=[seq(op(calcDerivs(deriv_lda2[i],[rho])),i=1..3),op(calcDerivs(deriv_lda2[3],[norm_drho]))]:
eqs_lda2:=sostConst(eqs_lda): sameNameSameDef(eqs_lda2,deriv_lda1[i])$i=1..2; sameNameSameDef(eqs_lda2,deriv_lda2[i])$i=1..3; sameNameSameDef(eqs_lda2,deriv_lda3[i])$i=1..4; seq(sameNameSameDef(deriv_lda1[i],deriv_lda2[j])$i=1..2,j=1..3); seq(sameNameSameDef(deriv_lda1[i],deriv_lda3[j])$i=1..2,j=1..4); seq(sameNameSameDef(deriv_lda2[i],deriv_lda3[j])$i=1..3,j=1..4);
NiRJJXRydWVHSSpwcm90ZWN0ZWRHRiRGIw==
NiVJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0Yj
NiZJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiM=
NihJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0Yj
NipJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0YjRiNGIw==
Ni5JJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj
eqs_lda3:=combineEqs([eqs_lda2,op(deriv_lda1),op(deriv_lda2),op(deriv_lda3)]):
eqs_lda4:=enforceDependencies([my_rho=rho,my_norm_drho=norm_drho, op(subs(rho=my_rho,norm_drho=my_norm_drho,eqs_lda3))]):
res_eqs_lda:={exc,exc_rho,exc_norm_drho,exc_rho_rho,exc_norm_drho_rho,exc_norm_drho_norm_drho, exc_rho_rho_rho,exc_norm_drho_rho_rho,exc_norm_drho_norm_drho_rho, exc_norm_drho_norm_drho_norm_drho}; for my_symb in res_eqs_lda do print(my_symb,unk([op(eqs_lda4),result=my_symb])); end do;
NiM+SSxyZXNfZXFzX2xkYUc2IjwsSS5leGNfbm9ybV9kcmhvR0YlSTZleGNfbm9ybV9kcmhvX3Job19yaG9HRiVJPGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX3Job0dGJUkoZXhjX3Job0dGJUkkZXhjR0YlSThleGNfbm9ybV9kcmhvX25vcm1fZHJob0dGJUkwZXhjX3Job19yaG9fcmhvR0YlSTJleGNfbm9ybV9kcmhvX3Job0dGJUksZXhjX3Job19yaG9HRiVJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0dGJQ==
NiRJLmV4Y19ub3JtX2RyaG9HNiI8JUkjUGlHSSpwcm90ZWN0ZWRHRidJKm5vcm1fZHJob0dGJEkkcmhvR0Yk
NiRJNmV4Y19ub3JtX2RyaG9fcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=
NiRJPGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=
NiRJKGV4Y19yaG9HNiI8JUkjUGlHSSpwcm90ZWN0ZWRHRidJKm5vcm1fZHJob0dGJEkkcmhvR0Yk
NiRJJGV4Y0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=
NiRJOGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==
NiRJMGV4Y19yaG9fcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=
NiRJMmV4Y19ub3JtX2RyaG9fcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==
NiRJLGV4Y19yaG9fcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==
NiRJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=
glob_eqs_lda4:={my_rho,my_norm_drho}union res_eqs_lda;
NiM+SS5nbG9iX2Vxc19sZGE0RzYiPC5JLmV4Y19ub3JtX2RyaG9HRiVJNmV4Y19ub3JtX2RyaG9fcmhvX3Job0dGJUknbXlfcmhvR0YlSTxleGNfbm9ybV9kcmhvX25vcm1fZHJob19yaG9HRiVJKGV4Y19yaG9HRiVJJGV4Y0dGJUk4ZXhjX25vcm1fZHJob19ub3JtX2RyaG9HRiVJMGV4Y19yaG9fcmhvX3Job0dGJUkyZXhjX25vcm1fZHJob19yaG9HRiVJLW15X25vcm1fZHJob0dGJUksZXhjX3Job19yaG9HRiVJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0dGJQ==
cs_eqs_lda4:=CompSeq(locals=loc(eqs_lda4)minus glob_eqs_lda4, globals=glob_eqs_lda4,params=[rho,norm_drho,tau],eqs_lda4): r_eqs_lda4:=convert(cs_eqs_lda4,procedure):

## Fortran code

Fortran(r_eqs_lda4,defaulttype=float,optimize);
Warning, The following variable name replacements were made: ["cg", "cg0", "cg1", "cg10", "cg11", "cg12", "cg13", "cg14", "cg15", "cg16", "cg17", "cg18", "cg19", "cg2", "cg20", "cg21", "cg22", "cg23", "cg24", "cg25", "cg26", "cg27", "cg28", "cg29", "cg3", "cg30", "cg31", "cg32", "cg33", "cg34", "cg35", "cg36", "cg37", "cg38", "cg39", "cg4", "cg40", "cg41", "cg42", "cg43", "cg44", "cg45", "cg46", "cg47", "cg48", "cg49", "cg5", "cg50", "cg51", "cg52", "cg53", "cg54", "cg55", "cg56", "cg57", "cg58", "cg59", "cg6", "cg60", "cg61", "cg62", "cg63", "cg64", "cg65", "cg66", "cg7", "cg8", "cg9"] = ["norm_drho", "k_s1rho", "k_f", "epsilon_cGGArhorho", "epsilon_cGGArho", "ex_unifrho", "snorm_drho", "k_frhorho", "trhorho", "ex_unif", "srho1rho", "tnorm_drhorho", "Hnorm_drhorho", "Hnorm_drho", "k_srhorho", "Arhorho", "e_c_u_0", "trho1rho", "ex_unif1rho", "Fxrhorho", "Fxnorm_drho1rho", "e_c_u_02rho", "Fxnorm_drhonorm_drho", "Fxrho1rho", "epsilon_cGGA", "Fx1rhorho", "snorm_drho1rho", "kfrhorho", "tnorm_drho", "A1rhorho", "Arho1rho", "kfrhorhorho", "e_c_u_0rho1rho", "tnorm_drhorhorho", "s1rhorho", "e_c_u_0rho", "k_s", "trhorhorho", "rsrhorhorho", "t1rhorho", "k_f2rho", "k_s2rho", "k_srho1rho", "snorm_drhorho", "Fxnorm_drhorho", "ex_unif2rho", "k_srho", "ex_unifrho1rho", "ex_unif1rhorho", "ex_ldarhorhorho", "tnorm_drho1rho", "k_s1rhorho", "e_c_u_01rho", "Arhorhorho", "srhorho", "Fxnorm_drho", "gamma_var", "e_c_u_0rhorho", "rsrhorho", "ex_unifrhorho", "k_frho", "t2norm_drho", "e_c_u_01rhorho", "k_frhorhorho", "r_eqs_lda4", "e_c_u_0rhorhorho", "s2norm_drho", "Hnorm_drhonorm_drho"]
doubleprecision function cg66 (rho, cg, tau) doubleprecision exc_norm_drho_rho_rho doubleprecision exc_norm_drho doubleprecision exc_rho doubleprecision exc_rho_rho doubleprecision exc doubleprecision exc_norm_drho_norm_drho_rho doubleprecision exc_norm_drho_norm_drho doubleprecision exc_norm_drho_rho doubleprecision exc_rho_rho_rho doubleprecision exc_norm_drho_norm_drho_norm_drho doubleprecision my_rho doubleprecision my_norm_drho common exc_norm_drho_rho_rho, exc_norm_drho, exc_rho, exc_rho_rh #o, exc, exc_norm_drho_norm_drho_rho, exc_norm_drho_norm_drho, exc_ #norm_drho_rho, exc_rho_rho_rho, exc_norm_drho_norm_drho_norm_drho, # my_rho, my_norm_drho doubleprecision rho doubleprecision cg doubleprecision tau doubleprecision rs2rho doubleprecision t1021 doubleprecision t325 doubleprecision cg0 doubleprecision t738 doubleprecision t603 doubleprecision t281 doubleprecision t339 doubleprecision t133 doubleprecision t1076 doubleprecision t1885 doubleprecision t234 doubleprecision rs doubleprecision cg1 doubleprecision t525 doubleprecision cg2 doubleprecision rsrho doubleprecision cg3 doubleprecision t652 doubleprecision Arho doubleprecision s doubleprecision t1167 doubleprecision t915 doubleprecision t927 doubleprecision t573 doubleprecision cg4 doubleprecision t1720 doubleprecision cg5 doubleprecision t1865 doubleprecision t1871 doubleprecision cg6 doubleprecision t1627 doubleprecision t905 doubleprecision cg7 doubleprecision t407 doubleprecision cg8 doubleprecision t1932 doubleprecision t131 doubleprecision t132 doubleprecision t134 doubleprecision t136 doubleprecision t77 doubleprecision t79 doubleprecision t80 doubleprecision t81 doubleprecision t1079 doubleprecision t1019 doubleprecision t1501 doubleprecision t898 doubleprecision t1480 doubleprecision t962 doubleprecision t903 doubleprecision t349 doubleprecision t1286 doubleprecision cg9 doubleprecision t1074 doubleprecision cg10 doubleprecision cg11 doubleprecision cg12 doubleprecision cg13 doubleprecision cg14 doubleprecision Fx doubleprecision t1237 doubleprecision cg15 doubleprecision t658 doubleprecision t1648 doubleprecision t1584 doubleprecision t432 doubleprecision t1080 doubleprecision t1081 doubleprecision t460 doubleprecision t462 doubleprecision t464 doubleprecision t467 doubleprecision t470 doubleprecision t471 doubleprecision t1702 doubleprecision Fxrho doubleprecision cg16 doubleprecision t1433 doubleprecision t1443 doubleprecision t291 doubleprecision t294 doubleprecision cg17 doubleprecision t423 doubleprecision t145 doubleprecision t146 doubleprecision t149 doubleprecision t150 doubleprecision t152 doubleprecision cg18 doubleprecision cg19 doubleprecision cg20 doubleprecision t210 doubleprecision t211 doubleprecision t951 doubleprecision t664 doubleprecision t384 doubleprecision t1083 doubleprecision t1747 doubleprecision t1497 doubleprecision t586 doubleprecision t429 doubleprecision t63 doubleprecision t1636 doubleprecision t921 doubleprecision t1rho doubleprecision t1330 doubleprecision t1333 doubleprecision cg21 doubleprecision t380 doubleprecision t383 doubleprecision t389 doubleprecision t392 doubleprecision t1086 doubleprecision t741 doubleprecision kf2rho doubleprecision s2rho doubleprecision t900 doubleprecision t1842 doubleprecision t960 doubleprecision t906 doubleprecision t229 doubleprecision t230 doubleprecision cg22 doubleprecision cg23 doubleprecision t282 doubleprecision t285 doubleprecision t287 doubleprecision t288 doubleprecision t418 doubleprecision t22 doubleprecision t1089 doubleprecision t992 doubleprecision t852 doubleprecision t618 doubleprecision t97 doubleprecision t964 doubleprecision t217 doubleprecision t218 doubleprecision t219 doubleprecision t1852 doubleprecision t1837 doubleprecision t1327 doubleprecision t1329 doubleprecision t574 doubleprecision t doubleprecision t64 doubleprecision t494 doubleprecision t1891 doubleprecision t1068 doubleprecision t1090 doubleprecision t1091 doubleprecision t100 doubleprecision t101 doubleprecision t102 doubleprecision t1686 doubleprecision t1071 doubleprecision t433 doubleprecision t436 doubleprecision t437 doubleprecision t438 doubleprecision t442 doubleprecision t1236 integer t1 integer t2 doubleprecision cg24 doubleprecision t1786 doubleprecision t750 doubleprecision t1004 doubleprecision t1571 doubleprecision t94 doubleprecision cg25 doubleprecision t74 doubleprecision t75 doubleprecision t1094 doubleprecision cg26 doubleprecision t980 doubleprecision cg27 doubleprecision t1910 doubleprecision t545 doubleprecision t1477 doubleprecision t1328 doubleprecision mu doubleprecision t194 doubleprecision t197 doubleprecision t206 doubleprecision t1484 doubleprecision t1050 doubleprecision t1451 doubleprecision t1794 doubleprecision t184 doubleprecision t1458 doubleprecision t1459 doubleprecision t1455 doubleprecision t943 doubleprecision t760 doubleprecision t890 doubleprecision t824 doubleprecision t1533 doubleprecision A1rho doubleprecision cg28 doubleprecision t1096 doubleprecision t269 doubleprecision t273 doubleprecision t274 doubleprecision t279 doubleprecision cg29 doubleprecision t1913 doubleprecision t1273 doubleprecision t1098 doubleprecision kfrho doubleprecision t1324 doubleprecision cg30 doubleprecision t908 doubleprecision t1054 doubleprecision t358 doubleprecision t84 doubleprecision t85 doubleprecision cg31 doubleprecision kf doubleprecision t806 doubleprecision cg32 doubleprecision cg33 doubleprecision t293 doubleprecision t754 doubleprecision t1133 doubleprecision t984 doubleprecision t891 doubleprecision t1049 doubleprecision t1058 doubleprecision t553 integer t3 integer t4 doubleprecision t5 doubleprecision t1759 doubleprecision t1159 doubleprecision t311 doubleprecision t911 doubleprecision cg34 doubleprecision t2rho doubleprecision t1924 doubleprecision t807 doubleprecision t6 doubleprecision t7 doubleprecision t8 doubleprecision t260 doubleprecision t1588 doubleprecision t1811 doubleprecision t1815 doubleprecision t108 doubleprecision t109 doubleprecision t110 doubleprecision t111 doubleprecision t112 doubleprecision t76 doubleprecision cg35 doubleprecision t57 doubleprecision t58 doubleprecision t59 doubleprecision t60 doubleprecision t559 doubleprecision t566 doubleprecision t571 doubleprecision cg36 doubleprecision t1102 doubleprecision cg37 doubleprecision t930 doubleprecision t190 doubleprecision t235 doubleprecision t236 doubleprecision t237 doubleprecision t240 doubleprecision t241 doubleprecision t242 doubleprecision t244 doubleprecision t245 doubleprecision t1514 doubleprecision t11 doubleprecision t160 doubleprecision t163 doubleprecision t164 doubleprecision t167 doubleprecision t168 doubleprecision t171 doubleprecision t172 doubleprecision t173 doubleprecision t909 doubleprecision t66 doubleprecision t1883 doubleprecision Fx2rho doubleprecision t1517 doubleprecision t1520 doubleprecision t996 doubleprecision cg38 doubleprecision t224 doubleprecision t1425 doubleprecision t1943 doubleprecision t117 doubleprecision t120 doubleprecision t121 doubleprecision t122 doubleprecision t125 doubleprecision t129 doubleprecision t357 doubleprecision t416 doubleprecision srho doubleprecision t318 doubleprecision t321 doubleprecision t323 doubleprecision t326 doubleprecision t329 doubleprecision t330 doubleprecision t1105 doubleprecision cg39 doubleprecision t68 doubleprecision t69 doubleprecision t12 doubleprecision t1166 doubleprecision t1552 doubleprecision t1240 doubleprecision cg40 doubleprecision t1578 doubleprecision cg41 doubleprecision t72 doubleprecision t73 doubleprecision t1111 doubleprecision A doubleprecision t15 doubleprecision t1438 doubleprecision t882 doubleprecision t808 doubleprecision t1406 doubleprecision trho doubleprecision t1087 doubleprecision cg42 doubleprecision t1053 doubleprecision cg43 doubleprecision t61 doubleprecision t62 doubleprecision Fx1rho doubleprecision t153 doubleprecision t154 doubleprecision t157 doubleprecision t158 doubleprecision t159 doubleprecision t1806 doubleprecision t246 doubleprecision t17 doubleprecision t19 doubleprecision cg44 doubleprecision cg45 doubleprecision A2rho doubleprecision cg46 doubleprecision cg47 doubleprecision cg48 doubleprecision t23 doubleprecision t324 doubleprecision t1446 doubleprecision t1951 doubleprecision t1956 doubleprecision t972 doubleprecision t250 doubleprecision t253 doubleprecision t254 doubleprecision t255 doubleprecision t258 doubleprecision t259 doubleprecision t261 doubleprecision t262 doubleprecision t263 doubleprecision t1684 doubleprecision t88 doubleprecision t89 doubleprecision cg49 doubleprecision t1176 doubleprecision t528 doubleprecision t532 doubleprecision t536 doubleprecision cg50 doubleprecision cg51 doubleprecision cg52 doubleprecision cg53 doubleprecision t576 doubleprecision t1112 doubleprecision t1172 doubleprecision t348 doubleprecision t351 doubleprecision t352 doubleprecision t354 doubleprecision t356 doubleprecision cg54 doubleprecision s1rho doubleprecision t361 doubleprecision t365 doubleprecision t366 doubleprecision t369 doubleprecision t373 doubleprecision t375 doubleprecision t376 doubleprecision t377 doubleprecision cg55 doubleprecision t1207 doubleprecision t1208 doubleprecision t1848 doubleprecision t1006 doubleprecision cg56 doubleprecision t1766 doubleprecision t415 doubleprecision t177 doubleprecision t178 doubleprecision t179 doubleprecision t180 doubleprecision t182 doubleprecision t186 doubleprecision t98 doubleprecision t1683 doubleprecision cg57 doubleprecision t1439 doubleprecision t393 doubleprecision t398 doubleprecision t402 doubleprecision t403 doubleprecision t405 doubleprecision t406 doubleprecision cg58 doubleprecision cg59 doubleprecision t956 doubleprecision cg60 doubleprecision t546 doubleprecision t549 doubleprecision t730 doubleprecision t1180 doubleprecision t612 doubleprecision t506 doubleprecision t797 doubleprecision t513 doubleprecision t518 doubleprecision t523 doubleprecision t493 doubleprecision t874 doubleprecision t500 doubleprecision t501 doubleprecision t335 doubleprecision t336 doubleprecision t342 doubleprecision t345 doubleprecision t346 doubleprecision cg61 doubleprecision cg62 doubleprecision t36 doubleprecision t1506 doubleprecision t1563 doubleprecision t1564 doubleprecision cg63 doubleprecision t686 doubleprecision t522 doubleprecision t91 doubleprecision t1061 doubleprecision t913 doubleprecision t453 doubleprecision t457 doubleprecision t967 doubleprecision cg64 doubleprecision cg65 doubleprecision t1187 doubleprecision t611 doubleprecision t1829 doubleprecision t1833 doubleprecision t49 doubleprecision t424 doubleprecision t425 doubleprecision t426 doubleprecision t428 doubleprecision t430 doubleprecision t958 doubleprecision t295 doubleprecision t299 doubleprecision t301 doubleprecision t302 doubleprecision t303 doubleprecision t304 doubleprecision t55 integer t51 doubleprecision t474 doubleprecision t477 doubleprecision t478 doubleprecision t479 doubleprecision t482 doubleprecision t486 doubleprecision t490 doubleprecision t1442 doubleprecision t914 doubleprecision t876 doubleprecision t878 doubleprecision t879 doubleprecision t877 doubleprecision t1100 doubleprecision t1876 doubleprecision t628 doubleprecision t629 doubleprecision t634 doubleprecision t138 doubleprecision t140 doubleprecision t141 doubleprecision t142 doubleprecision t1130 doubleprecision t1194 my_rho = rho my_norm_drho = cg t1 = 3 ** (0.1D1 / 0.3D1) t2 = 4 ** (0.1D1 / 0.3D1) t3 = t2 ** 2 t4 = t1 * t3 t5 = 0.1D1 / 0.3141592654D1 t6 = 0.1D1 / rho t7 = t5 * t6 t8 = t7 ** (0.1D1 / 0.3D1) rs = dble(t4) * t8 / 0.4D1 t11 = 0.1D1 + 0.21370D0 * rs t12 = sqrt(rs) t15 = t12 * rs t17 = rs ** 0.20D1 t19 = 0.75957D1 * t12 + 0.35876D1 * rs + 0.16382D1 * t15 + 0.492 #94D0 * t17 t22 = 0.1D1 + 0.1608182432D2 / t19 t23 = log(t22) cg22 = -0.62182D-1 * t11 * t23 t36 = log(0.1D1 + 0.3216468318D2 / (0.141189D2 * t12 + 0.61977D1 # * rs + 0.33662D1 * t15 + 0.62517D0 * t17)) t49 = log(0.1D1 + 0.2960857464D1 / (0.10357D2 * t12 + 0.36231D1 #* rs + 0.88026D0 * t15 + 0.49671D0 * t17)) t51 = 2 ** (0.1D1 / 0.3D1) t55 = log(0.2D1) t57 = 0.3141592654D1 ** 2 t58 = 0.1D1 / t57 cg59 = (0.1D1 - t55) * t58 t59 = t57 * rho t60 = t59 ** (0.1D1 / 0.3D1) cg1 = dble(t1) * t60 t61 = cg1 * t5 t62 = sqrt(t61) cg40 = 0.2D1 * t62 t63 = 0.1D1 / cg40 t64 = cg * t63 t = t64 * t6 / 0.2D1 t66 = 0.1D1 / cg59 t68 = exp(-cg22 * t66) t69 = -0.1D1 + t68 A = 0.66725D-1 * t66 / t69 t72 = t ** 2 t73 = t66 * t72 t74 = A * t72 t75 = 0.1D1 + t74 t76 = A ** 2 t77 = t72 ** 2 t79 = 0.1D1 + t74 + t76 * t77 t80 = 0.1D1 / t79 t81 = t75 * t80 t84 = 0.1D1 + 0.66725D-1 * t73 * t81 t85 = log(t84) cg3 = cg22 + cg59 * t85 mu = 0.2224166667D-1 * t57 kf = cg1 cg16 = -0.3D1 / 0.4D1 * t5 * kf t88 = 0.1D1 / kf t89 = cg * t88 s = t89 * t6 / 0.2D1 t91 = s ** 2 t94 = 0.1D1 + 0.1243781095D1 * mu * t91 Fx = 0.1804D1 - 0.804D0 / t94 t97 = rho * cg16 exc = t97 * Fx + rho * cg3 t98 = t8 ** 2 t100 = 0.1D1 / t98 * t5 t101 = rho ** 2 t102 = 0.1D1 / t101 rsrho = -dble(t4) * t100 * t102 / 0.12D2 t108 = t19 ** 2 t109 = 0.1D1 / t108 t110 = t11 * t109 t111 = 0.1D1 / t12 t112 = t111 * rsrho t117 = rs ** 0.10D1 t120 = 0.3797850000D1 * t112 + 0.35876D1 * rsrho + 0.2457300000D #1 * t12 * rsrho + 0.985880D0 * t117 * rsrho t121 = 0.1D1 / t22 t122 = t120 * t121 cg4 = -0.1328829340D-1 * rsrho * t23 + 0.9999999999D0 * t110 * t #122 t125 = t60 ** 2 cg62 = dble(t1) / t125 * t57 / 0.3D1 t129 = 0.1D1 / t62 cg5 = t129 * cg62 * t5 t131 = cg40 ** 2 t132 = 0.1D1 / t131 t133 = cg * t132 t134 = t6 * cg5 t136 = t64 * t102 trho = -t133 * t134 / 0.2D1 - t136 / 0.2D1 t138 = cg59 ** 2 t140 = t69 ** 2 t141 = 0.1D1 / t140 t142 = 0.1D1 / t138 * t141 Arho = 0.66725D-1 * t142 * cg4 * t68 t145 = t66 * t t146 = t81 * trho t149 = Arho * t72 t150 = A * t t152 = 0.2D1 * t150 * trho t153 = t149 + t152 t154 = t153 * t80 t157 = t79 ** 2 t158 = 0.1D1 / t157 t159 = t75 * t158 t160 = A * t77 t163 = t72 * t t164 = t76 * t163 t167 = t149 + t152 + 0.2D1 * t160 * Arho + 0.4D1 * t164 * trho t168 = t159 * t167 t171 = 0.133450D0 * t145 * t146 + 0.66725D-1 * t73 * t154 - 0.66 #725D-1 * t73 * t168 t172 = cg59 * t171 t173 = 0.1D1 / t84 cg11 = cg4 + t172 * t173 kfrho = cg62 cg12 = -0.3D1 / 0.4D1 * t5 * kfrho t177 = kf ** 2 t178 = 0.1D1 / t177 t179 = cg * t178 t180 = t6 * kfrho t182 = t89 * t102 srho = -t179 * t180 / 0.2D1 - t182 / 0.2D1 t184 = t94 ** 2 t186 = 0.1D1 / t184 * mu Fxrho = 0.2000000001D1 * t186 * s * srho t190 = rho * cg12 exc_rho = cg16 * Fx + t190 * Fx + t97 * Fxrho + cg3 + rho * cg11 cg33 = t63 * t6 / 0.2D1 t194 = t81 * cg33 t197 = t66 * t163 t206 = 0.2D1 * t150 * cg33 + 0.4D1 * t164 * cg33 t210 = 0.133450D0 * t145 * t194 + 0.133450D0 * t197 * A * cg33 * # t80 - 0.66725D-1 * t73 * t159 * t206 t211 = cg59 * t210 cg2 = t211 * t173 cg13 = t88 * t6 / 0.2D1 cg58 = 0.2000000001D1 * t186 * s * cg13 exc_norm_drho = t97 * cg58 + rho * cg2 t217 = 0.1D1 / t98 / t7 * t58 t218 = t101 ** 2 t219 = 0.1D1 / t218 t224 = 0.1D1 / t101 / rho cg60 = -dble(t4) * t217 * t219 / 0.18D2 + dble(t4) * t100 * t224 # / 0.6D1 t229 = 0.1328829340D-1 * cg60 * t23 t230 = rsrho * t109 t234 = 0.1D1 / t108 / t19 t235 = t11 * t234 t236 = t120 ** 2 t237 = t236 * t121 t240 = 0.1D1 / t15 t241 = rsrho ** 2 t242 = t240 * t241 t244 = t111 * cg60 t245 = 0.3797850000D1 * t244 t246 = 0.35876D1 * cg60 t250 = 0.2457300000D1 * t12 * cg60 t253 = 0.985880D0 * t117 * cg60 t254 = -0.1898925000D1 * t242 + t245 + t246 + 0.1228650000D1 * t #111 * t241 + t250 + 0.9858800D0 * t241 + t253 t255 = t254 * t121 t258 = t108 ** 2 t259 = 0.1D1 / t258 t260 = t11 * t259 t261 = t22 ** 2 t262 = 0.1D1 / t261 t263 = t236 * t262 cg6 = -t229 + 0.4274000000D0 * t230 * t122 - 0.2000000000D1 * t2 #35 * t237 + 0.9999999999D0 * t110 * t255 + 0.1608182432D2 * t260 * # t263 cg55 = cg4 t269 = t57 ** 2 cg14 = -0.2D1 / 0.9D1 * dble(t1) / t125 / t59 * t269 t273 = 0.1D1 / t62 / t61 t274 = cg62 ** 2 t279 = t129 * cg14 * t5 cg20 = -t273 * t274 * t58 / 0.2D1 + t279 cg0 = cg5 t281 = 0.1D1 / t131 / cg40 t282 = cg * t281 t285 = t102 * cg5 t287 = t133 * t285 / 0.2D1 t288 = t6 * cg20 t291 = t102 * cg0 t293 = t133 * t291 / 0.2D1 t294 = t64 * t224 cg15 = t282 * t134 * cg0 + t287 - t133 * t288 / 0.2D1 + t293 + t #294 t295 = t6 * cg0 t1rho = -t133 * t295 / 0.2D1 - t136 / 0.2D1 t299 = 0.1D1 / t138 / cg59 t301 = 0.1D1 / t140 / t69 t302 = t299 * t301 t303 = t68 ** 2 t304 = cg4 * t303 t311 = t299 * t141 cg21 = 0.133450D0 * t302 * t304 * cg55 + 0.66725D-1 * t142 * cg6 # * t68 - 0.66725D-1 * t311 * cg4 * cg55 * t68 A1rho = 0.66725D-1 * t142 * cg55 * t68 t318 = t66 * t1rho t321 = A1rho * t72 t323 = 0.2D1 * t150 * t1rho t324 = t321 + t323 t325 = t324 * t80 t326 = t325 * trho t329 = t145 * t75 t330 = t158 * trho t335 = t321 + t323 + 0.2D1 * t160 * A1rho + 0.4D1 * t164 * t1rho t336 = t330 * t335 t339 = t81 * cg15 t342 = t154 * t1rho t345 = cg21 * t72 t346 = Arho * t t348 = 0.2D1 * t346 * t1rho t349 = A1rho * t t351 = 0.2D1 * t349 * trho t352 = A * t1rho t354 = 0.2D1 * t352 * trho t356 = 0.2D1 * t150 * cg15 t357 = t345 + t348 + t351 + t354 + t356 t358 = t357 * t80 t361 = t153 * t158 t365 = t158 * t167 t366 = t365 * t1rho t369 = t324 * t158 t373 = t73 * t75 t375 = 0.1D1 / t157 / t79 t376 = t375 * t167 t377 = t376 * t335 t380 = A1rho * t77 t383 = A * t163 t384 = Arho * t1rho t389 = trho * A1rho t392 = t76 * t72 t393 = trho * t1rho t398 = t345 + t348 + t351 + t354 + t356 + 0.2D1 * t380 * Arho + #0.8D1 * t383 * t384 + 0.2D1 * t160 * cg21 + 0.8D1 * t383 * t389 + #0.12D2 * t392 * t393 + 0.4D1 * t164 * cg15 t402 = 0.133450D0 * t318 * t146 + 0.133450D0 * t145 * t326 - 0.1 #33450D0 * t329 * t336 + 0.133450D0 * t145 * t339 + 0.133450D0 * t1 #45 * t342 + 0.66725D-1 * t73 * t358 - 0.66725D-1 * t73 * t361 * t3 #35 - 0.133450D0 * t329 * t366 - 0.66725D-1 * t73 * t369 * t167 + 0 #.133450D0 * t373 * t377 - 0.66725D-1 * t73 * t159 * t398 t403 = cg59 * t402 t405 = t84 ** 2 t406 = 0.1D1 / t405 t407 = t81 * t1rho t415 = 0.133450D0 * t145 * t407 + 0.66725D-1 * t73 * t325 - 0.66 #725D-1 * t73 * t159 * t335 t416 = t406 * t415 t418 = cg59 * t415 cg10 = cg6 + t403 * t173 - t172 * t416 cg32 = cg14 cg61 = -0.3D1 / 0.4D1 * t5 * cg32 cg24 = cg12 t423 = 0.1D1 / t177 / kf t424 = cg * t423 t425 = kfrho ** 2 t426 = t6 * t425 t428 = t102 * kfrho t429 = t179 * t428 t430 = t6 * cg32 t432 = t179 * t430 / 0.2D1 t433 = t89 * t224 cg57 = t424 * t426 + t429 - t432 + t433 s1rho = srho t436 = mu ** 2 t437 = 0.1D1 / t184 / t94 * t436 t438 = t91 * srho t442 = s1rho * srho cg25 = -0.9950248765D1 * t437 * t438 * s1rho + 0.2000000001D1 * #t186 * t442 + 0.2000000001D1 * t186 * s * cg57 Fx1rho = 0.2000000001D1 * t186 * s * s1rho t453 = rho * cg61 t457 = rho * cg24 exc_rho_rho = cg24 * Fx + cg16 * Fx1rho + cg12 * Fx + t453 * Fx #+ t190 * Fx1rho + cg16 * Fxrho + t457 * Fxrho + t97 * cg25 + cg55 #+ t418 * t173 + cg11 + rho * cg10 t460 = t132 * t6 t462 = t63 * t102 cg18 = -t460 * cg5 / 0.2D1 - t462 / 0.2D1 t464 = t66 * trho t467 = t154 * cg33 t470 = t158 * cg33 t471 = t470 * t167 t474 = t81 * cg18 t477 = t73 * A t478 = cg33 * t80 t479 = t478 * trho t482 = Arho * cg33 t486 = A * cg18 t490 = t197 * A t493 = t158 * t206 t494 = t493 * trho t500 = t375 * t206 t501 = t500 * t167 t506 = A * trho t513 = cg33 * trho t518 = 0.2D1 * t346 * cg33 + 0.2D1 * t506 * cg33 + 0.2D1 * t150 #* cg18 + 0.8D1 * t383 * t482 + 0.12D2 * t392 * t513 + 0.4D1 * t164 # * cg18 t522 = 0.133450D0 * t464 * t194 + 0.133450D0 * t145 * t467 - 0.1 #33450D0 * t329 * t471 + 0.133450D0 * t145 * t474 + 0.400350D0 * t4 #77 * t479 + 0.133450D0 * t197 * t482 * t80 + 0.133450D0 * t197 * t #486 * t80 - 0.133450D0 * t490 * t471 - 0.133450D0 * t329 * t494 - #0.66725D-1 * t73 * t361 * t206 + 0.133450D0 * t373 * t501 - 0.6672 #5D-1 * t73 * t159 * t518 t523 = cg59 * t522 t525 = t406 * t171 cg19 = t523 * t173 - t211 * t525 t528 = t178 * t6 cg47 = -t528 * kfrho / 0.2D1 - t88 * t102 / 0.2D1 t532 = t91 * cg13 t536 = srho * cg13 cg48 = -0.9950248765D1 * t437 * t532 * srho + 0.2000000001D1 * t #186 * t536 + 0.2000000001D1 * t186 * s * cg47 exc_norm_drho_rho = cg16 * cg58 + t190 * cg58 + t97 * cg48 + cg2 # + rho * cg19 t545 = cg33 ** 2 t546 = t66 * t545 t549 = A * t545 t553 = t470 * t206 t559 = t206 ** 2 t566 = 0.2D1 * t549 + 0.12D2 * t392 * t545 t571 = cg59 * (0.133450D0 * t546 * t81 + 0.667250D0 * t73 * t549 # * t80 - 0.266900D0 * t329 * t553 - 0.266900D0 * t490 * t553 + 0.1 #33450D0 * t73 * t75 * t375 * t559 - 0.66725D-1 * t73 * t159 * t566 #) t573 = t210 ** 2 t574 = cg59 * t573 cg9 = t571 * t173 - t574 * t406 t576 = cg13 ** 2 cg28 = -0.9950248765D1 * t437 * t91 * t576 + 0.2000000001D1 * t1 #86 * t576 exc_norm_drho_norm_drho = t97 * cg28 + rho * cg9 t586 = 0.1D1 / t57 / 0.3141592654D1 cg42 = -0.5D1 / 0.54D2 * dble(t4) / t98 / t58 / t102 * t586 / t2 #18 / t101 + dble(t4) * t217 / t218 / rho / 0.3D1 - dble(t4) * t100 # * t219 / 0.2D1 rs2rho = rsrho t603 = cg60 * t109 t611 = 0.3797850000D1 * t111 * rs2rho + 0.35876D1 * rs2rho + 0.2 #457300000D1 * t12 * rs2rho + 0.985880D0 * t117 * rs2rho t612 = t611 * t121 t618 = t122 * t611 t628 = -0.1898925000D1 * t240 * rsrho * rs2rho + t245 + t246 + 0 #.1228650000D1 * t112 * rs2rho + t250 + 0.9858800D0 * rsrho * rs2rh #o + t253 t629 = t628 * t121 t634 = t120 * t262 * t611 t652 = rs2rho * t109 t658 = rs ** 2 t664 = t240 * cg60 t686 = 0.2848387500D1 / t12 / t658 * t241 * rs2rho - 0.379785000 #0D1 * t664 * rsrho - 0.1898925000D1 * t664 * rs2rho + 0.3797850000 #D1 * t111 * cg42 + 0.35876D1 * cg42 - 0.6143250000D0 * t242 * rs2r #ho + 0.2457300000D1 * t244 * rsrho + 0.1228650000D1 * t244 * rs2rh #o + 0.2457300000D1 * t12 * cg42 + 0.19717600D1 * cg60 * rsrho + 0. #9858800D0 * cg60 * rs2rho + 0.985880D0 * t117 * cg42 cg7 = -0.1328829340D-1 * cg42 * t23 + 0.2137000000D0 * t603 * t6 #12 + 0.4274000000D0 * t603 * t122 - 0.8548000000D0 * rsrho * t234 #* t618 + 0.4274000000D0 * t230 * t629 + 0.6873371714D1 * rsrho * t #259 * t634 - 0.4274000000D0 * rs2rho * t234 * t237 + 0.6000000000D #1 * t260 * t237 * t611 - 0.4000000000D1 * t235 * t629 * t120 - 0.9 #649094592D2 * t11 / t258 / t19 * t263 * t611 + 0.2137000000D0 * t6 #52 * t255 - 0.2000000000D1 * t235 * t255 * t611 + 0.9999999999D0 * # t110 * t686 * t121 + 0.1608182432D2 * t260 * t254 * t262 * t611 + # 0.3436685857D1 * rs2rho * t259 * t263 + 0.3216364864D2 * t260 * t #628 * t262 * t120 + 0.5172501469D3 * t11 / t258 / t108 * t236 / t2 #61 / t22 * t611 cg37 = -t229 + 0.2137000000D0 * t230 * t612 + 0.2137000000D0 * t #652 * t122 - 0.2000000000D1 * t235 * t618 + 0.9999999999D0 * t110 #* t629 + 0.1608182432D2 * t260 * t634 cg64 = cg37 cg27 = -0.1328829340D-1 * rs2rho * t23 + 0.9999999999D0 * t110 * # t612 cg65 = 0.10D2 / 0.27D2 * dble(t1) / t125 / t101 * t57 cg44 = kfrho t730 = cg1 ** 2 t738 = t273 * cg14 t741 = t58 * cg44 cg46 = -t273 * cg62 * t741 / 0.2D1 + t279 cg54 = cg46 cg45 = t129 * cg44 * t5 t750 = t131 ** 2 t754 = cg5 * cg0 t760 = t6 * cg46 cg41 = -0.3D1 * cg / t750 * t6 * t754 * cg45 - t282 * t285 * cg0 # + t282 * t760 * cg0 + t282 * t134 * cg54 - t282 * t285 * cg45 - t #133 * t224 * cg5 + t133 * t102 * cg46 / 0.2D1 + t282 * t288 * cg45 # + t133 * t102 * cg20 / 0.2D1 - t133 * t6 * (0.3D1 / 0.4D1 / t62 / # t730 / t58 * t274 * t586 * cg44 - t738 * t58 * cg62 - t738 * t741 # / 0.2D1 + t129 * cg65 * t5) / 0.2D1 - t282 * t291 * cg45 - t133 * # t224 * cg0 + t133 * t102 * cg54 / 0.2D1 - t133 * t224 * cg45 - 0. #3D1 * t64 * t219 t797 = t133 * t102 * cg45 / 0.2D1 cg23 = t282 * t134 * cg45 + t287 - t133 * t760 / 0.2D1 + t797 + #t294 cg43 = t282 * t295 * cg45 + t293 - t133 * t6 * cg54 / 0.2D1 + t7 #97 + t294 t2rho = -t133 * t6 * cg45 / 0.2D1 - t136 / 0.2D1 t806 = t138 ** 2 t807 = 0.1D1 / t806 t808 = t140 ** 2 t824 = t303 * cg55 * cg27 t852 = cg55 * cg27 * t68 cg56 = 0.400350D0 * t807 / t808 * cg4 * t303 * t68 * cg55 * cg27 # + 0.133450D0 * t302 * cg37 * t303 * cg55 - 0.400350D0 * t807 * t3 #01 * cg4 * t824 + 0.133450D0 * t302 * t304 * cg64 + 0.133450D0 * t #302 * cg6 * t303 * cg27 + 0.66725D-1 * t142 * cg7 * t68 - 0.66725D #-1 * t311 * cg6 * cg27 * t68 - 0.66725D-1 * t311 * cg37 * cg55 * t #68 - 0.66725D-1 * t311 * cg4 * cg64 * t68 + 0.66725D-1 * t807 * t1 #41 * cg4 * t852 cg35 = 0.133450D0 * t302 * t304 * cg27 + 0.66725D-1 * t142 * cg3 #7 * t68 - 0.66725D-1 * t311 * cg4 * cg27 * t68 cg34 = 0.133450D0 * t302 * t824 + 0.66725D-1 * t142 * cg64 * t68 # - 0.66725D-1 * t311 * t852 A2rho = 0.66725D-1 * t142 * cg27 * t68 t874 = A2rho * t72 t876 = 0.2D1 * t150 * t2rho t877 = t874 + t876 t878 = t877 * t80 t879 = t878 * trho t882 = t66 * t2rho t890 = t874 + t876 + 0.2D1 * t160 * A2rho + 0.4D1 * t164 * t2rho t891 = t335 * t890 t898 = t73 * t153 t900 = t375 * t335 * t890 t903 = cg35 * t72 t905 = 0.2D1 * t346 * t2rho t906 = A2rho * t t908 = 0.2D1 * t906 * trho t909 = A * t2rho t911 = 0.2D1 * t909 * trho t913 = 0.2D1 * t150 * cg23 t914 = t903 + t905 + t908 + t911 + t913 t915 = t914 * t80 t921 = t882 * t75 t927 = A2rho * t77 t930 = Arho * t2rho t943 = t903 + t905 + t908 + t911 + t913 + 0.2D1 * t927 * Arho + #0.8D1 * t383 * t930 + 0.2D1 * t160 * cg35 + 0.8D1 * t383 * trho * #A2rho + 0.12D2 * t392 * trho * t2rho + 0.4D1 * t164 * cg23 t951 = 0.133450D0 * t318 * t879 + 0.133450D0 * t882 * t339 + 0.2 #66900D0 * t329 * t375 * trho * t891 + 0.133450D0 * t145 * t325 * c #g23 + 0.133450D0 * t898 * t900 + 0.133450D0 * t145 * t915 * t1rho #+ 0.133450D0 * t882 * t326 - 0.133450D0 * t921 * t336 + 0.133450D0 # * t145 * t154 * cg43 + 0.133450D0 * t373 * t375 * t943 * t335 + 0 #.133450D0 * t73 * t877 * t377 t956 = cg34 * t72 t958 = 0.2D1 * t349 * t2rho t960 = 0.2D1 * t906 * t1rho t962 = 0.2D1 * t909 * t1rho t964 = 0.2D1 * t150 * cg43 t967 = A1rho * t2rho t972 = t1rho * A2rho t980 = t956 + t958 + t960 + t962 + t964 + 0.2D1 * t927 * A1rho + # 0.8D1 * t383 * t967 + 0.2D1 * t160 * cg34 + 0.8D1 * t383 * t972 + # 0.12D2 * t392 * t1rho * t2rho + 0.4D1 * t164 * cg43 t984 = t956 + t958 + t960 + t962 + t964 t992 = t357 * t158 t996 = t145 * t877 t1004 = t145 * t153 t1006 = t158 * t335 * t2rho t1019 = -0.133450D0 * t329 * t158 * cg23 * t335 - 0.66725D-1 * t #73 * t361 * t980 - 0.66725D-1 * t73 * t984 * t158 * t167 + 0.13345 #0D0 * t145 * t358 * t2rho - 0.66725D-1 * t73 * t992 * t890 - 0.133 #450D0 * t996 * t336 - 0.133450D0 * t996 * t366 - 0.133450D0 * t329 # * t330 * t980 - 0.133450D0 * t1004 * t1006 + 0.266900D0 * t329 * #t376 * t1rho * t890 - 0.133450D0 * t329 * t365 * cg43 - 0.66725D-1 # * t73 * t369 * t943 t1021 = t984 * t80 t1049 = t73 * t324 t1050 = t376 * t890 t1053 = t318 * t75 t1054 = t330 * t890 t1058 = t158 * t1rho * t890 t1061 = 0.133450D0 * t145 * t1021 * trho - 0.133450D0 * t921 * t #366 + 0.266900D0 * t329 * t376 * t335 * t2rho + 0.133450D0 * t373 #* t375 * t398 * t890 - 0.66725D-1 * t73 * t914 * t158 * t335 + 0.1 #33450D0 * t145 * t878 * cg15 - 0.133450D0 * t329 * t158 * cg15 * t #890 + 0.133450D0 * t66 * cg43 * t146 + 0.133450D0 * t1049 * t1050 #- 0.133450D0 * t1053 * t1054 - 0.133450D0 * t1004 * t1058 t1068 = t145 * t324 t1071 = t967 * trho t1074 = cg21 * t t1076 = 0.2D1 * t1074 * t2rho t1079 = 0.2D1 * cg35 * t * t1rho t1080 = t930 * t1rho t1081 = 0.2D1 * t1080 t1083 = 0.2D1 * t346 * cg43 t1086 = 0.2D1 * cg34 * t * trho t1087 = 0.2D1 * t1071 t1089 = 0.2D1 * t349 * cg23 t1090 = t972 * trho t1091 = 0.2D1 * t1090 t1094 = 0.2D1 * A * cg43 * trho t1096 = 0.2D1 * t352 * cg23 t1098 = 0.2D1 * t906 * cg15 t1100 = 0.2D1 * t909 * cg15 t1102 = 0.2D1 * t150 * cg41 t1105 = t76 * t t1111 = 0.24D2 * t74 * t1071 + t1076 + t1079 + t1081 + t1083 + t #1086 + t1087 + t1089 + t1091 + t1094 + t1096 + t1098 + t1100 + t11 #02 + 0.24D2 * t74 * t1090 + 0.24D2 * t1105 * t393 * t2rho + 0.24D2 # * t74 * t1080 t1112 = cg56 * t72 t1130 = A2rho * t163 t1133 = A1rho * t163 t1159 = t1112 + 0.2D1 * t380 * cg35 + 0.2D1 * t927 * cg21 + 0.4D #1 * t164 * cg41 + 0.2D1 * t160 * cg56 + 0.8D1 * t383 * trho * cg34 # + 0.12D2 * t392 * trho * cg43 + 0.8D1 * t383 * cg23 * A1rho + 0.8 #D1 * t1130 * t389 + 0.8D1 * t1133 * t930 + 0.12D2 * t392 * cg23 * #t1rho + 0.8D1 * t383 * cg35 * t1rho + 0.2D1 * cg34 * t77 * Arho + #0.8D1 * t1130 * t384 + 0.12D2 * t392 * cg15 * t2rho + 0.8D1 * t383 # * Arho * cg43 + 0.8D1 * t383 * cg21 * t2rho + 0.8D1 * t383 * cg15 # * A2rho t1166 = t157 ** 2 t1167 = 0.1D1 / t1166 t1172 = t877 * t158 t1176 = t1112 + t1076 + t1079 + t1081 + t1083 + t1086 + t1087 + #t1089 + t1091 + t1094 + t1096 + t1098 + t1100 + t1102 t1180 = t365 * t2rho t1187 = t81 * cg23 t1194 = 0.133450D0 * t145 * t81 * cg41 + 0.133450D0 * t373 * t37 #6 * t980 - 0.133450D0 * t1068 * t1054 - 0.66725D-1 * t73 * t159 * #(t1111 + t1159) + 0.133450D0 * t882 * t342 - 0.400350D0 * t373 * t #1167 * t167 * t891 - 0.66725D-1 * t73 * t1172 * t398 + 0.66725D-1 #* t73 * t1176 * t80 - 0.133450D0 * t1068 * t1180 - 0.133450D0 * t3 #29 * t158 * t398 * t2rho + 0.133450D0 * t318 * t1187 - 0.133450D0 #* t329 * t158 * t943 * t1rho t1207 = 0.133450D0 * t145 * t81 * t2rho + 0.66725D-1 * t73 * t87 #8 - 0.66725D-1 * t73 * t159 * t890 t1208 = t406 * t1207 t1236 = 0.133450D0 * t882 * t146 + 0.133450D0 * t145 * t879 - 0. #133450D0 * t329 * t1054 + 0.133450D0 * t145 * t1187 + 0.133450D0 * # t145 * t154 * t2rho + 0.66725D-1 * t73 * t915 - 0.66725D-1 * t73 #* t361 * t890 - 0.133450D0 * t329 * t1180 - 0.66725D-1 * t73 * t11 #72 * t167 + 0.133450D0 * t373 * t1050 - 0.66725D-1 * t73 * t159 * #t943 t1237 = cg59 * t1236 t1240 = 0.1D1 / t405 / t84 t1273 = 0.133450D0 * t882 * t407 + 0.133450D0 * t145 * t878 * t1 #rho - 0.133450D0 * t329 * t1058 + 0.133450D0 * t145 * t81 * cg43 + # 0.133450D0 * t145 * t325 * t2rho + 0.66725D-1 * t73 * t1021 - 0.6 #6725D-1 * t73 * t369 * t890 - 0.133450D0 * t329 * t1006 - 0.66725D #-1 * t73 * t1172 * t335 + 0.133450D0 * t373 * t900 - 0.66725D-1 * #t73 * t159 * t980 cg36 = cg65 kf2rho = cg44 cg50 = cg61 cg51 = cg50 cg49 = -0.3D1 / 0.4D1 * t5 * kf2rho t1286 = t177 ** 2 cg17 = t424 * t180 * kf2rho + t429 / 0.2D1 - t432 + t179 * t102 #* kf2rho / 0.2D1 + t433 cg39 = cg17 s2rho = -t179 * t6 * kf2rho / 0.2D1 - t182 / 0.2D1 t1324 = t184 ** 2 t1327 = 0.1D1 / t1324 * t436 * mu t1328 = t91 * s t1329 = t1327 * t1328 t1330 = t442 * s2rho t1333 = t437 * s cg29 = -0.9950248765D1 * t437 * t438 * s2rho + 0.2000000001D1 * #t186 * s2rho * srho + 0.2000000001D1 * t186 * s * cg17 cg30 = -0.9950248765D1 * t437 * t91 * s1rho * s2rho + 0.20000000 #01D1 * t186 * s2rho * s1rho + 0.2000000001D1 * t186 * s * cg39 Fx2rho = 0.2000000001D1 * t186 * s * s2rho cg52 = cg51 * Fx + cg24 * Fx2rho + cg49 * Fx1rho + cg16 * cg30 + # cg50 * Fx + cg12 * Fx2rho + cg61 * Fx - 0.3D1 / 0.4D1 * rho * t5 #* cg36 * Fx + t453 * Fx2rho + cg12 * Fx1rho + rho * cg50 * Fx1rho #+ t190 * cg30 + cg49 * Fxrho + cg16 * cg29 + cg24 * Fxrho + rho * #cg51 * Fxrho + t457 * cg29 + cg16 * cg25 + rho * cg49 * cg25 + t97 # * (0.7425558783D2 * t1329 * t1330 - 0.2985074630D2 * t1333 * t133 #0 - 0.9950248765D1 * t437 * t91 * cg17 * s1rho - 0.9950248765D1 * #t437 * t438 * cg39 + 0.2000000001D1 * t186 * cg39 * srho + 0.20000 #00001D1 * t186 * s1rho * cg17 - 0.9950248765D1 * t437 * t91 * cg57 # * s2rho + 0.2000000001D1 * t186 * s2rho * cg57 + 0.2000000001D1 * # t186 * s * (-0.3D1 * cg / t1286 * t426 * kf2rho - t424 * t102 * t #425 + 0.2D1 * t424 * t430 * kfrho - 0.2D1 * t424 * t428 * kf2rho - # 0.2D1 * t179 * t224 * kfrho + 0.3D1 / 0.2D1 * t179 * t102 * cg32 #+ t424 * t430 * kf2rho - t179 * t6 * cg36 / 0.2D1 - t179 * t224 * #kf2rho - 0.3D1 * t89 * t219)) exc_rho_rho_rho = cg52 + cg64 + cg59 * t1273 * t173 - t418 * t12 #08 + cg37 + t1237 * t173 - t172 * t1208 + cg10 + rho * (cg7 + cg59 # * (t951 + t1019 + t1061 + t1194) * t173 - t403 * t1208 - t1237 * #t416 + 0.2D1 * t172 * t1240 * t415 * t1207 - t172 * t406 * t1273) t1406 = t132 * t102 cg38 = t281 * t6 * t754 + t1406 * cg5 / 0.2D1 - t460 * cg20 / 0. #2D1 + t1406 * cg0 / 0.2D1 + t63 * t224 cg53 = -t460 * cg0 / 0.2D1 - t462 / 0.2D1 t1425 = cg33 * A1rho t1433 = 0.2D1 * t349 * cg33 + 0.2D1 * t352 * cg33 + 0.2D1 * t150 # * cg53 + 0.8D1 * t383 * t1425 + 0.12D2 * t392 * cg33 * t1rho + 0. #4D1 * t164 * cg53 t1438 = t197 * Arho t1439 = t470 * t335 t1442 = cg18 * t158 t1443 = t1442 * t335 t1446 = Arho * cg53 t1451 = t167 * t335 t1455 = t464 * t75 t1458 = t375 * cg33 t1459 = t1458 * t1451 t1477 = 0.133450D0 * t66 * cg15 * t194 + 0.133450D0 * t373 * t37 #5 * t1433 * t167 - 0.133450D0 * t1438 * t1439 - 0.133450D0 * t490 #* t1443 + 0.133450D0 * t197 * t1446 * t80 - 0.400350D0 * t373 * t1 #167 * t206 * t1451 - 0.133450D0 * t1455 * t1439 + 0.266900D0 * t32 #9 * t1459 - 0.66725D-1 * t73 * t369 * t518 + 0.133450D0 * t373 * t #500 * t398 + 0.133450D0 * t145 * t325 * cg18 + 0.133450D0 * t318 * # t474 - 0.133450D0 * t329 * t158 * t518 * t1rho t1480 = t500 * t335 t1484 = t478 * t1rho t1497 = trho * t335 t1501 = t81 * cg53 t1506 = t145 * A t1514 = t158 * cg53 * t167 t1517 = t470 * t398 t1520 = -0.133450D0 * t329 * t1443 + 0.133450D0 * t898 * t1480 + # 0.400350D0 * t73 * Arho * t1484 - 0.66725D-1 * t73 * t361 * t1433 # + 0.400350D0 * t477 * cg18 * t80 * t1rho + 0.133450D0 * t145 * t3 #58 * cg33 - 0.400350D0 * t477 * t470 * t1497 + 0.133450D0 * t464 * # t1501 - 0.133450D0 * t1068 * t494 + 0.800700D0 * t1506 * t478 * t #393 + 0.400350D0 * t73 * A1rho * t479 - 0.133450D0 * t329 * t1514 #- 0.133450D0 * t490 * t1517 t1533 = t375 * t518 t1552 = cg21 * cg33 t1563 = 0.133450D0 * t197 * A * cg38 * t80 - 0.133450D0 * t197 * # A1rho * t471 + 0.400350D0 * t477 * cg53 * t80 * trho + 0.133450D0 # * t373 * t1533 * t335 - 0.133450D0 * t490 * t1514 - 0.133450D0 * #t1004 * t1439 + 0.133450D0 * t145 * t81 * cg38 + 0.266900D0 * t490 # * t1459 + 0.133450D0 * t145 * t154 * cg53 + 0.400350D0 * t477 * t #478 * cg15 + 0.133450D0 * t197 * t1552 * t80 - 0.133450D0 * t329 * # t158 * t1433 * trho - 0.133450D0 * t329 * t493 * cg15 t1564 = t167 * t1rho t1571 = t325 * cg33 t1578 = A1rho * cg18 t1584 = t384 * cg33 t1588 = t389 * cg33 t1627 = 0.2D1 * t1074 * cg33 + 0.2D1 * t1584 + 0.2D1 * t346 * cg #53 + 0.2D1 * t1588 + 0.2D1 * A * cg15 * cg33 + 0.2D1 * t506 * cg53 # + 0.2D1 * t349 * cg18 + 0.2D1 * t352 * cg18 + 0.2D1 * t150 * cg38 # + 0.8D1 * t1133 * t482 + 0.24D2 * t74 * t1584 + 0.8D1 * t383 * t1 #446 + 0.8D1 * t383 * t1552 + 0.24D2 * t74 * t1588 + 0.24D2 * t1105 # * t513 * t1rho + 0.12D2 * t392 * cg53 * trho + 0.12D2 * t392 * cg #33 * cg15 + 0.8D1 * t383 * t1578 + 0.12D2 * t392 * cg18 * t1rho + #0.4D1 * t164 * cg38 t1636 = t493 * t1rho t1648 = -0.400350D0 * t477 * t470 * t1564 + 0.266900D0 * t329 * #t500 * t1497 + 0.133450D0 * t464 * t1571 - 0.133450D0 * t1053 * t4 #71 - 0.133450D0 * t1053 * t494 + 0.133450D0 * t197 * t1578 * t80 - # 0.66725D-1 * t73 * t159 * t1627 - 0.66725D-1 * t73 * t992 * t206 #+ 0.133450D0 * t1049 * t501 - 0.133450D0 * t1004 * t1636 - 0.13345 #0D0 * t1068 * t471 + 0.133450D0 * t318 * t467 + 0.266900D0 * t329 #* t500 * t1564 - 0.133450D0 * t329 * t1517 t1683 = 0.133450D0 * t318 * t194 + 0.133450D0 * t145 * t1571 - 0 #.133450D0 * t329 * t1439 + 0.133450D0 * t145 * t1501 + 0.400350D0 #* t477 * t1484 + 0.133450D0 * t197 * t1425 * t80 + 0.133450D0 * t1 #97 * A * cg53 * t80 - 0.133450D0 * t490 * t1439 - 0.133450D0 * t32 #9 * t1636 - 0.66725D-1 * t73 * t369 * t206 + 0.133450D0 * t373 * t #1480 - 0.66725D-1 * t73 * t159 * t1433 t1684 = cg59 * t1683 t1686 = t1240 * t171 cg31 = cg47 t1702 = t536 * s1rho t1720 = t91 * cg47 cg26 = -0.9950248765D1 * t437 * t532 * s1rho + 0.2000000001D1 * #t186 * s1rho * cg13 + 0.2000000001D1 * t186 * s * cg31 exc_norm_drho_rho_rho = cg24 * cg58 + cg16 * cg26 + cg12 * cg58 #+ t453 * cg58 + t190 * cg26 + cg16 * cg48 + t457 * cg48 + t97 * (0 #.7425558783D2 * t1329 * t1702 - 0.2985074630D2 * t1333 * t1702 - 0 #.9950248765D1 * t437 * t91 * cg31 * srho - 0.9950248765D1 * t437 * # t532 * cg57 + 0.2000000001D1 * t186 * cg57 * cg13 + 0.2000000001D #1 * t186 * srho * cg31 - 0.9950248765D1 * t437 * t1720 * s1rho + 0 #.2000000001D1 * t186 * s1rho * cg47 + 0.2000000001D1 * t186 * s * #(t423 * t6 * t425 + t178 * t102 * kfrho - t528 * cg32 / 0.2D1 + t8 #8 * t224)) + t1684 * t173 - t211 * t416 + cg19 + rho * (cg59 * (t1 #477 + t1520 + t1563 + t1648) * t173 - t523 * t416 - t1684 * t525 + # 0.2D1 * t211 * t1686 * t415 - t211 * t406 * t402) t1747 = t470 * t518 t1759 = t375 * t559 t1766 = Arho * t545 t1786 = t1442 * t206 t1794 = -0.266900D0 * t490 * t1747 - 0.800700D0 * t477 * t470 * #t206 * trho + 0.1334500D1 * t477 * t478 * cg18 - 0.266900D0 * t100 #4 * t553 + 0.266900D0 * t329 * t1759 * trho + 0.266900D0 * t373 * #t1533 * t206 - 0.66725D-1 * t73 * t159 * (0.2D1 * t1766 + 0.4D1 * #t486 * cg33 + 0.24D2 * t74 * t1766 + 0.24D2 * t1105 * t545 * trho #+ 0.24D2 * t392 * cg18 * cg33) - 0.266900D0 * t1455 * t553 - 0.133 #450D0 * t546 * t168 - 0.266900D0 * t490 * t1786 - 0.266900D0 * t32 #9 * t1786 + 0.266900D0 * t66 * cg18 * t194 t1806 = t500 * cg33 * t167 t1811 = t545 * t80 t1815 = t375 * t566 t1829 = t545 * t158 t1833 = t1167 * t559 t1837 = 0.133450D0 * t73 * t153 * t375 * t559 - 0.133450D0 * t32 #9 * t158 * t566 * trho - 0.266900D0 * t1438 * t553 + 0.533800D0 * #t329 * t1806 - 0.266900D0 * t329 * t1747 + 0.1334500D1 * t1506 * t #1811 * trho + 0.133450D0 * t373 * t1815 * t167 + 0.133450D0 * t546 # * t154 + 0.533800D0 * t490 * t1806 - 0.66725D-1 * t73 * t361 * t5 #66 + 0.667250D0 * t73 * t1766 * t80 - 0.667250D0 * t477 * t1829 * #t167 - 0.400350D0 * t373 * t1833 * t167 t1842 = t406 * t210 t1848 = t1328 * t576 t1852 = s * t576 exc_norm_drho_norm_drho_rho = cg16 * cg28 + t190 * cg28 + t97 * #(0.7425558783D2 * t1327 * t1848 * srho - 0.2985074630D2 * t437 * t #1852 * srho - 0.1990049753D2 * t437 * t1720 * cg13 + 0.4000000002D #1 * t186 * cg47 * cg13) + cg9 + rho * (cg59 * (t1794 + t1837) * t1 #73 - t571 * t525 - 0.2D1 * t523 * t1842 + 0.2D1 * t574 * t1686) cg63 = cg33 t1865 = A * cg63 t1871 = 0.2D1 * t1865 * cg33 + 0.12D2 * t392 * cg33 * cg63 t1876 = cg63 * t158 * t566 t1883 = 0.2D1 * t150 * cg63 + 0.4D1 * t164 * cg63 t1885 = t1458 * t206 * t1883 t1891 = t158 * t1871 * cg33 t1910 = t1759 * cg63 t1913 = t66 * cg63 t1924 = t159 * t1883 t1932 = 0.266900D0 * t373 * t500 * t1871 - 0.133450D0 * t490 * t #1876 + 0.533800D0 * t490 * t1885 + 0.533800D0 * t329 * t1885 - 0.2 #66900D0 * t329 * t1891 - 0.266900D0 * t490 * t1891 + 0.133450D0 *
#t373 * t1815 * t1883 - 0.1601400D1 * t197 * t75 * t158 * t76 * t54 #5 * cg63 - 0.133450D0 * t329 * t1876 + 0.1601400D1 * t1506 * t1811 # * cg63 + 0.266900D0 * t329 * t1910 - 0.266900D0 * t1913 * t75 * t #553 - 0.1334500D1 * t477 * t470 * t206 * cg63 - 0.667250D0 * t477 #* t1829 * t1883 - 0.133450D0 * t546 * t1924 + 0.266900D0 * t490 * #t1910 - 0.400350D0 * t373 * t1833 * t1883 t1943 = 0.133450D0 * t145 * t81 * cg63 + 0.133450D0 * t197 * t18 #65 * t80 - 0.66725D-1 * t73 * t1924 t1951 = t470 * t1883 t1956 = t493 * cg63 cg8 = cg13 exc_norm_drho_norm_drho_norm_drho = t97 * (0.7425558783D2 * t132 #7 * t1848 * cg8 - 0.2985074630D2 * t437 * t1852 * cg8) + rho * (cg #59 * t1932 * t173 - t571 * t406 * t1943 - 0.2D1 * cg59 * (0.133450 #D0 * t1913 * t194 + 0.667250D0 * t477 * t478 * cg63 - 0.133450D0 * # t329 * t1951 - 0.133450D0 * t490 * t1951 - 0.133450D0 * t329 * t1 #956 - 0.133450D0 * t490 * t1956 + 0.133450D0 * t373 * t500 * t1883 # - 0.66725D-1 * t73 * t159 * t1871) * t1842 + 0.2D1 * t574 * t1240 # * t1943) cg66 = exc_norm_drho_norm_drho_norm_drho return end

# LSD

loc(eqs_ex_lda)intersect loc(eqs_pbec2);
NiM8I0klYmV0YUc2Ig==
loc(eqs_ex_lda);
NiM8Kkkic0c2Ikkma2FwcGFHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0YlSSNtdUdGJUklYmV0YUdGJQ==
toRn:=convert(loc(eqs_ex_lda)minus {beta,kappa,mu},list);
NiM+SSV0b1JuRzYiNydJInNHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0Yl
eqs_ex_a:=subs(op(map(x->x=x||_a,toRn)),rho=2*rhoa,norm_drho=2*norm_drhoa,eqs_ex_lda); eqs_ex_b:=subs(op(map(x->x=x||_b,toRn)),rho=2*rhob,norm_drho=2*norm_drhob,eqs_ex_lda);
NiM+SSllcXNfZXhfYUc2IjcqL0kma2FwcGFHRiUkIiQvKSEiJC9JJWJldGFHRiUkIiZEbichIicvSSNtdUdGJSwkKiZGLSIiIkkjUGlHSSpwcm90ZWN0ZWRHRjciIiMjRjUiIiQvSSVrZl9hR0YlKihGOkY5RjhGOSomRjZGOEklcmhvYUdGJUY1RjkvSSpleF91bmlmX2FHRiUsJComRjYhIiJGPEY1I0YrIiIlL0kkc19hR0YlLCQqKEkrbm9ybV9kcmhvYUdGJUY1RjxGREY/RkQjRjVGOC9JJUZ4X2FHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSlleF9sZGFfYUdGJSwkKihGP0Y1RkFGNUZORjVGOA==
NiM+SSllcXNfZXhfYkc2IjcqL0kma2FwcGFHRiUkIiQvKSEiJC9JJWJldGFHRiUkIiZEbichIicvSSNtdUdGJSwkKiZGLSIiIkkjUGlHSSpwcm90ZWN0ZWRHRjciIiMjRjUiIiQvSSVrZl9iR0YlKihGOkY5RjhGOSomRjZGOEklcmhvYkdGJUY1RjkvSSpleF91bmlmX2JHRiUsJComRjYhIiJGPEY1I0YrIiIlL0kkc19iR0YlLCQqKEkrbm9ybV9kcmhvYkdGJUY1RjxGREY/RkQjRjVGOC9JJUZ4X2JHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSlleF9sZGFfYkdGJSwkKihGP0Y1RkFGNUZORjVGOA==
unk(eqs_ex_a); unk(eqs_ex_b);
NiM8JUklcmhvYUc2IkkjUGlHSSpwcm90ZWN0ZWRHRidJK25vcm1fZHJob2FHRiU=
NiM8JUklcmhvYkc2IkkjUGlHSSpwcm90ZWN0ZWRHRidJK25vcm1fZHJob2JHRiU=
sameNameSameDef(eqs_pbec2,eqs_ex_a); sameNameSameDef(eqs_pbec2,eqs_ex_b); sameNameSameDef(eqs_ex_a,eqs_ex_b);
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
eqs_lsd:=combineEqs([[rho=rhoa+rhob],eqs_pbec2,eqs_ex_a,eqs_ex_b,[scale_ec=1,scale_ex=1,exc=scale_ex*(ex_lda_a+ex_lda_b)/2+scale_ec*ec]]): unk(eqs_lsd);
NiM8KEklcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJKm5vcm1fZHJob0dGJUkrbm9ybV9kcmhvYUdGJUkrbm9ybV9kcmhvYkdGJQ==
arg_lsd_names:=[rhoa,rhob,norm_drho,norm_drhoa,norm_drhob];
NiM+SS5hcmdfbHNkX25hbWVzRzYiNydJJXJob2FHRiVJJXJob2JHRiVJKm5vcm1fZHJob0dGJUkrbm9ybV9kcmhvYUdGJUkrbm9ybV9kcmhvYkdGJQ==
eqs_lsd2:=rmDefs(costanti,eqs_lsd): unk(eqs_lsd2);
deriv_lsd1:=calcDerivs(eqs_lsd2,arg_lsd_names):
deriv_lsd2:=[seq(seq(op(calcDerivs(deriv_lsd1[i],[arg_lsd_names[j]])),i=1..j),j=1..nops(arg_lsd_names))]:
#deriv_lsd3:=[seq(seq(op(calcDerivs(deriv_lsd2[i],[arg_lsd_names[j]])),i=1..((j+1)*j/2)),j=1..nops(arg_lsd_names))]:
n_deriv1:=map(x->lhs(op(-1,x)),deriv_lsd1); n_deriv2:=map(x->lhs(op(-1,x)),deriv_lsd2); #n_deriv3:=map(x->lhs(op(-1,x)),deriv_lsd3);
NiM+SSluX2Rlcml2MUc2IjcnSSlleGNfcmhvYUdGJUkpZXhjX3Job2JHRiVJLmV4Y19ub3JtX2RyaG9HRiVJL2V4Y19ub3JtX2RyaG9hR0YlSS9leGNfbm9ybV9kcmhvYkdGJQ==
'sameNameSameDef(eqs_lsd2,deriv_lsd1[i])'$i=1..nops(deriv_lsd1); 'sameNameSameDef(eqs_lsd2,deriv_lsd2[i])'$i=1..nops(deriv_lsd1); #foldl(`and`,sameNameSameDef(eqs_lsd2,deriv_lsd3[i])$i=1..nops(deriv_lsd3)); foldl(`and`,seq(sameNameSameDef(deriv_lsd1[i],deriv_lsd2[j])$i=1..nops(deriv_lsd1),j=1..nops(deriv_lsd2))); #foldl(`and`,seq(sameNameSameDef(deriv_lsd1[i],deriv_lsd3[j])$i=1..nops(deriv_lsd1),j=1..nops(deriv_lsd3))); #foldl(`and`,seq(sameNameSameDef(deriv_lsd2[i],deriv_lsd3[j])$i=1..nops(deriv_lsd2),j=1..nops(deriv_lsd3)));
NidJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGIw==
NidJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGIw==
NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=
eqs_lsd3:=combineEqs([eqs_lsd2,op(deriv_lsd1),op(deriv_lsd2)]): # ,op(deriv_lsd3) # removed 3 deriv
eqs_lsd4:=enforceDependencies([my_rhoa=rhoa,my_rhob=rhob, my_norm_drho=norm_drho,my_norm_drhoa=norm_drhoa,my_norm_drhob=norm_drhob, op(subs(rhoa=my_rhoa,rhob=my_rhob,norm_drho=my_norm_drho, norm_drhoa=my_norm_drhoa,norm_drhob=my_norm_drhob,eqs_lsd3))]):
res_eqs_lsd:=[exc,op(n_deriv1),op(n_deriv2)]:#,op(n_deriv3)]: # removed 3 deriv res_eqs_lsd2:=[]: for my_symb in res_eqs_lsd do if not rhs(getDef(my_symb,eqs_lsd4))=0 then res_eqs_lsd2:=[op(res_eqs_lsd2),my_symb]: end if; end do;
for my_symb in res_eqs_lsd2 do print(my_symb,unk([op(eqs_lsd4),result=my_symb])); end do; my_symb:='my_symb':
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for i from 1 to nops(eqs_lsd3) do for j from i+1 to nops(eqs_lsd3) do if eqUses(eqs_lsd3[i],eqs_lsd3[j]) then print(i,j,eqs_lsd3[i],uses,eqs_lsd3[j]); end if; end do; end do; i:='i':j:='j':
glob_eqs_lsd4:=[my_rhoa,my_rhob,my_norm_drho,my_norm_drhoa,my_norm_drhob,op(res_eqs_lsd2)]; args_lsd:=[rhoa,rhob,norm_drho,norm_drhoa,norm_drhob];
NiM+SSlhcmdzX2xzZEc2IjcnSSVyaG9hR0YlSSVyaG9iR0YlSSpub3JtX2RyaG9HRiVJK25vcm1fZHJob2FHRiVJK25vcm1fZHJob2JHRiU=
cs_eqs_lsd4:=CompSeq(locals=loc2(eqs_lsd4)minus convert(glob_eqs_lsd4,set), globals=[op(glob_eqs_lsd4),op(costanti)],params=args_lsd,eqs_lsd4): r_eqs_lsd4:=convert(cs_eqs_lsd4,procedure):

## Fortran code

Fortran(r_eqs_lsd4,defaulttype=float,optimize);
Warning, The following variable name replacements were made: ["cg", "cg0", "cg1", "cg10", "cg11", "cg12", "cg13", "cg14", "cg15", "cg16", "cg17", "cg18", "cg19", "cg2", "cg20", "cg21", "cg22", "cg23", "cg24", "cg25", "cg26", "cg27", "cg28", "cg29", "cg3", "cg30", "cg31", "cg32", "cg33", "cg34", "cg35", "cg36", "cg37", "cg38", "cg39", "cg4", "cg40", "cg41", "cg42", "cg43", "cg44", "cg45", "cg46", "cg47", "cg48", "cg49", "cg5", "cg50", "cg51", "cg52", "cg53", "cg54", "cg55", "cg56", "cg57", "cg58", "cg59", "cg6", "cg60", "cg61", "cg62", "cg63", "cg64", "cg65", "cg66", "cg67", "cg68", "cg69", "cg7", "cg70", "cg71", "cg72", "cg73", "cg74", "cg75", "cg76", "cg77", "cg78", "cg79", "cg8", "cg80", "cg81", "cg82", "cg83", "cg84", "cg85", "cg86", "cg87", "cg88", "cg89", "cg9", "cg90", "cg91", "cg92", "cg93"] = ["norm_drho", "norm_drhoa", "norm_drhob", "e_c_u_0rhoarhob", "rsrhoarhob", "Arhobrhob", "alpha_c1rhoa", "epsilon_c_unifrhoarhob", "phi1rhoa", "s_anorm_drhoa", "e_c_u_0", "ex_unif_arhoa", "alpha_c", "s_b1rhob", "epsilon_c_unif", "k_s", "kf_a", "Fx_a", "kf_b", "Fx_b", "chirhoa", "epsilon_cGGA", "e_c_u_0rhobrhob", "s_a", "s_a1rhoa", "Fx_a1rhoa", "ex_unif_b", "s_b", "Arhoarhoa", "ex_unif_brhob", "rsrhobrhob", "Fx_b1rhob", "frhoarhob", "k_frhoa", "k_srhoa", "epsilon_cGGArhob", "chirhoarhob", "epsilon_c_unifrhoarhoa", "phirhoa", "s_arhoa", "chirhob", "Fx_arhoa", "kf_arhoarhoa", "ex_unif_a1rhoa", "kf_brhobrhob", "ex_unif_b1rhob", "epsilon_c_unifrhob", "trhoanorm_drho", "kf_arhoa", "phirhob", "k_frhob", "k_srhob", "Arhoarhob", "trhoarhob", "Fx_brhob", "rsrhoarhoa", "s_brhob", "epsilon_cGGArhoa", "Hnorm_drho", "frhobrhob", "kf_brhob", "tnorm_drho", "e_c_u_01rhob", "chirhobrhob", "alpha_crhob", "e_c_u_0rhob", "e_c_u_1rhob", "Fx_anorm_drhoa", "epsilon_c_unifrhoa", "s_bnorm_drhob", "Fx_bnorm_drhob", "e_c_u_0rhoarhoa", "alpha_crhoa", "e_c_u_1rhoa", "phirhoarhoa", "e_c_u_0rhoa", "chirhoarhoa", "trhobnorm_drho", "k_s1rhob", "epsilon_c_unif1rhoa", "phirhobrhob", "alpha_c1rhob", "epsilon_c_unif1rhob", "ex_unif_a", "k_frhoarhob", "e_c_u_01rhoa", "trhoarhoa", "k_s1rhoa", "k_frhoarhoa", "phi1rhob", "trhobrhob", "epsilon_c_unifrhobrhob", "phirhoarhob", "frhoarhoa", "r_eqs_lsd4"]
doubleprecision function cg93 (rhoa, rhob, cg, cg0, cg1) doubleprecision my_rhoa doubleprecision my_rhob doubleprecision my_norm_drho doubleprecision my_norm_drhoa doubleprecision my_norm_drhob doubleprecision exc doubleprecision exc_rhoa doubleprecision exc_rhob doubleprecision exc_norm_drho doubleprecision exc_norm_drhoa doubleprecision exc_norm_drhob doubleprecision exc_rhoa_rhoa doubleprecision exc_rhoa_rhob doubleprecision exc_rhob_rhob doubleprecision exc_rhoa_norm_drho doubleprecision exc_rhob_norm_drho doubleprecision exc_norm_drho_norm_drho doubleprecision exc_rhoa_norm_drhoa doubleprecision exc_norm_drhoa_norm_drhoa doubleprecision exc_rhob_norm_drhob doubleprecision exc_norm_drhob_norm_drhob doubleprecision kappa doubleprecision beta doubleprecision mu doubleprecision gamma_var doubleprecision p_1 doubleprecision A_1 doubleprecision alpha_1_1 doubleprecision beta_1_1 doubleprecision beta_2_1 doubleprecision beta_3_1 doubleprecision beta_4_1 doubleprecision p_2 doubleprecision A_2 doubleprecision alpha_1_2 doubleprecision beta_1_2 doubleprecision beta_2_2 doubleprecision beta_3_2 doubleprecision beta_4_2 doubleprecision p_3 doubleprecision A_3 doubleprecision alpha_1_3 doubleprecision beta_1_3 doubleprecision beta_2_3 doubleprecision beta_3_3 doubleprecision beta_4_3 doubleprecision scale_ec doubleprecision scale_ex common my_rhoa, my_rhob, my_norm_drho, my_norm_drhoa, my_norm_dr #hob, exc, exc_rhoa, exc_rhob, exc_norm_drho, exc_norm_drhoa, exc_n #orm_drhob, exc_rhoa_rhoa, exc_rhoa_rhob, exc_rhob_rhob, exc_rhoa_n #orm_drho, exc_rhob_norm_drho, exc_norm_drho_norm_drho, exc_rhoa_no #rm_drhoa, exc_norm_drhoa_norm_drhoa, exc_rhob_norm_drhob, exc_norm #_drhob_norm_drhob, kappa, beta, mu, gamma_var, p_1, A_1, alpha_1_1 #, beta_1_1, beta_2_1, beta_3_1, beta_4_1, p_2, A_2, alpha_1_2, bet #a_1_2, beta_2_2, beta_3_2, beta_4_2, p_3, A_3, alpha_1_3, beta_1_3 #, beta_2_3, beta_3_3, beta_4_3, scale_ec, scale_ex doubleprecision rhoa doubleprecision rhob doubleprecision cg doubleprecision cg0 doubleprecision cg1 doubleprecision t187 doubleprecision t190 doubleprecision t191 doubleprecision t192 doubleprecision t194 doubleprecision t153 doubleprecision t156 integer t66 doubleprecision t1440 doubleprecision t1550 doubleprecision t1552 doubleprecision t56 doubleprecision t57 doubleprecision t58 doubleprecision t59 doubleprecision t1228 doubleprecision t1231 doubleprecision cg2 doubleprecision cg3 doubleprecision t198 doubleprecision t199 doubleprecision t200 doubleprecision t201 doubleprecision t205 doubleprecision t1865 doubleprecision t1739 doubleprecision t1765 doubleprecision t1767 doubleprecision cg4 doubleprecision cg5 doubleprecision cg6 doubleprecision cg7 doubleprecision cg8 doubleprecision t1346 doubleprecision t1630 doubleprecision t1501 doubleprecision t212 doubleprecision t213 doubleprecision t215 doubleprecision t1829 doubleprecision t211 doubleprecision t74 doubleprecision t75 doubleprecision t1283 doubleprecision t219 doubleprecision t220 doubleprecision t222 doubleprecision t226 doubleprecision t221 doubleprecision t232 doubleprecision t233 doubleprecision t234 doubleprecision t1193 doubleprecision t240 doubleprecision t242 doubleprecision t244 doubleprecision t245 doubleprecision t246 doubleprecision t248 doubleprecision t249 doubleprecision t250 doubleprecision t252 doubleprecision t254 doubleprecision t1293 integer t69 doubleprecision t12 doubleprecision t1922 doubleprecision t1674 doubleprecision t1677 doubleprecision t1680 doubleprecision t256 doubleprecision t257 doubleprecision t259 doubleprecision t262 doubleprecision t266 doubleprecision t268 doubleprecision t269 doubleprecision t274 doubleprecision t272 doubleprecision t273 doubleprecision t277 doubleprecision t278 doubleprecision t280 doubleprecision t281 doubleprecision t282 doubleprecision t284 doubleprecision t285 doubleprecision t286 doubleprecision t289 doubleprecision t456 doubleprecision t1462 doubleprecision t1465 doubleprecision cg9 doubleprecision t293 doubleprecision t294 doubleprecision t297 doubleprecision t298 doubleprecision t302 doubleprecision t303 doubleprecision t306 doubleprecision t299 doubleprecision t310 doubleprecision t311 doubleprecision t312 doubleprecision t313 doubleprecision t314 doubleprecision t317 doubleprecision t318 doubleprecision t324 doubleprecision t325 doubleprecision t326 doubleprecision t578 doubleprecision t321 doubleprecision t329 doubleprecision t335 doubleprecision t337 doubleprecision t340 doubleprecision t341 doubleprecision t344 doubleprecision t346 doubleprecision t350 doubleprecision t368 doubleprecision t396 doubleprecision t403 doubleprecision t405 doubleprecision t407 doubleprecision t409 doubleprecision t410 doubleprecision t411 doubleprecision t413 doubleprecision t415 doubleprecision t417 doubleprecision t427 doubleprecision t429 doubleprecision t432 doubleprecision t436 doubleprecision t1327 doubleprecision t439 doubleprecision t442 doubleprecision t444 doubleprecision t445 doubleprecision t453 doubleprecision t457 doubleprecision t460 doubleprecision t466 doubleprecision t467 doubleprecision t471 doubleprecision t468 doubleprecision t477 doubleprecision t676 doubleprecision t481 doubleprecision t475 doubleprecision t488 doubleprecision t1050 doubleprecision t494 doubleprecision t493 doubleprecision t506 doubleprecision t505 doubleprecision cg10 doubleprecision cg11 doubleprecision t519 doubleprecision t518 doubleprecision t525 doubleprecision t523 doubleprecision t536 doubleprecision t538 doubleprecision t543 doubleprecision t544 doubleprecision t548 doubleprecision t549 doubleprecision t561 doubleprecision t556 doubleprecision t576 doubleprecision t579 doubleprecision t563 doubleprecision t580 doubleprecision t588 doubleprecision t1555 doubleprecision t590 doubleprecision t595 doubleprecision t596 doubleprecision t600 doubleprecision t611 doubleprecision t606 doubleprecision t624 doubleprecision t626 doubleprecision t627 doubleprecision t628 doubleprecision t1377 doubleprecision t636 doubleprecision t638 doubleprecision t1288 doubleprecision t643 doubleprecision t644 doubleprecision t648 doubleprecision t659 doubleprecision t654 doubleprecision t672 doubleprecision t1285 doubleprecision t1286 doubleprecision t1291 doubleprecision t674 doubleprecision t675 doubleprecision t681 doubleprecision t687 doubleprecision t63 doubleprecision t64 doubleprecision t705 doubleprecision t708 doubleprecision t711 doubleprecision t1743 doubleprecision t726 doubleprecision t733 doubleprecision t736 doubleprecision t745 doubleprecision t750 doubleprecision t755 doubleprecision t763 doubleprecision t767 doubleprecision t768 doubleprecision cg12 doubleprecision t775 doubleprecision t779 doubleprecision t776 doubleprecision t785 doubleprecision t789 doubleprecision t795 doubleprecision t798 doubleprecision t801 doubleprecision f1rhoa doubleprecision cg13 doubleprecision cg14 doubleprecision t812 doubleprecision t820 doubleprecision t821 doubleprecision t822 doubleprecision t823 doubleprecision t825 doubleprecision t828 doubleprecision t839 doubleprecision t840 doubleprecision t851 doubleprecision cg15 doubleprecision t858 doubleprecision t865 doubleprecision t867 doubleprecision t1713 doubleprecision t876 doubleprecision t879 doubleprecision t880 doubleprecision t904 doubleprecision t914 doubleprecision t908 doubleprecision t909 doubleprecision t911 doubleprecision t917 doubleprecision t919 doubleprecision cg16 doubleprecision t924 doubleprecision t936 doubleprecision t944 doubleprecision t953 doubleprecision t959 doubleprecision t962 doubleprecision t965 doubleprecision cg17 doubleprecision t967 doubleprecision t966 doubleprecision t1603 doubleprecision t985 doubleprecision t998 doubleprecision t999 doubleprecision t1000 doubleprecision t1001 doubleprecision t1033 doubleprecision t1031 doubleprecision rs doubleprecision rho doubleprecision chi doubleprecision t1038 doubleprecision t1514 doubleprecision cg18 doubleprecision cg19 doubleprecision cg20 doubleprecision f doubleprecision t1069 doubleprecision t1071 doubleprecision phi doubleprecision cg21 doubleprecision t doubleprecision A doubleprecision cg22 doubleprecision cg23 doubleprecision cg24 doubleprecision cg25 doubleprecision cg26 doubleprecision rsrhoa doubleprecision cg27 doubleprecision cg28 doubleprecision t1104 doubleprecision t1106 doubleprecision cg29 doubleprecision t77 doubleprecision t78 doubleprecision t14 doubleprecision t15 doubleprecision cg30 doubleprecision cg31 doubleprecision t162 doubleprecision t163 doubleprecision t164 doubleprecision t165 doubleprecision cg32 doubleprecision t130 doubleprecision t79 doubleprecision t80 doubleprecision cg33 doubleprecision cg34 doubleprecision cg35 doubleprecision t305 doubleprecision t1741 doubleprecision t1640 doubleprecision t18 doubleprecision t82 doubleprecision cg36 doubleprecision t682 doubleprecision t84 doubleprecision t85 doubleprecision t112 doubleprecision t113 doubleprecision t115 doubleprecision t116 doubleprecision t118 doubleprecision t119 doubleprecision t123 doubleprecision t20 doubleprecision t21 doubleprecision t22 doubleprecision t23 doubleprecision cg37 doubleprecision t27 doubleprecision t28 doubleprecision t564 doubleprecision t1520 doubleprecision t167 doubleprecision t171 doubleprecision t1830 doubleprecision t1831 doubleprecision frhoa doubleprecision cg38 doubleprecision cg39 doubleprecision trhoa doubleprecision Arhoa doubleprecision t1748 doubleprecision t1871 doubleprecision t1876 doubleprecision cg40 doubleprecision cg41 doubleprecision cg42 doubleprecision t122 doubleprecision t1330 doubleprecision t1rhoa doubleprecision t32 doubleprecision t868 doubleprecision cg43 doubleprecision cg44 doubleprecision rsrhob doubleprecision cg45 integer t124 doubleprecision t125 doubleprecision t126 doubleprecision t129 doubleprecision t131 doubleprecision cg46 doubleprecision cg47 doubleprecision t1411 doubleprecision t34 doubleprecision t87 doubleprecision t88 doubleprecision cg48 doubleprecision cg49 doubleprecision cg50 doubleprecision t1632 doubleprecision t1635 doubleprecision t1638 doubleprecision cg51 doubleprecision t1698 doubleprecision t550 doubleprecision t1801 doubleprecision t90 doubleprecision t91 doubleprecision t1766 doubleprecision t1529 doubleprecision frhob doubleprecision cg52 doubleprecision cg53 doubleprecision cg54 doubleprecision trhob doubleprecision t38 doubleprecision f1rhob doubleprecision t1164 doubleprecision A1rhoa doubleprecision cg55 doubleprecision cg56 doubleprecision t1949 doubleprecision cg57 doubleprecision t1588 doubleprecision t1590 doubleprecision t1591 doubleprecision t175 doubleprecision t176 doubleprecision t177 doubleprecision t178 doubleprecision t179 doubleprecision t183 doubleprecision Arhob doubleprecision t382 doubleprecision t39 doubleprecision t92 doubleprecision t93 doubleprecision t94 doubleprecision cg58 doubleprecision cg59 doubleprecision cg60 doubleprecision cg61 doubleprecision cg62 doubleprecision t40 doubleprecision t41 doubleprecision cg63 doubleprecision t1482 doubleprecision cg64 doubleprecision cg65 doubleprecision cg66 doubleprecision cg67 doubleprecision cg68 doubleprecision t95 doubleprecision t96 doubleprecision cg69 doubleprecision cg70 doubleprecision cg71 doubleprecision cg72 doubleprecision cg73 doubleprecision t1 doubleprecision cg74 doubleprecision t100 doubleprecision t101 doubleprecision t102 doubleprecision t1599 doubleprecision t1602 doubleprecision cg75 doubleprecision cg76 doubleprecision cg77 doubleprecision t97 doubleprecision t98 doubleprecision t1888 doubleprecision t70 doubleprecision t71 doubleprecision t45 doubleprecision t46 doubleprecision t336 doubleprecision cg78 doubleprecision cg79 doubleprecision cg80 doubleprecision cg81 doubleprecision cg82 doubleprecision cg83 doubleprecision cg84 doubleprecision t133 doubleprecision t135 doubleprecision t137 doubleprecision t140 doubleprecision t2 integer t3 doubleprecision t472 doubleprecision t502 doubleprecision t1711 doubleprecision t1712 doubleprecision t1rhob doubleprecision t50 doubleprecision cg85 doubleprecision cg86 doubleprecision cg87 doubleprecision t52 doubleprecision t1269 doubleprecision t1342 doubleprecision t1489 doubleprecision t1492 integer t4 integer t5 integer t6 doubleprecision t1901 doubleprecision t72 doubleprecision t73 doubleprecision cg88 doubleprecision A1rhob doubleprecision cg89 doubleprecision t142 doubleprecision t143 doubleprecision t7 doubleprecision t8 doubleprecision t9 doubleprecision cg90 doubleprecision t103 doubleprecision t104 doubleprecision t105 doubleprecision t107 doubleprecision t108 doubleprecision t110 doubleprecision t111 doubleprecision cg91 doubleprecision t1304 doubleprecision t146 doubleprecision t147 doubleprecision t148 doubleprecision t150 doubleprecision cg92 my_rhoa = rhoa my_rhob = rhob my_norm_drho = cg my_norm_drhoa = cg0 my_norm_drhob = cg1 rho = rhoa + rhob t1 = rhoa - rhob t2 = 0.1D1 / rho chi = t1 * t2 t3 = 3 ** (0.1D1 / 0.3D1) t4 = 4 ** (0.1D1 / 0.3D1) t5 = t4 ** 2 t6 = t3 * t5 t7 = 0.1D1 / 0.3141592654D1 t8 = t7 * t2 t9 = t8 ** (0.1D1 / 0.3D1) rs = dble(t6) * t9 / 0.4D1 t12 = 0.1D1 + alpha_1_1 * rs t14 = 0.1D1 / A_1 t15 = sqrt(rs) t18 = t15 * rs t20 = p_1 + 0.1D1 t21 = rs ** t20 t22 = beta_4_1 * t21 t23 = beta_1_1 * t15 + beta_2_1 * rs + beta_3_1 * t18 + t22 t27 = 0.1D1 + t14 / t23 / 0.2D1 t28 = log(t27) cg17 = -0.2D1 * A_1 * t12 * t28 t32 = 0.1D1 + alpha_1_2 * rs t34 = 0.1D1 / A_2 t38 = p_2 + 0.1D1 t39 = rs ** t38 t40 = beta_4_2 * t39 t41 = beta_1_2 * t15 + beta_2_2 * rs + beta_3_2 * t18 + t40 t45 = 0.1D1 + t34 / t41 / 0.2D1 t46 = log(t45) t50 = 0.1D1 + alpha_1_3 * rs t52 = 0.1D1 / A_3 t56 = p_3 + 0.1D1 t57 = rs ** t56 t58 = beta_4_3 * t57 t59 = beta_1_3 * t15 + beta_2_3 * rs + beta_3_3 * t18 + t58 t63 = 0.1D1 + t52 / t59 / 0.2D1 t64 = log(t63) cg19 = 0.2D1 * A_3 * t50 * t64 t66 = 2 ** (0.1D1 / 0.3D1) t69 = 1 / (2 * t66 - 2) t70 = 0.1D1 + chi t71 = t70 ** (0.1D1 / 0.3D1) t72 = t71 * t70 t73 = 0.1D1 - chi t74 = t73 ** (0.1D1 / 0.3D1) t75 = t74 * t73 f = (t72 + t75 - 0.2D1) * dble(t69) t77 = cg19 * f t78 = 0.9D1 / 0.8D1 / dble(t69) t79 = chi ** 2 t80 = t79 ** 2 t82 = t78 * (0.1D1 - t80) t84 = -0.2D1 * A_2 * t32 * t46 - cg17 t85 = t84 * f cg20 = cg17 + t77 * t82 + t85 * t80 t87 = t71 ** 2 t88 = t74 ** 2 phi = t87 / 0.2D1 + t88 / 0.2D1 t90 = 0.3141592654D1 ** 2 t91 = t90 * rho t92 = t91 ** (0.1D1 / 0.3D1) t93 = dble(t3) * t92 * t7 t94 = sqrt(t93) cg21 = 0.2D1 * t94 t95 = 0.1D1 / phi t96 = cg * t95 t97 = 0.1D1 / cg21 t98 = t97 * t2 t = t96 * t98 / 0.2D1 t100 = 0.1D1 / gamma_var t101 = beta * t100 t102 = cg20 * t100 t103 = phi ** 2 t104 = t103 * phi t105 = 0.1D1 / t104 t107 = exp(-t102 * t105) t108 = t107 - 0.1D1 A = t101 / t108 t110 = gamma_var * t104 t111 = t ** 2 t112 = A * t111 t113 = 0.1D1 + t112 t115 = A ** 2 t116 = t111 ** 2 t118 = 0.1D1 + t112 + t115 * t116 t119 = 0.1D1 / t118 t122 = 0.1D1 + t101 * t111 * t113 * t119 t123 = log(t122) cg27 = cg20 + t110 * t123 t124 = t3 * t66 t125 = t90 * rhoa t126 = t125 ** (0.1D1 / 0.3D1) cg22 = dble(t124) * t126 cg83 = -0.3D1 / 0.4D1 * t7 * cg22 t129 = 0.1D1 / cg22 t130 = cg0 * t129 t131 = 0.1D1 / rhoa cg29 = t130 * t131 / 0.2D1 t133 = cg29 ** 2 t135 = 0.1D1 / kappa t137 = 0.1D1 + mu * t133 * t135 cg23 = 0.1D1 + kappa - kappa / t137 t140 = rhoa * cg83 t142 = t90 * rhob t143 = t142 ** (0.1D1 / 0.3D1) cg24 = dble(t124) * t143 cg31 = -0.3D1 / 0.4D1 * t7 * cg24 t146 = 0.1D1 / cg24 t147 = cg1 * t146 t148 = 0.1D1 / rhob cg32 = t147 * t148 / 0.2D1 t150 = cg32 ** 2 t153 = 0.1D1 + mu * t150 * t135 cg25 = 0.1D1 + kappa - kappa / t153 t156 = rhob * cg31 exc = scale_ex * (0.2D1 * t140 * cg23 + 0.2D1 * t156 * cg25) / 0 #.2D1 + scale_ec * rho * cg27 t162 = rho ** 2 t163 = 0.1D1 / t162 t164 = t1 * t163 cg26 = t2 - t164 t165 = t9 ** 2 t167 = 0.1D1 / t165 * t7 rsrhoa = -dble(t6) * t167 * t163 / 0.12D2 t171 = A_1 * alpha_1_1 t175 = t23 ** 2 t176 = 0.1D1 / t175 t177 = t12 * t176 t178 = 0.1D1 / t15 t179 = beta_1_1 * t178 t183 = beta_3_1 * t15 t187 = 0.1D1 / rs t190 = t179 * rsrhoa / 0.2D1 + beta_2_1 * rsrhoa + 0.3D1 / 0.2D1 # * t183 * rsrhoa + t22 * t20 * rsrhoa * t187 t191 = 0.1D1 / t27 t192 = t190 * t191 cg76 = -0.2D1 * t171 * rsrhoa * t28 + t177 * t192 t194 = A_2 * alpha_1_2 t198 = t41 ** 2 t199 = 0.1D1 / t198 t200 = t32 * t199 t201 = beta_1_2 * t178 t205 = beta_3_2 * t15 t211 = t201 * rsrhoa / 0.2D1 + beta_2_2 * rsrhoa + 0.3D1 / 0.2D1 # * t205 * rsrhoa + t40 * t38 * rsrhoa * t187 t212 = 0.1D1 / t45 t213 = t211 * t212 cg74 = -0.2D1 * t194 * rsrhoa * t46 + t200 * t213 t215 = A_3 * alpha_1_3 t219 = t59 ** 2 t220 = 0.1D1 / t219 t221 = t50 * t220 t222 = beta_1_3 * t178 t226 = beta_3_3 * t15 t232 = t222 * rsrhoa / 0.2D1 + beta_2_3 * rsrhoa + 0.3D1 / 0.2D1 # * t226 * rsrhoa + t58 * t56 * rsrhoa * t187 t233 = 0.1D1 / t63 t234 = t232 * t233 cg73 = 0.2D1 * t215 * rsrhoa * t64 - t221 * t234 frhoa = (0.4D1 / 0.3D1 * t71 * cg26 - 0.4D1 / 0.3D1 * t74 * cg26 #) * dble(t69) t240 = cg73 * f t242 = cg19 * frhoa t244 = t79 * chi t245 = t78 * t244 t246 = t245 * cg26 t248 = 0.4D1 * t77 * t246 t249 = cg74 - cg76 t250 = t249 * f t252 = t84 * frhoa t254 = t244 * cg26 t256 = 0.4D1 * t85 * t254 cg7 = cg76 + t240 * t82 + t242 * t82 - t248 + t250 * t80 + t252 #* t80 + t256 t257 = 0.1D1 / t71 t259 = 0.1D1 / t74 cg42 = t257 * cg26 / 0.3D1 - t259 * cg26 / 0.3D1 t262 = t92 ** 2 cg38 = dble(t3) / t262 * t90 / 0.3D1 t266 = 0.1D1 / t94 cg39 = t266 * cg38 * t7 t268 = 0.1D1 / t103 t269 = cg * t268 t272 = cg21 ** 2 t273 = 0.1D1 / t272 t274 = t273 * t2 t277 = t97 * t163 t278 = t96 * t277 trhoa = -t269 * t98 * cg42 / 0.2D1 - t96 * t274 * cg39 / 0.2D1 - # t278 / 0.2D1 t280 = t108 ** 2 t281 = 0.1D1 / t280 t282 = cg7 * t100 t284 = t103 ** 2 t285 = 0.1D1 / t284 t286 = t285 * cg42 t289 = -t282 * t105 + 0.3D1 * t102 * t286 Arhoa = -t101 * t281 * t289 * t107 t293 = gamma_var * t103 t294 = t123 * cg42 t297 = t101 * t t298 = t113 * t119 t299 = t298 * trhoa t302 = Arhoa * t111 t303 = A * t t305 = 0.2D1 * t303 * trhoa t306 = t302 + t305 t310 = t101 * t111 t311 = t118 ** 2 t312 = 0.1D1 / t311 t313 = t113 * t312 t314 = A * t116 t317 = t111 * t t318 = t115 * t317 t321 = t302 + t305 + 0.2D1 * t314 * Arhoa + 0.4D1 * t318 * trhoa t324 = 0.2D1 * t297 * t299 + t101 * t111 * t306 * t119 - t310 * #t313 * t321 t325 = 0.1D1 / t122 t326 = t324 * t325 cg6 = cg7 + 0.3D1 * t293 * t294 + t110 * t326 t329 = t126 ** 2 cg51 = dble(t124) / t329 * t90 / 0.3D1 cg18 = -0.3D1 / 0.4D1 * t7 * cg51 t335 = cg22 ** 2 t336 = 0.1D1 / t335 t337 = cg0 * t336 t340 = rhoa ** 2 t341 = 0.1D1 / t340 cg43 = -t337 * t131 * cg51 / 0.2D1 - t130 * t341 / 0.2D1 t344 = t137 ** 2 t346 = 0.1D1 / t344 * mu cg45 = 0.2D1 * t346 * cg29 * cg43 t350 = rhoa * cg18 exc_rhoa = scale_ex * (0.2D1 * cg83 * cg23 + 0.2D1 * t350 * cg23 # + 0.2D1 * t140 * cg45) / 0.2D1 + scale_ec * (cg27 + rho * cg6) cg44 = -t2 - t164 rsrhob = rsrhoa t368 = t179 * rsrhob / 0.2D1 + beta_2_1 * rsrhob + 0.3D1 / 0.2D1 # * t183 * rsrhob + t22 * t20 * rsrhob * t187 cg67 = -0.2D1 * t171 * rsrhob * t28 + t177 * t368 * t191 t382 = t201 * rsrhob / 0.2D1 + beta_2_2 * rsrhob + 0.3D1 / 0.2D1 # * t205 * rsrhob + t40 * t38 * rsrhob * t187 cg68 = -0.2D1 * t194 * rsrhob * t46 + t200 * t382 * t212 t396 = t222 * rsrhob / 0.2D1 + beta_2_3 * rsrhob + 0.3D1 / 0.2D1 # * t226 * rsrhob + t58 * t56 * rsrhob * t187 cg66 = 0.2D1 * t215 * rsrhob * t64 - t221 * t396 * t233 frhob = (0.4D1 / 0.3D1 * t71 * cg44 - 0.4D1 / 0.3D1 * t74 * cg44 #) * dble(t69) t403 = cg66 * f t405 = cg19 * frhob t407 = t245 * cg44 t409 = 0.4D1 * t77 * t407 t410 = cg68 - cg67 t411 = t410 * f t413 = t84 * frhob t415 = t244 * cg44 t417 = 0.4D1 * t85 * t415 cg5 = cg67 + t403 * t82 + t405 * t82 - t409 + t411 * t80 + t413 #* t80 + t417 cg52 = t257 * cg44 / 0.3D1 - t259 * cg44 / 0.3D1 cg53 = cg38 cg54 = t266 * cg53 * t7 trhob = -t269 * t98 * cg52 / 0.2D1 - t96 * t274 * cg54 / 0.2D1 - # t278 / 0.2D1 t427 = cg5 * t100 t429 = t285 * cg52 t432 = -t427 * t105 + 0.3D1 * t102 * t429 Arhob = -t101 * t281 * t432 * t107 t436 = t123 * cg52 t439 = t298 * trhob t442 = Arhob * t111 t444 = 0.2D1 * t303 * trhob t445 = t442 + t444 t453 = t442 + t444 + 0.2D1 * t314 * Arhob + 0.4D1 * t318 * trhob t456 = 0.2D1 * t297 * t439 + t101 * t111 * t445 * t119 - t310 * #t313 * t453 t457 = t456 * t325 cg4 = cg5 + 0.3D1 * t293 * t436 + t110 * t457 t460 = t143 ** 2 cg62 = dble(t124) / t460 * t90 / 0.3D1 cg34 = -0.3D1 / 0.4D1 * t7 * cg62 t466 = cg24 ** 2 t467 = 0.1D1 / t466 t468 = cg1 * t467 t471 = rhob ** 2 t472 = 0.1D1 / t471 cg59 = -t468 * t148 * cg62 / 0.2D1 - t147 * t472 / 0.2D1 t475 = t153 ** 2 t477 = 0.1D1 / t475 * mu cg57 = 0.2D1 * t477 * cg32 * cg59 t481 = rhob * cg34 exc_rhob = scale_ex * (0.2D1 * cg31 * cg25 + 0.2D1 * t481 * cg25 # + 0.2D1 * t156 * cg57) / 0.2D1 + scale_ec * (cg27 + rho * cg4) t488 = t95 * t97 cg63 = t488 * t2 / 0.2D1 t493 = t101 * t317 t494 = A * cg63 t502 = 0.2D1 * t303 * cg63 + 0.4D1 * t318 * cg63 t505 = 0.2D1 * t297 * t298 * cg63 + 0.2D1 * t493 * t494 * t119 - # t310 * t313 * t502 t506 = t505 * t325 cg60 = t110 * t506 exc_norm_drho = scale_ec * rho * cg60 cg16 = t129 * t131 / 0.2D1 cg69 = 0.2D1 * t346 * cg29 * cg16 exc_norm_drhoa = scale_ex * t140 * cg69 cg70 = t146 * t148 / 0.2D1 cg71 = 0.2D1 * t477 * cg32 * cg70 exc_norm_drhob = scale_ex * t156 * cg71 t518 = 0.1D1 / t162 / rho
t519 = t1 * t518 cg77 = -0.2D1 * t163 + 0.2D1 * t519 t523 = 0.1D1 / t90 t525 = t162 ** 2 cg58 = -dble(t6) / t165 / t8 * t523 / t525 / 0.18D2 + dble(t6) * # t167 * t518 / 0.6D1 t536 = alpha_1_1 * rsrhoa t538 = t176 * t190 * t191 t543 = t12 / t175 / t23 t544 = t190 ** 2 t548 = 0.1D1 / t18 t549 = beta_1_1 * t548 t550 = rsrhoa ** 2 t556 = beta_3_1 * t178 t561 = t20 ** 2 t563 = rs ** 2 t564 = 0.1D1 / t563 t576 = t175 ** 2 t578 = t12 / t576 t579 = t27 ** 2 t580 = 0.1D1 / t579 cg72 = -0.2D1 * t171 * cg58 * t28 + 0.2D1 * t536 * t538 - 0.2D1 #* t543 * t544 * t191 + t177 * (-t549 * t550 / 0.4D1 + t179 * cg58 #/ 0.2D1 + beta_2_1 * cg58 + 0.3D1 / 0.4D1 * t556 * t550 + 0.3D1 / #0.2D1 * t183 * cg58 + t22 * t561 * t550 * t564 + t22 * t20 * cg58 #* t187 - t22 * t20 * t550 * t564) * t191 + t578 * t544 * t580 * t1 #4 / 0.2D1 cg85 = cg76 t588 = alpha_1_2 * rsrhoa t590 = t199 * t211 * t212 t595 = t32 / t198 / t41 t596 = t211 ** 2 t600 = beta_1_2 * t548 t606 = beta_3_2 * t178 t611 = t38 ** 2 t624 = t198 ** 2 t626 = t32 / t624 t627 = t45 ** 2 t628 = 0.1D1 / t627 t636 = alpha_1_3 * rsrhoa t638 = t220 * t232 * t233 t643 = t50 / t219 / t59 t644 = t232 ** 2 t648 = beta_1_3 * t548 t654 = beta_3_3 * t178 t659 = t56 ** 2 t672 = t219 ** 2 t674 = t50 / t672 t675 = t63 ** 2 t676 = 0.1D1 / t675 cg13 = cg73 t681 = 0.1D1 / t87 t682 = cg26 ** 2 t687 = 0.1D1 / t88 cg92 = (0.4D1 / 0.9D1 * t681 * t682 + 0.4D1 / 0.3D1 * t71 * cg77 # + 0.4D1 / 0.9D1 * t687 * t682 - 0.4D1 / 0.3D1 * t74 * cg77) * dbl #e(t69) f1rhoa = frhoa t705 = cg13 * f t708 = cg19 * f1rhoa t711 = t78 * t79 t726 = cg74 - cg85 t733 = t726 * f t736 = t84 * f1rhoa t745 = -0.4D1 * t77 * t245 * cg77 + (-0.2D1 * t194 * cg58 * t46 #+ 0.2D1 * t588 * t590 - 0.2D1 * t595 * t596 * t212 + t200 * (-t600 # * t550 / 0.4D1 + t201 * cg58 / 0.2D1 + beta_2_2 * cg58 + 0.3D1 / #0.4D1 * t606 * t550 + 0.3D1 / 0.2D1 * t205 * cg58 + t40 * t611 * t #550 * t564 + t40 * t38 * cg58 * t187 - t40 * t38 * t550 * t564) * #t212 + t626 * t596 * t628 * t34 / 0.2D1 - cg72) * f * t80 + t249 * # f1rhoa * t80 + 0.4D1 * t250 * t254 + t726 * frhoa * t80 + t84 * c #g92 * t80 + 0.4D1 * t252 * t254 + 0.4D1 * t733 * t254 + 0.4D1 * t7 #36 * t254 + 0.12D2 * t85 * t79 * t682 + 0.4D1 * t85 * t244 * cg77 cg41 = cg72 + (0.2D1 * t215 * cg58 * t64 - 0.2D1 * t636 * t638 + # 0.2D1 * t643 * t644 * t233 - t221 * (-t648 * t550 / 0.4D1 + t222 #* cg58 / 0.2D1 + beta_2_3 * cg58 + 0.3D1 / 0.4D1 * t654 * t550 + 0 #.3D1 / 0.2D1 * t226 * cg58 + t58 * t659 * t550 * t564 + t58 * t56 #* cg58 * t187 - t58 * t56 * t550 * t564) * t233 - t674 * t644 * t6 #76 * t52 / 0.2D1) * f * t82 + cg73 * f1rhoa * t82 - 0.4D1 * t240 * # t246 + cg13 * frhoa * t82 + cg19 * cg92 * t82 - 0.4D1 * t242 * t2 #46 - 0.4D1 * t705 * t246 - 0.4D1 * t708 * t246 - 0.12D2 * t77 * t7 #11 * t682 + t745 cg8 = cg85 + t705 * t82 + t708 * t82 - t248 + t733 * t80 + t736 #* t80 + t256 t750 = 0.1D1 / t72 t755 = 0.1D1 / t75 cg75 = -t750 * t682 / 0.9D1 + t257 * cg77 / 0.3D1 - t755 * t682 #/ 0.9D1 - t259 * cg77 / 0.3D1 cg15 = cg42 t763 = t90 ** 2 cg88 = -0.2D1 / 0.9D1 * dble(t3) / t262 / t91 * t763 t767 = 0.1D1 / t94 / t93 t768 = cg38 ** 2 cg87 = cg39 t775 = cg * t105 * t97 t776 = t2 * cg42 t779 = t269 * t273 t785 = t269 * t277 * cg42 / 0.2D1 t789 = t2 * cg39 t795 = t96 / t272 / cg21 t798 = t273 * t163 t801 = t96 * t798 * cg39 / 0.2D1 t812 = t96 * t97 * t518 cg86 = t775 * t776 * cg15 + t779 * t776 * cg87 / 0.2D1 + t785 - #t269 * t98 * cg75 / 0.2D1 + t779 * t789 * cg15 / 0.2D1 + t795 * t7 #89 * cg87 + t801 - t96 * t274 * (-t767 * t768 * t523 / 0.2D1 + t26 #6 * cg88 * t7) / 0.2D1 + t269 * t277 * cg15 / 0.2D1 + t96 * t798 * # cg87 / 0.2D1 + t812 t1rhoa = -t269 * t98 * cg15 / 0.2D1 - t96 * t274 * cg87 / 0.2D1 #- t278 / 0.2D1 t820 = t101 / t280 / t108 t821 = t107 ** 2 t822 = t289 * t821 t823 = cg8 * t100 t825 = t285 * cg15 t828 = -t823 * t105 + 0.3D1 * t102 * t825 t839 = 0.1D1 / t284 / phi t840 = t839 * cg42 t851 = t101 * t281 cg33 = 0.2D1 * t820 * t822 * t828 - t101 * t281 * (-cg41 * t100 #* t105 + 0.3D1 * t282 * t825 + 0.3D1 * t823 * t286 - 0.12D2 * t102 # * t840 * cg15 + 0.3D1 * t102 * t285 * cg75) * t107 - t851 * t289 #* t828 * t107 A1rhoa = -t101 * t281 * t828 * t107 t858 = gamma_var * phi t865 = A1rhoa * t111 t867 = 0.2D1 * t303 * t1rhoa t868 = t865 + t867 t876 = t865 + t867 + 0.2D1 * t314 * A1rhoa + 0.4D1 * t318 * t1rh #oa t879 = 0.2D1 * t297 * t298 * t1rhoa + t101 * t111 * t868 * t119 #- t310 * t313 * t876 t880 = t879 * t325 t904 = t306 * t119 t908 = cg33 * t111 t909 = Arhoa * t t911 = 0.2D1 * t909 * t1rhoa t914 = 0.2D1 * A1rhoa * t * trhoa t917 = 0.2D1 * A * t1rhoa * trhoa t919 = 0.2D1 * t303 * cg86 t924 = t306 * t312 t936 = t113 / t311 / t118 t944 = A * t317 t953 = t115 * t111 t959 = t908 + t911 + t914 + t917 + t919 + 0.2D1 * A1rhoa * t116 #* Arhoa + 0.8D1 * t944 * Arhoa * t1rhoa + 0.2D1 * t314 * cg33 + 0. #8D1 * t944 * trhoa * A1rhoa + 0.12D2 * t953 * trhoa * t1rhoa + 0.4 #D1 * t318 * cg86 t962 = 0.2D1 * t101 * t1rhoa * t299 + 0.2D1 * t297 * t868 * t119 # * trhoa - 0.2D1 * t297 * t313 * trhoa * t876 + 0.2D1 * t297 * t29 #8 * cg86 + 0.2D1 * t297 * t904 * t1rhoa + t101 * t111 * (t908 + t9 #11 + t914 + t917 + t919) * t119 - t310 * t924 * t876 - 0.2D1 * t29 #7 * t313 * t321 * t1rhoa - t310 * t868 * t312 * t321 + 0.2D1 * t31 #0 * t936 * t321 * t876 - t310 * t313 * t959 t965 = t122 ** 2 t966 = 0.1D1 / t965 t967 = t324 * t966 cg46 = -0.2D1 / 0.9D1 * dble(t124) / t329 / t125 * t763 cg47 = cg18 t985 = cg51 ** 2 cg3 = cg43 t998 = mu ** 2 t999 = 0.1D1 / t344 / t137 * t998 t1000 = t999 * t133 t1001 = cg43 * t135 cg30 = 0.2D1 * t346 * cg29 * cg3 exc_rhoa_rhoa = scale_ex * (0.2D1 * cg47 * cg23 + 0.2D1 * cg83 * # cg30 + 0.2D1 * cg18 * cg23 - 0.3D1 / 0.2D1 * rhoa * t7 * cg46 * c #g23 + 0.2D1 * t350 * cg30 + 0.2D1 * cg83 * cg45 + 0.2D1 * rhoa * c #g47 * cg45 + 0.2D1 * t140 * (-0.8D1 * t1000 * t1001 * cg3 + 0.2D1 #* t346 * cg3 * cg43 + 0.2D1 * t346 * cg29 * (cg0 / t335 / cg22 * t #131 * t985 + t337 * t341 * cg51 - t337 * t131 * cg46 / 0.2D1 + t13 #0 / t340 / rhoa))) / 0.2D1 + scale_ec * (cg8 + 0.3D1 * t293 * t123 # * cg15 + t110 * t880 + cg6 + rho * (cg41 + 0.6D1 * t858 * t294 * #cg15 + 0.3D1 * t293 * t880 * cg42 + 0.3D1 * t293 * t123 * cg75 + 0 #.3D1 * t293 * t326 * cg15 + t110 * t962 * t325 - t110 * t967 * t87 #9)) cg40 = 0.2D1 * t519 cg11 = cg58 t1031 = t176 * t368 * t191 t1033 = alpha_1_1 * rsrhob t1038 = rsrhoa * rsrhob t1050 = rsrhob * t564 * rsrhoa cg10 = -0.2D1 * t171 * cg11 * t28 + t536 * t1031 + t1033 * t538 #- 0.2D1 * t543 * t192 * t368 + t177 * (-t549 * t1038 / 0.4D1 + t17 #9 * cg11 / 0.2D1 + beta_2_1 * cg11 + 0.3D1 / 0.4D1 * t556 * t1038 #+ 0.3D1 / 0.2D1 * t183 * cg11 + t22 * t561 * t1050 + t22 * t20 * c #g11 * t187 - t22 * t20 * t1050) * t191 + t578 * t190 * t580 * t14 #* t368 / 0.2D1 t1069 = t199 * t382 * t212 t1071 = alpha_1_2 * rsrhob t1104 = t220 * t396 * t233 t1106 = alpha_1_3 * rsrhob cg37 = (0.4D1 / 0.9D1 * t681 * cg26 * cg44 + 0.4D1 / 0.3D1 * t71 # * cg40 + 0.4D1 / 0.9D1 * t687 * cg26 * cg44 - 0.4D1 / 0.3D1 * t74 # * cg40) * dble(t69) t1164 = t79 * cg26 * cg44 t1193 = -0.4D1 * t77 * t245 * cg40 + (-0.2D1 * t194 * cg11 * t46 # + t588 * t1069 + t1071 * t590 - 0.2D1 * t595 * t213 * t382 + t200 # * (-t600 * t1038 / 0.4D1 + t201 * cg11 / 0.2D1 + beta_2_2 * cg11 #+ 0.3D1 / 0.4D1 * t606 * t1038 + 0.3D1 / 0.2D1 * t205 * cg11 + t40 # * t611 * t1050 + t40 * t38 * cg11 * t187 - t40 * t38 * t1050) * t #212 + t626 * t211 * t628 * t34 * t382 / 0.2D1 - cg10) * f * t80 + #t249 * frhob * t80 + 0.4D1 * t250 * t415 + t410 * frhoa * t80 + t8 #4 * cg37 * t80 + 0.4D1 * t252 * t415 + 0.4D1 * t411 * t254 + 0.4D1 # * t413 * t254 + 0.12D2 * t85 * t1164 + 0.4D1 * t85 * t244 * cg40 cg14 = cg10 + (0.2D1 * t215 * cg11 * t64 - t636 * t1104 - t1106 #* t638 + 0.2D1 * t643 * t234 * t396 - t221 * (-t648 * t1038 / 0.4D #1 + t222 * cg11 / 0.2D1 + beta_2_3 * cg11 + 0.3D1 / 0.4D1 * t654 * # t1038 + 0.3D1 / 0.2D1 * t226 * cg11 + t58 * t659 * t1050 + t58 * #t56 * cg11 * t187 - t58 * t56 * t1050) * t233 - t674 * t232 * t676 # * t52 * t396 / 0.2D1) * f * t82 + cg73 * frhob * t82 - 0.4D1 * t2 #40 * t407 + cg66 * frhoa * t82 + cg19 * cg37 * t82 - 0.4D1 * t242 #* t407 - 0.4D1 * t403 * t246 - 0.4D1 * t405 * t246 - 0.12D2 * t77 #* t78 * t1164 + t1193 cg91 = -t750 * cg26 * cg44 / 0.9D1 + t257 * cg40 / 0.3D1 - t755 #* cg26 * cg44 / 0.9D1 - t259 * cg40 / 0.3D1 cg84 = cg88 t1228 = t269 * t277 * cg52 / 0.2D1 t1231 = t96 * t798 * cg54 / 0.2D1 cg56 = t775 * t776 * cg52 + t779 * t776 * cg54 / 0.2D1 + t785 - #t269 * t98 * cg91 / 0.2D1 + t779 * t789 * cg52 / 0.2D1 + t795 * t7 #89 * cg54 + t801 - t96 * t274 * (-t767 * cg38 * t523 * cg53 / 0.2D #1 + t266 * cg84 * t7) / 0.2D1 + t1228 + t1231 + t812 cg55 = 0.2D1 * t820 * t822 * t432 - t101 * t281 * (-cg14 * t100 #* t105 + 0.3D1 * t282 * t429 + 0.3D1 * t427 * t286 - 0.12D2 * t102 # * t840 * cg52 + 0.3D1 * t102 * t285 * cg91) * t107 - t851 * t289 #* t432 * t107 t1269 = t445 * t119 t1283 = cg55 * t111 t1285 = 0.2D1 * t909 * trhob t1286 = Arhob * t t1288 = 0.2D1 * t1286 * trhoa t1291 = 0.2D1 * A * trhob * trhoa t1293 = 0.2D1 * t303 * cg56 t1304 = t445 * t312 t1327 = t1283 + t1285 + t1288 + t1291 + t1293 + 0.2D1 * Arhob * #t116 * Arhoa + 0.8D1 * t944 * Arhoa * trhob + 0.2D1 * t314 * cg55 #+ 0.8D1 * t944 * trhoa * Arhob + 0.12D2 * t953 * trhoa * trhob + 0 #.4D1 * t318 * cg56 t1330 = 0.2D1 * t101 * trhob * t299 + 0.2D1 * t297 * t1269 * trh #oa - 0.2D1 * t297 * t313 * trhoa * t453 + 0.2D1 * t297 * t298 * cg #56 + 0.2D1 * t297 * t904 * trhob + t101 * t111 * (t1283 + t1285 + #t1288 + t1291 + t1293) * t119 - t310 * t924 * t453 - 0.2D1 * t297 #* t313 * t321 * trhob - t310 * t1304 * t321 + 0.2D1 * t310 * t936 #* t321 * t453 - t310 * t313 * t1327 exc_rhoa_rhob = scale_ec * (cg4 + cg6 + rho * (cg14 + 0.6D1 * t8 #58 * t294 * cg52 + 0.3D1 * t293 * t457 * cg42 + 0.3D1 * t293 * t12 #3 * cg91 + 0.3D1 * t293 * t326 * cg52 + t110 * t1330 * t325 - t110 # * t967 * t456)) cg65 = 0.2D1 * t163 + 0.2D1 * t519 cg35 = cg11 t1342 = t368 ** 2 t1346 = rsrhob ** 2 cg28 = -0.2D1 * t171 * cg35 * t28 + 0.2D1 * t1033 * t1031 - 0.2D #1 * t543 * t1342 * t191 + t177 * (-t549 * t1346 / 0.4D1 + t179 * c #g35 / 0.2D1 + beta_2_1 * cg35 + 0.3D1 / 0.4D1 * t556 * t1346 + 0.3 #D1 / 0.2D1 * t183 * cg35 + t22 * t561 * t1346 * t564 + t22 * t20 * # cg35 * t187 - t22 * t20 * t1346 * t564) * t191 + t578 * t1342 * t #580 * t14 / 0.2D1 cg64 = cg67 t1377 = t382 ** 2 t1411 = t396 ** 2 cg81 = cg66 t1440 = cg44 ** 2 cg61 = (0.4D1 / 0.9D1 * t681 * t1440 + 0.4D1 / 0.3D1 * t71 * cg6 #5 + 0.4D1 / 0.9D1 * t687 * t1440 - 0.4D1 / 0.3D1 * t74 * cg65) * d #ble(t69) f1rhob = frhob t1462 = cg81 * f t1465 = cg19 * f1rhob t1482 = cg68 - cg64 t1489 = t1482 * f t1492 = t84 * f1rhob t1501 = -0.4D1 * t77 * t245 * cg65 + (-0.2D1 * t194 * cg35 * t46 # + 0.2D1 * t1071 * t1069 - 0.2D1 * t595 * t1377 * t212 + t200 * (- #t600 * t1346 / 0.4D1 + t201 * cg35 / 0.2D1 + beta_2_2 * cg35 + 0.3 #D1 / 0.4D1 * t606 * t1346 + 0.3D1 / 0.2D1 * t205 * cg35 + t40 * t6 #11 * t1346 * t564 + t40 * t38 * cg35 * t187 - t40 * t38 * t1346 * #t564) * t212 + t626 * t1377 * t628 * t34 / 0.2D1 - cg28) * f * t80 # + t410 * f1rhob * t80 + 0.4D1 * t411 * t415 + t1482 * frhob * t80 # + t84 * cg61 * t80 + 0.4D1 * t413 * t415 + 0.4D1 * t1489 * t415 + # 0.4D1 * t1492 * t415 + 0.12D2 * t85 * t79 * t1440 + 0.4D1 * t85 * # t244 * cg65 cg90 = cg28 + (0.2D1 * t215 * cg35 * t64 - 0.2D1 * t1106 * t1104 # + 0.2D1 * t643 * t1411 * t233 - t221 * (-t648 * t1346 / 0.4D1 + t #222 * cg35 / 0.2D1 + beta_2_3 * cg35 + 0.3D1 / 0.4D1 * t654 * t134 #6 + 0.3D1 / 0.2D1 * t226 * cg35 + t58 * t659 * t1346 * t564 + t58 #* t56 * cg35 * t187 - t58 * t56 * t1346 * t564) * t233 - t674 * t1 #411 * t676 * t52 / 0.2D1) * f * t82 + cg66 * f1rhob * t82 - 0.4D1 #* t403 * t407 + cg81 * frhob * t82 + cg19 * cg61 * t82 - 0.4D1 * t #405 * t407 - 0.4D1 * t1462 * t407 - 0.4D1 * t1465 * t407 - 0.12D2 #* t77 * t711 * t1440 + t1501 cg82 = cg64 + t1462 * t82 + t1465 * t82 - t409 + t1489 * t80 + t #1492 * t80 + t417 cg80 = -t750 * t1440 / 0.9D1 + t257 * cg65 / 0.3D1 - t755 * t144 #0 / 0.9D1 - t259 * cg65 / 0.3D1 cg89 = cg52 t1514 = cg53 ** 2 cg79 = cg54 t1520 = t2 * cg52 t1529 = t2 * cg54 cg9 = t775 * t1520 * cg89 + t779 * t1520 * cg79 / 0.2D1 + t1228 #- t269 * t98 * cg80 / 0.2D1 + t779 * t1529 * cg89 / 0.2D1 + t795 * # t1529 * cg79 + t1231 - t96 * t274 * (-t767 * t1514 * t523 / 0.2D1 # + t266 * cg84 * t7) / 0.2D1 + t269 * t277 * cg89 / 0.2D1 + t96 * #t798 * cg79 / 0.2D1 + t812 t1rhob = -t269 * t98 * cg89 / 0.2D1 - t96 * t274 * cg79 / 0.2D1 #- t278 / 0.2D1 t1550 = cg82 * t100 t1552 = t285 * cg89 t1555 = -t1550 * t105 + 0.3D1 * t102 * t1552 cg12 = 0.2D1 * t820 * t432 * t821 * t1555 - t101 * t281 * (-cg90 # * t100 * t105 + 0.3D1 * t427 * t1552 + 0.3D1 * t1550 * t429 - 0.1 #2D2 * t102 * t839 * cg52 * cg89 + 0.3D1 * t102 * t285 * cg80) * t1 #07 - t851 * t432 * t1555 * t107 A1rhob = -t101 * t281 * t1555 * t107 t1588 = A1rhob * t111 t1590 = 0.2D1 * t303 * t1rhob t1591 = t1588 + t1590 t1599 = t1588 + t1590 + 0.2D1 * t314 * A1rhob + 0.4D1 * t318 * t #1rhob t1602 = 0.2D1 * t297 * t298 * t1rhob + t101 * t111 * t1591 * t11 #9 - t310 * t313 * t1599 t1603 = t1602 * t325 t1630 = cg12 * t111 t1632 = 0.2D1 * t1286 * t1rhob t1635 = 0.2D1 * A1rhob * t * trhob t1638 = 0.2D1 * A * t1rhob * trhob t1640 = 0.2D1 * t303 * cg9 t1674 = t1630 + t1632 + t1635 + t1638 + t1640 + 0.2D1 * A1rhob * # t116 * Arhob + 0.8D1 * t944 * Arhob * t1rhob + 0.2D1 * t314 * cg1 #2 + 0.8D1 * t944 * trhob * A1rhob + 0.12D2 * t953 * trhob * t1rhob # + 0.4D1 * t318 * cg9 t1677 = 0.2D1 * t101 * t1rhob * t439 + 0.2D1 * t297 * t1591 * t1 #19 * trhob - 0.2D1 * t297 * t313 * trhob * t1599 + 0.2D1 * t297 * #t298 * cg9 + 0.2D1 * t297 * t1269 * t1rhob + t101 * t111 * (t1630 #+ t1632 + t1635 + t1638 + t1640) * t119 - t310 * t1304 * t1599 - 0 #.2D1 * t297 * t313 * t453 * t1rhob - t310 * t1591 * t312 * t453 + #0.2D1 * t310 * t936 * t453 * t1599 - t310 * t313 * t1674 t1680 = t456 * t966 cg48 = -0.2D1 / 0.9D1 * dble(t124) / t460 / t142 * t763 cg49 = cg34 t1698 = cg62 ** 2 cg2 = cg59 t1711 = 0.1D1 / t475 / t153 * t998 t1712 = t1711 * t150 t1713 = cg59 * t135 cg36 = 0.2D1 * t477 * cg32 * cg2 exc_rhob_rhob = scale_ex * (0.2D1 * cg49 * cg25 + 0.2D1 * cg31 * # cg36 + 0.2D1 * cg34 * cg25 - 0.3D1 / 0.2D1 * rhob * t7 * cg48 * c #g25 + 0.2D1 * t481 * cg36 + 0.2D1 * cg31 * cg57 + 0.2D1 * rhob * c #g49 * cg57 + 0.2D1 * t156 * (-0.8D1 * t1712 * t1713 * cg2 + 0.2D1 #* t477 * cg2 * cg59 + 0.2D1 * t477 * cg32 * (cg1 / t466 / cg24 * t #148 * t1698 + t468 * t472 * cg62 - t468 * t148 * cg48 / 0.2D1 + t1 #47 / t471 / rhob))) / 0.2D1 + scale_ec * (cg82 + 0.3D1 * t293 * t1 #23 * cg89 + t110 * t1603 + cg4 + rho * (cg90 + 0.6D1 * t858 * t436 # * cg89 + 0.3D1 * t293 * t1603 * cg52 + 0.3D1 * t293 * t123 * cg80 # + 0.3D1 * t293 * t457 * cg89 + t110 * t1677 * t325 - t110 * t1680 # * t1602)) t1739 = t268 * t97 t1741 = t95 * t273 t1743 = t488 * t163 cg50 = -t1739 * t776 / 0.2D1 - t1741 * t789 / 0.2D1 - t1743 / 0. #2D1 t1748 = t101 * cg63 t1765 = t909 * cg63 t1766 = t494 * trhoa t1767 = t303 * cg50 t1801 = 0.2D1 * t1748 * t299 + 0.4D1 * t310 * t494 * t119 * trho #a - 0.2D1 * t297 * t313 * trhoa * t502 + 0.2D1 * t297 * t298 * cg5 #0 + 0.2D1 * t297 * t904 * cg63 + t101 * t111 * (0.2D1 * t1765 + 0. #2D1 * t1766 + 0.2D1 * t1767) * t119 - t310 * t924 * t502 - 0.2D1 * # t297 * t313 * t321 * cg63 - 0.2D1 * t493 * t494 * t312 * t321 + 0 #.2D1 * t310 * t936 * t321 * t502 - t310 * t313 * (0.2D1 * t1765 + #0.2D1 * t1766 + 0.2D1 * t1767 + 0.8D1 * t944 * Arhoa * cg63 + 0.12 #D2 * t953 * trhoa * cg63 + 0.4D1 * t318 * cg50) exc_rhoa_norm_drho = scale_ec * (cg60 + rho * (0.3D1 * t293 * t5 #06 * cg42 + t110 * t1801 * t325 - t110 * t967 * t505)) cg78 = -t1739 * t1520 / 0.2D1 - t1741 * t1529 / 0.2D1 - t1743 / #0.2D1 t1829 = t1286 * cg63 t1830 = t494 * trhob t1831 = t303 * cg78 t1865 = 0.2D1 * t1748 * t439 + 0.4D1 * t310 * t494 * t119 * trho #b - 0.2D1 * t297 * t313 * trhob * t502 + 0.2D1 * t297 * t298 * cg7 #8 + 0.2D1 * t297 * t1269 * cg63 + t101 * t111 * (0.2D1 * t1829 + 0 #.2D1 * t1830 + 0.2D1 * t1831) * t119 - t310 * t1304 * t502 - 0.2D1 # * t297 * t313 * t453 * cg63 - 0.2D1 * t493 * t494 * t312 * t453 + # 0.2D1 * t310 * t936 * t453 * t502 - t310 * t313 * (0.2D1 * t1829 #+ 0.2D1 * t1830 + 0.2D1 * t1831 + 0.8D1 * t944 * Arhob * cg63 + 0. #12D2 * t953 * trhob * cg63 + 0.4D1 * t318 * cg78) exc_rhob_norm_drho = scale_ec * (cg60 + rho * (0.3D1 * t293 * t5 #06 * cg52 + t110 * t1865 * t325 - t110 * t1680 * t505)) t1871 = cg63 ** 2 t1876 = A * t1871 t1888 = t502 ** 2 t1901 = t505 ** 2 exc_norm_drho_norm_drho = scale_ec * rho * (t110 * (0.2D1 * t101 # * t1871 * t113 * t119 + 0.10D2 * t310 * t1876 * t119 - 0.4D1 * t2 #97 * t313 * cg63 * t502 - 0.4D1 * t493 * t494 * t312 * t502 + 0.2D #1 * t310 * t936 * t1888 - t310 * t313 * (0.2D1 * t1876 + 0.12D2 * #t953 * t1871)) * t325 - t110 * t1901 * t966) exc_rhoa_norm_drhoa = scale_ex * (0.2D1 * cg83 * cg69 + 0.2D1 * #t350 * cg69 + 0.2D1 * t140 * (-0.8D1 * t1000 * t1001 * cg16 + 0.2D #1 * t346 * cg16 * cg43 + 0.2D1 * t346 * cg29 * (-t336 * t131 * cg5 #1 / 0.2D1 - t129 * t341 / 0.2D1))) / 0.2D1 t1922 = cg16 ** 2 exc_norm_drhoa_norm_drhoa = scale_ex * t140 * (-0.8D1 * t999 * t #133 * t1922 * t135 + 0.2D1 * t346 * t1922) exc_rhob_norm_drhob = scale_ex * (0.2D1 * cg31 * cg71 + 0.2D1 * #t481 * cg71 + 0.2D1 * t156 * (-0.8D1 * t1712 * t1713 * cg70 + 0.2D #1 * t477 * cg70 * cg59 + 0.2D1 * t477 * cg32 * (-t467 * t148 * cg6 #2 / 0.2D1 - t146 * t472 / 0.2D1))) / 0.2D1 t1949 = cg70 ** 2 exc_norm_drhob_norm_drhob = scale_ex * t156 * (-0.8D1 * t1711 * #t150 * t1949 * t135 + 0.2D1 * t477 * t1949) cg93 = exc_norm_drhob_norm_drhob return end
evalf(r_eqs_lsd4(0.1,0.1,0.3,0.15,0.15)); evalf(exc);
NiMkIStqcF4lMyIhIzU=
NiMkISs1aGhkKSohIzY=
evalf(r_eqs_lda4(0.2,0.3)); evalf(exc);
NiMkISsqemwxKyIhIzU=
NiMkISs1aGhkKSohIzY=
exc:='exc':exc_rhoa:='exc_rhoa':exc_rhob:='exc_rhob':exc_norm_drho:='exc_norm_drho': exc_norm_drhoa:='exc_norm_drhoa':exc_norm_drhob:='exc_norm_drhob': exc_rhoa_rhoa:='exc_rhoa_rhoa':exc_rhoa_rhob:='exc_rhoa_rhob':exc_rhob_rhob:='exc_rhob_rhob': exc_rhoa_norm_drho:='exc_rhoa_norm_drho':exc_rhob_norm_drho:='exc_rhob_norm_drho': exc_norm_drho_norm_drho:='exc_norm_drho_norm_drho': exc_rhoa_norm_drhoa:='exc_rhoa_norm_drhoa':exc_norm_drhoa_norm_drhoa:='exc_norm_drhoa_norm_drhoa': exc_rhob_norm_drhob:='exc_rhob_norm_drhob':exc_norm_drhob_norm_drhob:='exc_norm_drhob_norm_drhob': my_rho:='my_rho':my_norm_drho:='my_norm_drho':my_rhoa:='my_rhoa':my_rhob:='my_rhob': my_norm_drhoa:='my_norm_drhoa':my_norm_drhob:='my_norm_drhob':

exc_rho:='exc_rho':exc_rho_rho:='exc_rho_rho':exc_rho_norm_drho:='exc_rho_norm_drho':