enumerate all expressions w. some oberands and operators

expressions.R

##

{ 
  ## let's go ahead and generate the possibilities. 

  x <- 2
  y <- pi
  z <- exp(1)
  `%^%` <- `^`
  `%/%` <- `/`
  splitrows <- function(s) split(s, seq_len(dim(s)[[1]]))
  sym <- c("x", "y", "z")
  op <- c("%/%","%^%", "%*%")
  library(gtools)
  syms <- permutations(length(sym), length(sym), sym)
  ops <- permutations(length(op), length(sym)-1, op, repeats.allowed=TRUE)
  orders <- permutations(length(sym)-1, length(sym)-1)
  cases <- Reduce(merge,
                  list(data.frame(sym=I(splitrows(syms))),
                       data.frame(op=I(splitrows(ops))),
                       data.frame(order=I(splitrows(orders)))))

  results <- do.call(rbind, apply(
   cases, 1,
   function(case) {
     with(lapply(case, unlist), {
       expr <- sym #or lapply(sym, as.name)
       for ( i in seq_along(op)) {
         expr[c(order[i], order[i]+1)] <-
           paste("(", expr[[order[i]]], op[i], expr[[order[i]+1]], ")")
         #alternately
         #paste("`",op[i],"`(", expr[[order[i]]], ", ", expr[[order[i]+1]], ")", sep="")
         #alternately
         #list(call(op[i], expr[[order[i]]], op[i], expr[[order[i]+1]])
       }
       expr <- expr[[order[i]]]
       value <- eval(parse(text=expr))
       reparse <- deparse(parse(text=expr)[[1]])
       value2 <- eval(parse(text=reparse))
       same <- value == value2
       data.frame(expr, value, reparse, value2, same)
     })
   }))
}