Redo formula handling for well-formedness checks about contrastable HOT 4 CLOSED

1) varName ~ sum_code + 1 + 2
2) varName ~ sum_code + 1 * 2 + 2 

## Matrix call is included to give .simplify_formula something to work with
# Case where the repeated operator appears later
tst <- gear ~ matrix(c(0.75, -0.25, -0.25,
                                 -0.25/4, -0.25*2, 0.75^2.3,
                                 -0.25, -0.25, -0.25%in%c(1,2,3),
                                 -0.25, 0.75, -0.25) %>% abs(), nrow = 4) + 4 * 2 + - 2 + 2

# Case where the repeated operator appears immediately after the first ocurrence
tst2 <- gear ~ matrix(c(0.75, -0.25, -0.25,
                        -0.25/4, -0.25*2, 0.75^2.3,
                        -0.25, -0.25, -0.25%in%c(1,2,3),
                        -0.25, 0.75, -0.25) %>% abs(), nrow = 4) + 4 + 4

# Case where there is no repeated operator
tst3 <- gear ~ matrix(c(0.75, -0.25, -0.25,
                        -0.25/4, -0.25*2, 0.75^2.3,
                        -0.25, -0.25, -0.25%in%c(1,2,3),
                        -0.25, 0.75, -0.25) %>% abs(), nrow = 4) + 4 *2

# Case where the repeated operator appears MUCH later
tst4 <- gear ~ matrix(c(0.75, -0.25, -0.25,
                        -0.25/4, -0.25*2, 0.75^2.3,
                        -0.25, -0.25, -0.25%in%c(1,2,3),
                        -0.25, 0.75, -0.25) %>% abs(), nrow = 4) + 4 * 2 - 1 | 3 / 3 & 2 ^ 5 + 4

test_1 <- function(f) {
  s_f <- .simplify_formula(f)

  .any_dominated_by_identity(s_f[[3]])
}

test_2 <- function(f) {
  s_f <- .simplify_formula(f)
  c_f <- deparse1(s_f)
  
  grepl("([|+*-]).+(\\1)", c_f)
}

library(microbenchmark)
set.seed(111)
mb1 <- microbenchmark(test_1(tst), test_2(tst), times = 3000)
mb2 <- microbenchmark(test_1(tst2), test_2(tst2), times = 3000)
mb3 <- microbenchmark(test_1(tst3), test_2(tst3), times = 3000)
mb4 <- microbenchmark(test_1(tst4), test_2(tst4), times = 3000)

mb1;mb2;mb3;mb4

test_1 <- function(f) {
  s_f <- .simplify_formula(f)
  
  .any_dominated_by_identity(s_f[[3]])
  tryCatch(stop(1), error = \(e) TRUE)
}

test_2 <- function(f) {
  s_f <- .simplify_formula(f)
  c_f <- deparse1(s_f)
  
  grepl("([|+*-]).+(\\1)", c_f)
  tryCatch(stop(1), error = \(e) TRUE)
}

test_3 <- function(f) {
  tryCatch(.simplify_formula2(f),error = \(e) TRUE)
}

library(microbenchmark)
set.seed(111)
mb1 <- microbenchmark(test_1(tst), test_2(tst), test_3(tst), times = 3000)
mb2 <- microbenchmark(test_1(tst2), test_2(tst2),test_3(tst2), times = 3000)
mb3 <- microbenchmark(test_1(tst3), test_2(tst3),test_3(tst3), times = 3000)
mb4 <- microbenchmark(test_1(tst4), test_2(tst4),test_3(tst4), times = 3000)

mb1;mb2;mb3;mb4