NB. [Session started: 2006 2 22 18 27 38.253]
   eqn0=: 3 : '+/*:y.'                 NB. Set up equations
   eqn1=: 3 : '*/2-/\y.,{.y.'
   diffeqns=: 3 : '(eqn0 y.)-eqn1 y.'  NB. and differencer.

NB. Pick wide range of random arguments...
   (<./,>./)rndn=. (_1e4+?1e5$20001)%>:?1e5$1e3 
_9879 9658

   (<./,>./)|diffs=. 3 diffeqns\rndn
0.010086928 5.5282426e10

   close1s=. 10{./:|diffs     NB. Pick 10 closest results as
   seeds=. close1s{3[\rndn    NB.  starting points...
_0.63838384 0.37931034  _17.451852
 _6.4783599  5.4468339   6.1741868
. . .
_0.10789474 0.10091743   0.3027933

   diffeqns"1 seeds
0.010086928 0.011770021 _0.023991408 ... 0.096197183

NB. Start with 1st seed and look a little bit around it in 3-space: 
   $&.>nn=. (0{seeds) +&.>/ <steps _1 1 11
+--+--+--+
|11|11|11|
+--+--+--+
NB. where
steps=: 3 : 0
NB.* steps: vector of numbers from num, to num, in numsteps steps.
   'from to numsteps'=. y. 
   from+(to-from)*(numsteps-1)%~i.numsteps
)

NB. Make 11x11x11 neighborhood of seed (use odd number->0 0 0 to
NB. include original point so we can do no worse).
   $>>,&.>/&.>/ nn 
11 11 11 3

   <./,|dd=. diffeqns&> >,&.>/&.>/ nn
0.006545809
NB. This is an improvement.  Point on which it is based:
   >ix=. <($dd)#:(,|dd)i.<./,|dd
5 5 0

NB. Value of the new point:
   >ix{>,&.>/&.>/ nn
_0.63838384 0.37931034 _17.461852
   diffeqns >ix{>,&.>/&.>/ nn NB. Check it...
0.0065475394

NB. Use this point as new centroid for tighter neighborhood: 
   nn=. (>ix{>,&.>/&.>/ nn) +&.>/ <steps _0.1 0.1 11
   <./,|dd=. diffeqns&> >,&.>/&.>/ nn
0.00054704513
NB. Is further improvement...
   >ix=. <($dd)#:(,|dd)i.<./,|dd 
5 5 4
   >ix{>,&.>/&.>/ nn          NB. New point...
_0.63838384 0.37931034 _17.481852

NB. and so on until no significant improvement.

NB. Start with another seed...
   nn=. (1{seeds) +&.>/ <steps _1 1 11 
   <./,|dd=. diffeqns&> >,&.>/&.>/ nn
0.011770021
   diffeqns 1{seeds
0.011770021
NB. No improvement, so tighten the search neighborhood:
   nn=. (1{seeds) +&.>/ <steps _0.1 0.1 13
   <./,|dd=. diffeqns&> >,&.>/&.>/ nn
0.0029753954
   >ix=. <($dd)#:(,|dd)i.<./,|dd
8 4 4
   >ix{>,&.>/&.>/ nn
_6.4450266 5.4135006 6.1408534 

NB. Tighter around better point...
   nn=. (>ix{>,&.>/&.>/ nn) +&.>/ <steps _0.001 0.001 13
   <./,|dd=. diffeqns&> >,&.>/&.>/ nn
9.0611054e_5
   >ix=. <($dd)#:(,|dd)i.<./,|dd 
3 12 12
   >ix{>,&.>/&.>/ nn
_6.4455266 5.4145006 6.1418534

   NB. And so on...