[ringland@orange 337]$ maple quiz3_solution.txt
    |\^/|     Maple 11 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
# Maple
# quiz3_solution.txt
>
> print( "Problem 1" );
                                                                     "Problem 1"

# Largest number obtained with all mantissa bits 1,
# and exponent code 111111111111110
>
> max_expon_code := 2^15-2;
                                                               max_expon_code := 32766

> max_expon := max_expon_code - 16383;
                                                                 max_expon := 16383

> largest := evalf(2*2^max_expon,2);
                                                                                 4933
                                                               largest := 0.12 10

>
> machine_epsilon := evalf( 2^(-64), 2);
                                                                                      -19
                                                            machine_epsilon := 0.54 10

>
> print( "Problem 2" );
                                                                     "Problem 2"

>
# Complete the function "solve_smart"
# and show that it is more accurate than
# "solve_naive" by using it on the example below
# with the precision set to 2 decimal digits
>
> a:=21;
                                                                       a := 21

> b:=3100;
                                                                      b := 3100

> c:=-150;
                                                                      c := -150

> my_quadratic := a*x^2+b*x+c;
                                                                            2
                                                        my_quadratic := 21 x  + 3100 x - 150

>
> a := evalf(a);
                                                                      a := 21.

> b := evalf(b);
                                                                     b := 3100.

> c := evalf(c);
                                                                     c := -150.

>
> solve_naive:=proc(a,b,c)
>    return [ (-b + sqrt(b^2-4*a*c))/(2*a) ,
>                          (-b - sqrt(b^2-4*a*c))/(2*a) ];
> end proc:
>
> solve_smart:=proc(a,b,c)
>       local xp,xm;
>       xp := (-b + sqrt(b^2-4*a*c))/(2*a);
>       xm := (-b - sqrt(b^2-4*a*c))/(2*a);
>
>       ########################### part to be supplied
>       if b = 0 then
>               return [xm,xp];
>       elif b < 0 then
>               return [xp,c/(a*xp)];
>       else
>               return [xm,c/(a*xm)];
>       end if;
>    ###########################
> end proc:
>
> solve_exact:=solve(my_quadratic,x);
                                                                              1/2                  1/2
                                                                1550   5 96226       1550   5 96226
                                               solve_exact := - ---- + ----------, - ---- - ----------
                                                                 21        21         21        21

> evalf(solve_exact,10);
                                                              0.04837124, -147.6674189

>
> Digits := 2;  ############## part to be supplied
                                                                     Digits := 2

> solve_naive(a,b,c);
                                                                     [0., -150.]

> solve_smart(a,b,c);
                                                                   [-150., 0.047]

>
> quit
bytes used=1053500, alloc=851812, time=0.04
[4]-  Done                    gedit $1
[ringland@orange 337]$

We see that our "smart" algorithm gets 2 digits almost
correct for the root closer to 0, while the naive algorithm
gets no digits at all.

(I am curious why we are off by 1 in the second digit,
while Maple's algorithm "solve" manages to get both
digits correct. I have no answer at present.)