A digression around VA's SRC #012b

[Albert Chan]

I guess the reason simple horner's rule work well is we really don't need super accurate y=f(x)
FNROOT is interpolating the secant line for root, from points (x1,y1), (x2,y2)

x = x2 - (x2-x1) * [(y2-0)/(y2-y1)]

As |x2-x1| get smaller, only a rough final ratio suffice.

Another reason is FNROOT, unlike secant's method, keep an "anchor" from the other side.
Convergence is slower, but avoid the problem of huge errors when f(x) closing to root.

Because of FNROOT, both FNQ(x) and FNQ(y=x+1) versions converge exactly the same path.
FNQ(y=x+1) improved accuracy is wasted.

   X                    FNQ(X)              FNQ(Y=X+1)           EXACT FNQ(X)
-.997             -3.21319628854E-7     -3.21319628895E-7     -3.21319628893E-7
-.996              1.12009058650E-7      1.12009058650E-7      1.12009058650E-7
-.9965            -1.72129040193E-7     -1.72129040185E-7     -1.72129040185E-7
-.996197103203    -1.74709075393E-8     -1.74709075547E-8     -1.74709075547E-8
-.9961705078      -1.36946078247E-9     -1.36946080158E-9     -1.36946080144E-9
-.996168448294    -1.05051545133E-10    -1.05051550303E-10    -1.05051550266E-10
-.996084224147     5.37864589010E-8      5.37864589106E-8      5.37864589104E-8
-.996168284115    -4.14702160931E-12    -4.14700483334E-12    -4.14700478100E-12
-.996126254131     2.63582466399E-8      2.63582466500E-8      2.63582466496E-8
-.996168277503    -8.29143191590E-14    -8.29276460508E-14    -8.29276562553E-14
-.996147265817     1.30466902823E-8      1.30466902845E-8      1.30466902845E-8
-.996168277369    -5.55826356659E-16    -5.64092304694E-16    -5.64057294087E-16
-.996157771593     6.49034644324E-9      6.49034650739E-9      6.49034650714E-9
-.996168277368     5.28822647438E-17     5.03647313957E-17     5.05964697450E-17