4.7 Sub-expressions

The special assignment operator ':=' is used to assign sub-expressions to user-defined variables. Sub-expression variables are different from normal variables in that their propagated error is computed on-the-fly when required, i.e. when they are printed or are assigned to a normal variable using the '=' operator or at an operator node of a parsing tree when used in another expression. E.g.

   >x=1pm0.1
   >s:=sin(x);c:=cos(x);
   >sin(x)/cos(x) /* Compute tan(x) as sin(x)/cos(x) */
       1.55741 +/-    0.34255
   >s/c           /* Compute tan(x) using two PARTIAL_VAR */
       1.55741 +/-    0.34255
   >tan(x)        /* Direct computation of tan(x) */
       1.55741 +/-    0.34255
   >s2=s;
   >s2/c          /* Compute tan(x) with a normal variable
                     and one PARTIAL_VAR.  Error propagates 
                     differently */
       1.55741 +/-    0.26236