> I don't see how to do strength-reduction without introducing references,
> which appears to reduce performance more than is gained.

You might try converting your references to mutable fields.
Here's an example of the performance gain:

% cat ref.ml

let x = ref 1.0 in
let n = int_of_string Sys.argv.(1) in
for i = 1 to n do x := !x +. 1.0 done

% cat ref2.ml

type t = { mutable f:float };;
let x = { f = 1.0 } in
let n = int_of_string Sys.argv.(1) in
for i = 1 to n do x.f <- x.f +. 1.0 done

% ocamlopt -o ref{,.ml}

% ocamlopt -o ref2{,.ml}

% time ./ref 100000000
./ref 100000000  2.51s user 0.00s system 99% cpu 2.515 total

% time ./ref2 100000000
./ref2 100000000  1.54s user 0.01s system 100% cpu 1.542 total

The standard references take 1.6 times as much cpu time in this
case.

Issac
 
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