Polynomial Evaluation Execution Time

Execution time comparison for evaluation of 8th-order polynomials

Pseudocode for "naive" method:

integer i,j,k,count; real p,q,x; real array (a_i)_0:8
x ← 0
for k=1 to count do
  p ← 0
  for i=0 to 8 do
    q ← a_i
    for j=0 to i-1 do
      q ← q * x
    end for
    p ← p + q
  end for
  x ← x + 10^-6
end for

Pseudocode for "nested" method:

integer i,k,count; real p,x; real array (a_i)_0:8
x ← 0
for k=1 to count do
  p ← a₈
  for i=7 to 0 do
    p ← a_i + x * p
  end for
  x ← x + 10^-6
end for

Count: Method: Naive Nested