$ perl marpa-scannerless-calculator.pl --stdin
W=1; ( ( 0.3802 + ( 13.4739 * ( ( W / 0.9 )^(1/2) ) ) ) + ( 4.6272 * (
+ W / 0.9 ) ) )
^Z
result = 19.7242709884476
value of "W" = "1"
[download]

Wouldn't you know it, perl agrees

$ perl -E " $W=1; say ( ( 0.3802 + ( 13.4739 * sqrt( ( $W / 0.9 ) ) ) 
+) + ( 4.6272 * ( $W / 0.9 ) ) ); "
19.7242709884476
[download]

rule number enhanced courtesy of this/https://gist.github.com/4485844#file-scanless-pl

Being able to specify a qr{} would simplify this DSL immensely

Make of it what you will