Computing value of following polynomial was proposed as a benchmark:

(1) -> p := x^24+32*x^21+9*x^18+34*x^12+34*x^10+45*x^3

(1)

Naive solution have unimpressive speed:

)set messages time on

[eval(p, x, 0.5) for i in 1..1000];

Time: 0.12 (IN) + 0.09 (EV) + 0.01 (OT) = 0.22 sec

Simple reformulations do not give better results. However, assuming that we need double precision floating point results we can turn p into a compiled function. First we convert polynomial to use doubles as coefficients:

pf := p::POLY(DoubleFloat)

(2)

Time: 0 sec

Then we define corresponding function:

function(pf, 'dff, 'x)

(3)

Time: 0.01 (OT) = 0.01 sec

Now try it:

v := 0.5::SF

(4)

Time: 0 sec
[dff(v) for i in 1..10000];

Compiling function dff with type DoubleFloat -> DoubleFloat

Time: 0.15 (EV) + 0.01 (OT) = 0.16 sec

Now it is much better, but still slow. Main cost is interpreter loop. Try driver function:

do_it(v, n) == (res : SF := 0; for i in 1..n repeat res := res + dff(v); res)

Time: 0 sec
do_it(v, 1000000)

Compiling function do_it with type (DoubleFloat, PositiveInteger)
       -> DoubleFloat

(5)

Time: 0.61 (EV) + 0.01 (OT) = 0.62 sec

This is much better, around half microsecond per evaluation, but still slower than machine arithmetic. Profiling (not shown here) indicated that 99% of time is spent in exponentiation routine. So we would need better formula like Horner rule.