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Polishing numbers

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@@ -1,21 +1,21 @@
# Numeric vectors {#numbers} # Numeric vectors {#numbers}
```{r, results = "asis", echo = FALSE} ```{r, results = "asis", echo = FALSE}
status("drafting") status("polishing")
``` ```
## Introduction ## Introduction
In this chapter, you'll learn useful tools for creating and manipulating with numeric vectors. In this chapter, you'll learn useful tools for creating and manipulating numeric vectors.
We'll start by doing into a little more detail of `count()` before diving into various numeric transformations. We'll start by going into a little more detail of `count()` before diving into various numeric transformations.
You'll then learn about more general transformations that are often used with numeric vectors, but also work with other types. You'll then learn about more general transformations that can be applied to other types of vector, but are often used with numeric vectors.
Then you'll learn about a few more useful summaries before we finish up with a comparison of function variants that have similar names and similar actions, but are each designed for a specific use case. Then you'll learn about a few more useful summaries before we finish up with a comparison of function variants that have similar names and similar actions, but are each designed for a specific use case.
### Prerequisites ### Prerequisites
This chapter mostly uses functions from base R, which are available without loading any packages. This chapter mostly uses functions from base R, which are available without loading any packages.
But we still need the tidyverse because we'll use these base R functions inside of tidyverse functions like `mutate()` and `filter()`. But we still need the tidyverse because we'll use these base R functions inside of tidyverse functions like `mutate()` and `filter()`.
Like in the last chapter, we'll again use real examples from nycflights13, as well as toy examples made inline with `c()` and `tribble()`. Like in the last chapter, we'll use real examples from nycflights13, as well as toy examples made with `c()` and `tribble()`.
```{r setup, message = FALSE} ```{r setup, message = FALSE}
library(tidyverse) library(tidyverse)
@@ -24,9 +24,8 @@ library(nycflights13)
### Counts ### Counts
It's surprising how much data science you can do with just counts and a little basic arithmetic. It's surprising how much data science you can do with just counts and a little basic arithmetic, so dplyr strives to make counting as easy as possible with `count()`.
There are two ways to compute a count in dplyr. This function is great for quick exploration and checks during analysis:
The simplest is to use `count()`, which is great for quick exploration and checks during analysis:
```{r} ```{r}
flights |> count(dest) flights |> count(dest)
@@ -34,7 +33,16 @@ flights |> count(dest)
(Despite the advice in Chapter \@ref(code-style), I usually put `count()` on a single line because I'm usually using it at the console for a quick check that my calculation is working as expected.) (Despite the advice in Chapter \@ref(code-style), I usually put `count()` on a single line because I'm usually using it at the console for a quick check that my calculation is working as expected.)
Alternatively, you can count "by hand" which allows you to compute other summaries at the same time: If you want to see the most common values add `sort = TRUE`:
```{r}
flights |> count(dest, sort = TRUE)
```
And remember that if you want to see all the values, you can use `|> View()` or `|> print(n = Inf)`.
You can perform the same computation "by hand" with `group_by()`, `summarise()` and `n()`.
This is useful because it allows you to compute other summaries at the same time:
```{r} ```{r}
flights |> flights |>
@@ -45,17 +53,17 @@ flights |>
) )
``` ```
`n()` is a special a summary function because it doesn't take any arguments and instead reads information from the current group. `n()` is a special summary function that doesn't take any arguments and instead access information about the "current" group.
This means you can't use it outside of dplyr verbs: This means that it only works inside dplyr verbs:
```{r, error = TRUE} ```{r, error = TRUE}
n() n()
``` ```
There are a couple of related counts that you might find useful: There are a couple of variants of `n()` that you might find useful:
- `n_distinct(x)` counts the number of distinct (unique) values of one or more variables. - `n_distinct(x)` counts the number of distinct (unique) values of one or more variables.
For example, we could figure out which destinations are served by the most carriers? For example, we could figure out which destinations are served by the most carriers:
```{r} ```{r}
flights |> flights |>
@@ -66,7 +74,7 @@ There are a couple of related counts that you might find useful:
arrange(desc(carriers)) arrange(desc(carriers))
``` ```
- A weighted count is just a sum. - A weighted count is a sum.
For example you could "count" the number of miles each plane flew: For example you could "count" the number of miles each plane flew:
```{r} ```{r}
@@ -75,13 +83,14 @@ There are a couple of related counts that you might find useful:
summarise(miles = sum(distance)) summarise(miles = sum(distance))
``` ```
This comes up enough that `count()` has a `wt` argument that does this for you: Weighted counts are a common problem so `count()` has a `wt` argument that does the same thing:
```{r} ```{r}
flights |> count(tailnum, wt = distance) flights |> count(tailnum, wt = distance)
``` ```
- `sum()` and `is.na()` is also a powerful combination, allowing you to count the number of missing values: - You can count missing values by combining `sum()` and `is.na()`.
In the flights dataset this represents flights that are cancelled:
```{r} ```{r}
flights |> flights |>
@@ -92,27 +101,26 @@ There are a couple of related counts that you might find useful:
### Exercises ### Exercises
1. How can you use `count()` to count the number rows with a missing value for a given variable? 1. How can you use `count()` to count the number rows with a missing value for a given variable?
2. Expand the following calls to `count()` to use the core verbs of dplyr: 2. Expand the following calls to `count()` to instead use `group_by()`, `summarise()`, and `arrange()`:
1. `flights |> count(dest, sort = TRUE)` 1. `flights |> count(dest, sort = TRUE)`
2. `flights |> count(tailnum, wt = distance)` 2. `flights |> count(tailnum, wt = distance)`
## Numeric transformations ## Numeric transformations
Base R provides many useful transformation functions that you can use with `mutate()`. Transformation functions work well with `mutate()` because their output is the same length as the input.
We'll come back to this distinction later in Section \@ref(variants), but the key property that they all possess is that the output is the same length as the input. The vast majority of transformation functions are already built into base R.
It's impractical to list them all so this section will give show the most useful.
There's no way to list every possible function that you might use, so this section will aim give a selection of the most useful. As an example, while R provides all the trigonometric functions that you might dream of, I don't list them here because they're rarely needed for data science.
One category that I've deliberately omit is the trigonometric functions; R provides all the trig functions that you might expect, but they're rarely needed for data science.
### Arithmetic and recycling rules ### Arithmetic and recycling rules
We introduced the basics of arithmetic (`+`, `-`, `*`, `/`, `^`) in Chapter \@ref(workflow-basics) and have used them a bunch since. We introduced the basics of arithmetic (`+`, `-`, `*`, `/`, `^`) in Chapter \@ref(workflow-basics) and have used them a bunch since.
They don't need a huge amount of explanation, because they do what you learned in grade school. These functions don't need a huge amount of explanation because they do what you learned in grade school.
But we need to to briefly talk about the **recycling rules** which determine what happens when the left and right hand sides have different lengths. But we need to briefly talk about the **recycling rules** which determine what happens when the left and right hand sides have different lengths.
This is important for operations like `air_time / 60` because there are 336,776 numbers on the left hand side, and 1 number on the right hand side. This is important for operations like `flights |> mutate(air_time = air_time / 60)` because there are 336,776 numbers on the left of `/` but only one on the right.
R handles this by repeating, or **recycling**, the short vector. R handles mismatched lengths by **recycling,** or repeating, the short vector.
We can see this in operation more easily if we create some vectors outside of a data frame: We can see this in operation more easily if we create some vectors outside of a data frame:
```{r} ```{r}
@@ -122,14 +130,15 @@ x / 5
x / c(5, 5, 5, 5) x / c(5, 5, 5, 5)
``` ```
Generally, you want to recycle vectors of length 1, but R supports a rather more general rule where it will recycle any shorter length vector, usually (but not always) warning if the longer vector isn't a multiple of the shorter: Generally, you only want to recycle single numbers (i.e. vectors of length 1), but R will recycle any shorter length vector.
It usually (but not always) warning if the longer vector isn't a multiple of the shorter:
```{r} ```{r}
x * c(1, 2) x * c(1, 2)
x * c(1, 2, 3) x * c(1, 2, 3)
``` ```
This recycling can lead to a surprising result if you accidentally use `==` instead of `%in%` and the data frame has an unfortunate number of rows. These recycling rules are also applied to logical comparisons (`==`, `<`, `<=`, `>`, `>=`, `!=`) and can lead to a surprising result if you accidentally use `==` instead of `%in%` and the data frame has an unfortunate number of rows.
For example, take this code which attempts to find all flights in January and February: For example, take this code which attempts to find all flights in January and February:
```{r} ```{r}
@@ -138,11 +147,11 @@ flights |>
``` ```
The code runs without error, but it doesn't return what you want. The code runs without error, but it doesn't return what you want.
Because of the recycling rules it returns January flights that are in odd numbered rows and February flights that are in even numbered rows. Because of the recycling rules it finds flights in odd numbered rows that departed in January and flights in even numbered rows that departed in February.
There's no warning because `nycflights` has an even number of rows. And unforuntately there's no warning because `nycflights` has an even number of rows.
To protect you from this silent failure, most tidyverse functions uses stricter recycling that only recycles single values. To protect you from this type of silent failure, most tidyverse functions use a stricter form of recycling that only recycles single values.
Unfortunately that doesn't help here, or many other cases, because the key computation is performed by the base R function `==`, not `filter()`. Unfortunately that doesn't help here, or in many other cases, because the key computation is performed by the base R function `==`, not `filter()`.
### Minimum and maximum ### Minimum and maximum
@@ -159,8 +168,8 @@ df <- tribble(
df |> df |>
mutate( mutate(
min = pmin(x, y), min = pmin(x, y, na.rm = TRUE),
max = pmax(x, y) max = pmax(x, y, na.rm = TRUE)
) )
``` ```
@@ -169,8 +178,8 @@ We'll come back to those in Section \@ref(min-max-summary).
### Modular arithmetic ### Modular arithmetic
Modular arithmetic is the technical name for the type of math you did before you learned about real numbers, i.e. when you did division that yield a whole number and a remainder. Modular arithmetic is the technical name for the type of math you did before you learned about real numbers, i.e. division that yields a whole number and a remainder.
In R, these are provided by `%/%` which does integer division, and `%%` which computes the remainder: In R, `%/%` does integer division and `%%` computes the remainder:
```{r} ```{r}
1:10 %/% 3 1:10 %/% 3
@@ -215,7 +224,7 @@ flights |>
### Logarithms ### Logarithms
Logarithms are an incredibly useful transformation for dealing with data that ranges across multiple orders of magnitude. Logarithms are an incredibly useful transformation for dealing with data that ranges across multiple orders of magnitude.
They also convert multiplicative relationships to additive. They also convert exponential growth to linear growth.
For example, take compounding interest --- the amount of money you have at `year + 1` is the amount of money you had at `year` multiplied by the interest rate. For example, take compounding interest --- the amount of money you have at `year + 1` is the amount of money you had at `year` multiplied by the interest rate.
That gives a formula like `money = starting * interest ^ year`: That gives a formula like `money = starting * interest ^ year`:
@@ -229,7 +238,7 @@ money <- tibble(
) )
``` ```
If you plot this data, you'll get a curve: If you plot this data, you'll get an exponential curve:
```{r} ```{r}
ggplot(money, aes(year, money)) + ggplot(money, aes(year, money)) +
@@ -244,10 +253,10 @@ ggplot(money, aes(year, money)) +
scale_y_log10() scale_y_log10()
``` ```
We get a straight line because (after a little algebra) we get `log(money) = log(starting) + n * log(interest)`, which matches the pattern for a straight line, `y = m * x + b`. This a straight line because a little algebra reveals that `log(money) = log(starting) + n * log(interest)`, which matches the pattern for a line, `y = m * x + b`.
This is a useful pattern: if you see a (roughly) straight line after log-transforming the y-axis, you know that there's an underlying multiplicative relationship. This is a useful pattern: if you see a (roughly) straight line after log-transforming the y-axis, you know that there's underlying exponential growth.
If you're log-transforming your data with dplyr, instead of relying on ggplot2 to do it for you, you have a choice of three logarithms: `log()` (the natural log, base e), `log2()` (base 2), and `log10()` (base 10). If you're log-transforming your data with dplyr you have a choice of three logarithms provided by base R: `log()` (the natural log, base e), `log2()` (base 2), and `log10()` (base 10).
I recommend using `log2()` or `log10()`. I recommend using `log2()` or `log10()`.
`log2()` is easy to interpret because difference of 1 on the log scale corresponds to doubling on the original scale and a difference of -1 corresponds to halving; whereas `log10()` is easy to back-transform because (e.g) 3 is 10\^3 = 1000. `log2()` is easy to interpret because difference of 1 on the log scale corresponds to doubling on the original scale and a difference of -1 corresponds to halving; whereas `log10()` is easy to back-transform because (e.g) 3 is 10\^3 = 1000.
@@ -262,8 +271,8 @@ round(123.456)
``` ```
You can control the precision of the rounding with the second argument, `digits`. You can control the precision of the rounding with the second argument, `digits`.
`round(x, digits)` rounds to the nearest `10^-n` so `digits = 2` will give you. `round(x, digits)` rounds to the nearest `10^-n` so `digits = 2` will round to the nearest 0.01.
This definition is cool because it implies `round(x, -3)` will round to the nearest thousand: This definition is useful because it implies `round(x, -3)` will round to the nearest thousand, which indeed it does:
```{r} ```{r}
round(123.456, 2) # two digits round(123.456, 2) # two digits
@@ -278,11 +287,10 @@ There's one weirdness with `round()` that seems surprising at first glance:
round(c(1.5, 2.5)) round(c(1.5, 2.5))
``` ```
`round()` uses what's known as "round half to even" or Banker's rounding. `round()` uses what's known as "round half to even" or Banker's rounding: if a number is half way between two integers, it will be rounded to the **even** integer.
If a number is half way between two integers, it will be rounded to the **even** integer. This is a good strategy because it keeps the rounding unbiased: half of all 0.5s are rounded up, and half are rounded down.
This is the right general strategy because it keeps the rounding unbiased: half the 0.5s are rounded up, and half are rounded down.
`round()` is paired with `floor()` to round down and `ceiling()` to round up: `round()` is paired with `floor()` which always rounds down and `ceiling()` which always rounds up:
```{r} ```{r}
x <- 123.456 x <- 123.456
@@ -291,7 +299,7 @@ floor(x)
ceiling(x) ceiling(x)
``` ```
These functions don't have a digits argument, but instead, you can scale down, round, and then scale back up: These functions don't have a digits argument, so you can instead scale down, round, and then scale back up:
```{r} ```{r}
# Round down to nearest two digits # Round down to nearest two digits
@@ -312,16 +320,17 @@ round(x / 0.25) * 0.25
### Cumulative and rolling aggregates ### Cumulative and rolling aggregates
Base R provides `cumsum()`, `cumprod()`, `cummin()`, `cummax()` for running, or cumulative, sums, products, mins and maxes, and dplyr provides `cummean()` for cumulative means. Base R provides `cumsum()`, `cumprod()`, `cummin()`, `cummax()` for running, or cumulative, sums, products, mins and maxes.
dplyr provides `cummean()` for cumulative means.
Cumulative sums tend to come up the most in practice:
```{r} ```{r}
x <- 1:10 x <- 1:10
cumsum(x) cumsum(x)
cummean(x)
``` ```
If you need more complex rolling or sliding aggregates, try the [slider](https://davisvaughan.github.io/slider/) package by Davis Vaughan. If you need more complex rolling or sliding aggregates, try the [slider](https://davisvaughan.github.io/slider/) package by Davis Vaughan.
The example below illustrates some of its features. The following example illustrates some of its features.
```{r} ```{r}
library(slider) library(slider)
@@ -342,85 +351,92 @@ slide_vec(x, sum, .before = 2, .after = 2, .complete = TRUE)
## General transformations ## General transformations
These are often used with numbers, but can be applied to most other column types. The following sections describe some general transformations which are often used with numeric vectors, but can be applied to all other column types.
### Missing values {#missing-values-numbers} ### Missing values {#missing-values-numbers}
`coalesce()` You can fill in missing values with dplyr's `coalesce()`:
```{r}
x <- c(1, NA, 5, NA, 10)
coalesce(x, 0)
```
`coalesce()` is vectorised, so you can find the non-missing values from a pair of vectors:
```{r}
y <- c(2, 3, 4, NA, 5)
coalesce(x, y)
```
### Ranks ### Ranks
dplyr provides a number of ranking functions, but you should start with `dplyr::min_rank()`. dplyr provides a number of ranking functions inspired by SQL, but you should always start with `dplyr::min_rank()`.
It does the most usual way of dealing with ties (e.g. 1st, 2nd, 2nd, 4th). It uses the typical method for dealing with ties, e.g. 1st, 2nd, 2nd, 4th.
The default gives smallest values the small ranks; use `desc(x)` to give the largest values the smallest ranks.
```{r} ```{r}
y <- c(1, 2, 2, NA, 3, 4) x <- c(1, 2, 2, 3, 4, NA)
min_rank(y) min_rank(x)
min_rank(desc(y))
``` ```
If `min_rank()` doesn't do what you need, look at the variants `dplyr::row_number()`, `dplyr::dense_rank()`, `dplyr::percent_rank()`, `dplyr::cume_dist()`, `dplyr::ntile()`, as well as base R's `rank()`. Note that the smallest values get the lowest ranks; use `desc(x)` to give the largest values the smallest ranks:
`row_number()` can also be used without a variable within `mutate()`. ```{r}
min_rank(desc(x))
```
If `min_rank()` doesn't do what you need, look at the variants `dplyr::row_number()`, `dplyr::dense_rank()`, `dplyr::percent_rank()`, and `dplyr::cume_dist()`.
See the documentation for details.
```{r}
df <- data.frame(x = x)
df |> mutate(
row_number = row_number(x),
dense_rank = dense_rank(x),
percent_rank = percent_rank(x),
cume_dist = cume_dist(x)
)
```
You can achieve many of the same results by picking the appropriate `ties.method` argument to base R's `rank()`; you'll probably also want to set `na.last = "keep"` to keep `NA`s as `NA`.
`row_number()` can also be used without a variable when you're inside a dplyr verb, in which case it'll give within `mutate()`.
When combined with `%%` and `%/%` this can be a useful tool for dividing data into similarly sized groups: When combined with `%%` and `%/%` this can be a useful tool for dividing data into similarly sized groups:
```{r} ```{r}
flights |> flights |>
mutate( mutate(
row = row_number(), row = row_number(),
group_3 = row %/% (n() / 3), three_groups = (row - 1) %% 3,
group_3 = row %% 3, three_in_each_group = (row - 1) %/% 3,
.keep = "none" .keep = "none"
) )
``` ```
### Offset ### Offsets
`dplyr::lead()` and `dplyr::lag()` allow you to refer to leading or lagging values. `dplyr::lead()` and `dplyr::lag()` allow you to refer the values just before or just after the "current" value.
They return a vector of the same length but padded with NAs at the start or end They return a vector of the same length, padded with NAs at the start or end.
```{r} ```{r}
x <- c(2, 5, 11, 19, 35) x <- c(2, 5, 11, 11, 19, 35)
lag(x) lag(x)
lag(x, 2) lag(x, 2)
lead(x) lead(x)
``` ```
- `x - lag(x)` gives you the difference between the current and previous value. - `x - lag(x)` gives you the difference between the current and previous value.
- `x == lag(x)` tells you when the current value changes. See Section XXX for use with cumulative tricks.
If the rows are not already ordered, you can provide the `order_by` argument. ```{r}
x - lag(x)
```
### Positions - `x == lag(x)` tells you when the current value changes.
This is often useful combined with the cumulative tricks describe in Section \@ref(cumulative-tricks).
If your rows have a meaningful order, you can use base R's `[`, or dplyr's `first(x)`, `nth(x, 2)`, or `last(x)` to extract values at a certain position. ```{r}
For example, we can find the first and last departure for each day: x == lag(x)
```
```{r}
flights |>
group_by(year, month, day) |>
summarise(
first_dep = first(dep_time),
last_dep = last(dep_time)
)
```
The chief advantage of `first()` and `nth()` over `[` is that you can set a default value if that position does not exist (i.e. you're trying to get the 3rd element from a group that only has two elements).
The chief advantage of `last()` over `[`, is writing `last(x)` rather than `x[length(x)]`.
Additionally, if the rows aren't ordered, but there's a variable that defines the order, you can use `order_by` argument.
You can do this with `[` + `order_by()` but it requires a little thought.
Computing positions is complementary to filtering on ranks.
Filtering gives you all variables, with each observation in a separate row:
```{r}
flights |>
group_by(year, month, day) |>
mutate(r = min_rank(desc(sched_dep_time))) |>
filter(r %in% c(1, max(r)))
```
### Exercises ### Exercises
@@ -432,29 +448,34 @@ flights |>
3. What time of day should you fly if you want to avoid delays as much as possible? 3. What time of day should you fly if you want to avoid delays as much as possible?
4. For each destination, compute the total minutes of delay. 4. What does `flights |> group_by(dest() |> filter(row_number() < 4)` do?
What does `flights |> group_by(dest() |> filter(row_number(dep_delay) < 4)` do?
5. For each destination, compute the total minutes of delay.
For each flight, compute the proportion of the total delay for its destination. For each flight, compute the proportion of the total delay for its destination.
5. Delays are typically temporally correlated: even once the problem that caused the initial delay has been resolved, later flights are delayed to allow earlier flights to leave. 6. Delays are typically temporally correlated: even once the problem that caused the initial delay has been resolved, later flights are delayed to allow earlier flights to leave.
Using `lag()`, explore how the delay of a flight is related to the delay of the immediately preceding flight. Using `lag()`, explore how the delay of a flight is related to the delay of the immediately preceding flight.
6. Look at each destination. 7. Look at each destination.
Can you find flights that are suspiciously fast? Can you find flights that are suspiciously fast?
(i.e. flights that represent a potential data entry error). (i.e. flights that represent a potential data entry error).
Compute the air time of a flight relative to the shortest flight to that destination. Compute the air time of a flight relative to the shortest flight to that destination.
Which flights were most delayed in the air? Which flights were most delayed in the air?
7. Find all destinations that are flown by at least two carriers. 8. Find all destinations that are flown by at least two carriers.
Use that information to rank the carriers. Use that information to rank the carriers.
## Summaries ## Summaries
Just using means, counts, and sum can get you a long way, but R provides many other useful summary functions. Just using means, counts, and sum can get you a long way, but R provides many other useful summary functions.
Here are a section that you might find useful.
### Center ### Center
We've used `mean(x)`, but `median(x)` is also useful. We've mostly used `mean(x)` so far, but `median(x)` is also useful.
The mean is the sum divided by the length; the median is a value where 50% of `x` is above it, and 50% is below it. The mean is the sum divided by the length; the median is a value where 50% of `x` is above it, and 50% is below it.
This makes it more robust to unusual values.
```{r} ```{r}
flights |> flights |>
@@ -512,6 +533,34 @@ The interquartile range `IQR(x)` and median absolute deviation `mad(x)` are robu
IQR is `quantile(x, 0.75) - quantile(x, 0.25)`. IQR is `quantile(x, 0.75) - quantile(x, 0.25)`.
`mad()` is derivied similarly to `sd()`, but inside being the average of the squared distances from the mean, it's the median of the absolute differences from the median. `mad()` is derivied similarly to `sd()`, but inside being the average of the squared distances from the mean, it's the median of the absolute differences from the median.
### Positions
Base R provides a powerful tool for extracting subsets of vectors called `[`.
This book doesn't cover `[` until Section \@ref(vector-subsetting) so for now we'll introduce three specialized functions that are useful inside of `summarise()` if you want to extract values at a specified position: `first()`, `last()`, and `nth()`.
For example, we can find the first and last departure for each day:
```{r}
flights |>
group_by(year, month, day) |>
summarise(
first_dep = first(dep_time),
last_dep = last(dep_time)
)
```
Compared to `[`, these functions allow you to set a `default` value if requested position doesn't exist (e.g. you're trying to get the 3rd element from a group that only has two elements) and you can use `order_by` argument.
Extracting values at positions is complementary to filtering on ranks.
Filtering gives you all variables, with each observation in a separate row:
```{r}
flights |>
group_by(year, month, day) |>
mutate(r = min_rank(desc(sched_dep_time))) |>
filter(r %in% c(1, max(r)))
```
### With `mutate()` ### With `mutate()`
As the names suggest, the summary functions are typically paired with `summarise()`, but they can also be usefully paired with `mutate()`, particularly when you want do some sort of group standardization. As the names suggest, the summary functions are typically paired with `summarise()`, but they can also be usefully paired with `mutate()`, particularly when you want do some sort of group standardization.
@@ -564,3 +613,4 @@ sum(x)
cumsum(x) cumsum(x)
x + 10 x + 10
``` ```