MATLAB: Anyway to reduce the precision of solving symbolic equations

solve

I try to solve a system of symbolic equations, and the result is far more accurate than I actually need. In fact, 3-digits should be relatively good enough for me while it ends up offering 32 digits, which takes too long as I need to repeat the process hundreds of times. Is there any way to reduce the solve accuracy?
syms x y z t 'real'
warning('off')
line_p=[3,2,1]; % point on the line
line_d=[1,2,3]; % line direction
surf=x+y^2+z^3-10;
[x,y,z]=itsct_solve(line_p,line_d,surf)
function [x,y,z]=itsct_solve(line_p,line_d,surf)
syms x y z t 'real'
eq1=x-line_p(1)+line_d(1)*t; 
eq2=y-line_p(2)+line_d(2)*t;
eq3=z-line_p(3)+line_d(3)*t;
eq4=surf;
[x,y,z,t]=solve(eq1==0,eq2==0,eq3==0,eq4==0,'x','y','z','t');
x=vpa(x);
y=vpa(y);
z=vpa(z);
t=vpa(t);
end

Best Answer

You are using solve() which solve equation analytically and therefore takes a long time. Since you don't need very high precision, use vpasolve() to numerically solve the equation. It will increase speed several times. Also, each time you define syms inside a function, it will take a lot of time to create these symbolic variables. It is better to create them once outside the function and then pass it as input to function. For example, try this
syms x y z t 'real'
line_p=[3,2,1]; % point on the line
line_d=[1,2,3]; % line direction
surf=x+y^2+z^3-10;
tic
[x,y,z]=itsct_solve(x,y,z,t,line_p,line_d,surf);
toc
 function [x,y,z]=itsct_solve(x,y,z,t,line_p,line_d,surf)
  eq1=x-line_p(1)+line_d(1)*t; 
  eq2=y-line_p(2)+line_d(2)*t;
  eq3=z-line_p(3)+line_d(3)*t;
  eq4=surf;
  [x,y,z,t]=vpasolve(eq1==0,eq2==0,eq3==0,eq4==0,x,y,z,t);
end
Speed Comparison:
On my machine, your original code takes time
Elapsed time is 0.496555 seconds.
The optimized code takes time
Elapsed time is 0.048141 seconds.
There is above 10x speed improvement.
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