diff --git a/src/gleam_community/maths/arithmetics.gleam b/src/gleam_community/maths/arithmetics.gleam
index ee27306..b44f80a 100644
--- a/src/gleam_community/maths/arithmetics.gleam
+++ b/src/gleam_community/maths/arithmetics.gleam
@@ -442,7 +442,7 @@ pub fn int_sum(arr: List(Int)) -> Int {
 pub fn float_product(
   arr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case arr, weights {
     [], _ ->
       1.0
@@ -452,22 +452,16 @@ pub fn float_product(
       |> list.fold(1.0, fn(acc, a) { a *. acc })
       |> Ok
     _, option.Some(warr) -> {
-      let results =
-        list.zip(arr, warr)
-        |> list.map(fn(a) {
-          pair.first(a)
-          |> elementary.power(pair.second(a))
-        })
-        |> result.all
-      case results {
-        Ok(prods) ->
-          prods
-          |> list.fold(1.0, fn(acc, a) { a *. acc })
-          |> Ok
-        Error(msg) ->
-          msg
-          |> Error
-      }
+      list.zip(arr, warr)
+      |> list.map(fn(a: #(Float, Float)) -> Result(Float, Nil) {
+        pair.first(a)
+        |> elementary.power(pair.second(a))
+      })
+      |> result.all
+      |> result.map(fn(prods) {
+        prods
+        |> list.fold(1.0, fn(acc: Float, a: Float) -> Float { a *. acc })
+      })
     }
   }
 }
diff --git a/src/gleam_community/maths/combinatorics.gleam b/src/gleam_community/maths/combinatorics.gleam
index 726ae52..a3a4e7e 100644
--- a/src/gleam_community/maths/combinatorics.gleam
+++ b/src/gleam_community/maths/combinatorics.gleam
@@ -130,12 +130,10 @@ pub fn combination(
   n: Int,
   k: Int,
   mode: option.Option(CombinatoricsMode),
-) -> Result(Int, String) {
+) -> Result(Int, Nil) {
   case n, k {
-    _, _ if n < 0 ->
-      "Invalid input argument: n < 0. Valid input is n >= 0." |> Error
-    _, _ if k < 0 ->
-      "Invalid input argument: k < 0. Valid input is k >= 0." |> Error
+    _, _ if n < 0 -> Error(Nil)
+    _, _ if k < 0 -> Error(Nil)
     _, _ -> {
       case mode {
         option.Some(WithRepetitions) -> combination_with_repetitions(n, k)
@@ -145,12 +143,11 @@ pub fn combination(
   }
 }
 
-fn combination_with_repetitions(n: Int, k: Int) -> Result(Int, String) {
-  { n + k - 1 }
-  |> combination_without_repetitions(k)
+fn combination_with_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
+  combination_without_repetitions(n + k - 1, k)
 }
 
-fn combination_without_repetitions(n: Int, k: Int) -> Result(Int, String) {
+fn combination_without_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
   case n, k {
     _, _ if k == 0 || k == n -> {
       1 |> Ok
@@ -202,17 +199,11 @@ fn combination_without_repetitions(n: Int, k: Int) -> Result(Int, String) {
 ///     </a>
 /// </div>
 ///
-pub fn factorial(n) -> Result(Int, String) {
+pub fn factorial(n) -> Result(Int, Nil) {
   case n {
-    _ if n < 0 ->
-      "Invalid input argument: n < 0. Valid input is n >= 0."
-      |> Error
-    0 ->
-      1
-      |> Ok
-    1 ->
-      1
-      |> Ok
+    _ if n < 0 -> Error(Nil)
+    0 -> Ok(1)
+    1 -> Ok(1)
     _ ->
       list.range(1, n)
       |> list.fold(1, fn(acc, x) { acc * x })
@@ -300,22 +291,16 @@ pub fn permutation(
   n: Int,
   k: Int,
   mode: option.Option(CombinatoricsMode),
-) -> Result(Int, String) {
-  case n, k {
-    _, _ if n < 0 ->
-      "Invalid input argument: n < 0. Valid input is n >= 0." |> Error
-    _, _ if k < 0 ->
-      "Invalid input argument: k < 0. Valid input is k >= 0." |> Error
-    _, _ -> {
-      case mode {
-        option.Some(WithRepetitions) -> permutation_with_repetitions(n, k)
-        _ -> permutation_without_repetitions(n, k)
-      }
-    }
+) -> Result(Int, Nil) {
+  case n, k, mode {
+    _, _, _ if n < 0 -> Error(Nil)
+    _, _, _ if k < 0 -> Error(Nil)
+    _, _, option.Some(WithRepetitions) -> permutation_with_repetitions(n, k)
+    _, _, _ -> permutation_without_repetitions(n, k)
   }
 }
 
-fn permutation_without_repetitions(n: Int, k: Int) -> Result(Int, String) {
+fn permutation_without_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
   case n, k {
     _, _ if k < 0 || k > n -> {
       0 |> Ok
@@ -330,7 +315,7 @@ fn permutation_without_repetitions(n: Int, k: Int) -> Result(Int, String) {
   }
 }
 
-fn permutation_with_repetitions(n: Int, k: Int) -> Result(Int, String) {
+fn permutation_with_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
   let n_float = conversion.int_to_float(n)
   let k_float = conversion.int_to_float(k)
   // 'n' ank 'k' are positive integers, so no errors here...
@@ -388,29 +373,20 @@ pub fn list_combination(
   arr: List(a),
   k: Int,
   mode: option.Option(CombinatoricsMode),
-) -> Result(iterator.Iterator(List(a)), String) {
-  case k {
-    _ if k < 0 ->
-      "Invalid input argument: k < 0. Valid input is k >= 0."
-      |> Error
-    _ ->
-      case mode {
-        option.Some(WithRepetitions) ->
-          list_combination_with_repetitions(arr, k)
-        _ -> list_combination_without_repetitions(arr, k)
-      }
+) -> Result(iterator.Iterator(List(a)), Nil) {
+  case k, mode {
+    _, _ if k < 0 -> Error(Nil)
+    _, option.Some(WithRepetitions) -> list_combination_with_repetitions(arr, k)
+    _, _ -> list_combination_without_repetitions(arr, k)
   }
 }
 
 fn list_combination_without_repetitions(
   arr: List(a),
   k: Int,
-) -> Result(iterator.Iterator(List(a)), String) {
+) -> Result(iterator.Iterator(List(a)), Nil) {
   case k, list.length(arr) {
-    _, arr_length if k > arr_length -> {
-      "Invalid input argument: k > length(arr). Valid input is 0 <= k <= length(arr)."
-      |> Error
-    }
+    _, arr_length if k > arr_length -> Error(Nil)
     // Special case: When k = n, then the entire list is the only valid combination
     _, arr_length if k == arr_length -> {
       iterator.single(arr) |> Ok
@@ -446,7 +422,7 @@ fn do_list_combination_without_repetitions(
 fn list_combination_with_repetitions(
   arr: List(a),
   k: Int,
-) -> Result(iterator.Iterator(List(a)), String) {
+) -> Result(iterator.Iterator(List(a)), Nil) {
   Ok(do_list_combination_with_repetitions(iterator.from_list(arr), k, []))
 }
 
@@ -528,17 +504,12 @@ pub fn list_permutation(
   arr: List(a),
   k: Int,
   mode: option.Option(CombinatoricsMode),
-) -> Result(iterator.Iterator(List(a)), String) {
-  case k {
-    _ if k < 0 ->
-      "Invalid input argument: k < 0. Valid input is k >= 0."
-      |> Error
-    _ ->
-      case mode {
-        option.Some(WithRepetitions) ->
-          list_permutation_with_repetitions(arr, k)
-        _ -> list_permutation_without_repetitions(arr, k)
-      }
+) -> Result(iterator.Iterator(List(a)), Nil) {
+  case k, mode {
+    _, _ if k < 0 -> Error(Nil)
+    _, option.Some(WithRepetitions) ->
+      Ok(list_permutation_with_repetitions(arr, k))
+    _, _ -> list_permutation_without_repetitions(arr, k)
   }
 }
 
@@ -558,12 +529,9 @@ fn remove_first_by_index(
 fn list_permutation_without_repetitions(
   arr: List(a),
   k: Int,
-) -> Result(iterator.Iterator(List(a)), String) {
+) -> Result(iterator.Iterator(List(a)), Nil) {
   case k, list.length(arr) {
-    _, arr_length if k > arr_length -> {
-      "Invalid input argument: k > length(arr). Valid input is 0 <= k <= length(arr)."
-      |> Error
-    }
+    _, arr_length if k > arr_length -> Error(Nil)
     _, _ -> {
       let indexed_arr = list.index_map(arr, fn(x, i) { #(i, x) })
       Ok(do_list_permutation_without_repetitions(
@@ -594,9 +562,9 @@ fn do_list_permutation_without_repetitions(
 fn list_permutation_with_repetitions(
   arr: List(a),
   k: Int,
-) -> Result(iterator.Iterator(List(a)), String) {
+) -> iterator.Iterator(List(a)) {
   let indexed_arr = list.index_map(arr, fn(x, i) { #(i, x) })
-  Ok(do_list_permutation_with_repetitions(indexed_arr, k))
+  do_list_permutation_with_repetitions(indexed_arr, k)
 }
 
 fn do_list_permutation_with_repetitions(
diff --git a/src/gleam_community/maths/elementary.gleam b/src/gleam_community/maths/elementary.gleam
index 9c9be4a..491cab7 100644
--- a/src/gleam_community/maths/elementary.gleam
+++ b/src/gleam_community/maths/elementary.gleam
@@ -98,14 +98,10 @@ import gleam/option
 ///     </a>
 /// </div>
 ///
-pub fn acos(x: Float) -> Result(Float, String) {
+pub fn acos(x: Float) -> Result(Float, Nil) {
   case x >=. -1.0 && x <=. 1.0 {
-    True ->
-      do_acos(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x >= -1 or x <= 1. Valid input is -1. <= x <= 1."
-      |> Error
+    True -> Ok(do_acos(x))
+    False -> Error(Nil)
   }
 }
 
@@ -150,14 +146,10 @@ fn do_acos(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn acosh(x: Float) -> Result(Float, String) {
+pub fn acosh(x: Float) -> Result(Float, Nil) {
   case x >=. 1.0 {
-    True ->
-      do_acosh(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x < 1. Valid input is x >= 1."
-      |> Error
+    True -> Ok(do_acosh(x))
+    False -> Error(Nil)
   }
 }
 
@@ -205,14 +197,10 @@ fn do_acosh(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn asin(x: Float) -> Result(Float, String) {
+pub fn asin(x: Float) -> Result(Float, Nil) {
   case x >=. -1.0 && x <=. 1.0 {
-    True ->
-      do_asin(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x >= -1 or x <= 1. Valid input is -1. <= x <= 1."
-      |> Error
+    True -> Ok(do_asin(x))
+    False -> Error(Nil)
   }
 }
 
@@ -394,14 +382,10 @@ fn do_atan2(a: Float, b: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn atanh(x: Float) -> Result(Float, String) {
+pub fn atanh(x: Float) -> Result(Float, Nil) {
   case x >. -1.0 && x <. 1.0 {
-    True ->
-      do_atanh(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x > -1 or x < 1. Valid input is -1. < x < 1."
-      |> Error
+    True -> Ok(do_atanh(x))
+    False -> Error(Nil)
   }
 }
 
@@ -753,14 +737,10 @@ fn do_exponential(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn natural_logarithm(x: Float) -> Result(Float, String) {
+pub fn natural_logarithm(x: Float) -> Result(Float, Nil) {
   case x >. 0.0 {
-    True ->
-      do_natural_logarithm(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x <= 0. Valid input is x > 0."
-      |> Error
+    True -> Ok(do_natural_logarithm(x))
+    False -> Error(Nil)
   }
 }
 
@@ -810,30 +790,19 @@ fn do_natural_logarithm(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn logarithm(x: Float, base: option.Option(Float)) -> Result(Float, String) {
-  case x >. 0.0 {
-    True ->
-      case base {
-        option.Some(a) ->
-          case a >. 0.0 && a != 1.0 {
-            True -> {
-              // Apply the "change of base formula"
-              let assert Ok(numerator) = logarithm_10(x)
-              let assert Ok(denominator) = logarithm_10(a)
-              numerator /. denominator
-              |> Ok
-            }
-            False ->
-              "Invalid input argument: base <= 0 or base == 1. Valid input is base > 0 and base != 1."
-              |> Error
-          }
-        _ ->
-          "Invalid input argument: base <= 0 or base == 1. Valid input is base > 0 and base != 1."
-          |> Error
+pub fn logarithm(x: Float, base: option.Option(Float)) -> Result(Float, Nil) {
+  case x >. 0.0, base {
+    True, option.Some(a) ->
+      case a >. 0.0 && a != 1.0 {
+        False -> Error(Nil)
+        True -> {
+          // Apply the "change of base formula"
+          let assert Ok(numerator) = logarithm_10(x)
+          let assert Ok(denominator) = logarithm_10(a)
+          Ok(numerator /. denominator)
+        }
       }
-    _ ->
-      "Invalid input argument: x <= 0. Valid input is x > 0."
-      |> Error
+    _, _ -> Error(Nil)
   }
 }
 
@@ -877,14 +846,10 @@ pub fn logarithm(x: Float, base: option.Option(Float)) -> Result(Float, String)
 ///     </a>
 /// </div>
 ///
-pub fn logarithm_2(x: Float) -> Result(Float, String) {
+pub fn logarithm_2(x: Float) -> Result(Float, Nil) {
   case x >. 0.0 {
-    True ->
-      do_logarithm_2(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x <= 0. Valid input is x > 0."
-      |> Error
+    True -> Ok(do_logarithm_2(x))
+    False -> Error(Nil)
   }
 }
 
@@ -932,14 +897,10 @@ fn do_logarithm_2(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn logarithm_10(x: Float) -> Result(Float, String) {
+pub fn logarithm_10(x: Float) -> Result(Float, Nil) {
   case x >. 0.0 {
-    True ->
-      do_logarithm_10(x)
-      |> Ok
-    False ->
-      "Invalid input argument: x <= 0. Valid input is x > 0."
-      |> Error
+    True -> Ok(do_logarithm_10(x))
+    False -> Error(Nil)
   }
 }
 
@@ -993,7 +954,7 @@ fn do_logarithm_10(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn power(x: Float, y: Float) -> Result(Float, String) {
+pub fn power(x: Float, y: Float) -> Result(Float, Nil) {
   let fractional = do_ceiling(y) -. y >. 0.0
   // In the following check:
   // 1. If the base (x) is negative and the exponent (y) is fractional
@@ -1002,9 +963,7 @@ pub fn power(x: Float, y: Float) -> Result(Float, String) {
   //    expression is equivalent to the exponent (y) divided by 0 and an
   //    error should be returned
   case { x <. 0.0 && fractional } || { x == 0.0 && y <. 0.0 } {
-    True ->
-      "Invalid input argument: x < 0 and y is fractional or x = 0 and y < 0."
-      |> Error
+    True -> Error(Nil)
     False ->
       do_power(x, y)
       |> Ok
@@ -1055,19 +1014,13 @@ fn do_ceiling(a: Float) -> Float
 ///     </a>
 /// </div>
 ///
-pub fn square_root(x: Float) -> Result(Float, String) {
+pub fn square_root(x: Float) -> Result(Float, Nil) {
   // In the following check:
   // 1. If x is negative then return an error as it will otherwise be an
   // imaginary number
   case x <. 0.0 {
-    True ->
-      "Invalid input argument: x < 0."
-      |> Error
-    False -> {
-      let assert Ok(result) = power(x, 1.0 /. 2.0)
-      result
-      |> Ok
-    }
+    True -> Error(Nil)
+    False -> power(x, 1.0 /. 2.0)
   }
 }
 
@@ -1107,19 +1060,13 @@ pub fn square_root(x: Float) -> Result(Float, String) {
 ///     </a>
 /// </div>
 ///
-pub fn cube_root(x: Float) -> Result(Float, String) {
+pub fn cube_root(x: Float) -> Result(Float, Nil) {
   // In the following check:
   // 1. If x is negative then return an error as it will otherwise be an
   // imaginary number
   case x <. 0.0 {
-    True ->
-      "Invalid input argument: x < 0."
-      |> Error
-    False -> {
-      let assert Ok(result) = power(x, 1.0 /. 3.0)
-      result
-      |> Ok
-    }
+    True -> Error(Nil)
+    False -> power(x, 1.0 /. 3.0)
   }
 }
 
@@ -1162,25 +1109,13 @@ pub fn cube_root(x: Float) -> Result(Float, String) {
 ///     </a>
 /// </div>
 ///
-pub fn nth_root(x: Float, n: Int) -> Result(Float, String) {
+pub fn nth_root(x: Float, n: Int) -> Result(Float, Nil) {
   // In the following check:
   // 1. If x is negative then return an error as it will otherwise be an
   // imaginary number
-  case x <. 0.0 {
-    True ->
-      "Invalid input argument: x < 0. Valid input is x > 0"
-      |> Error
-    False ->
-      case n >= 1 {
-        True -> {
-          let assert Ok(result) = power(x, 1.0 /. int.to_float(n))
-          result
-          |> Ok
-        }
-        False ->
-          "Invalid input argument: n < 1. Valid input is n >= 2."
-          |> Error
-      }
+  case x >=. 0.0 && n >= 1 {
+    True -> power(x, 1.0 /. int.to_float(n))
+    False -> Error(Nil)
   }
 }
 
diff --git a/src/gleam_community/maths/metrics.gleam b/src/gleam_community/maths/metrics.gleam
index dd4dd7a..6c8959c 100644
--- a/src/gleam_community/maths/metrics.gleam
+++ b/src/gleam_community/maths/metrics.gleam
@@ -59,6 +59,7 @@ import gleam/int
 import gleam/list
 import gleam/option
 import gleam/pair
+import gleam/result
 import gleam/set
 import gleam_community/maths/arithmetics
 import gleam_community/maths/conversion
@@ -72,21 +73,15 @@ fn validate_lists(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Bool, String) {
+) -> Result(Bool, Nil) {
   case xarr, yarr {
-    [], _ ->
-      "Invalid input argument: The list xarr is empty."
-      |> Error
-    _, [] ->
-      "Invalid input argument: The list yarr is empty."
-      |> Error
+    [], _ -> Error(Nil)
+    _, [] -> Error(Nil)
     _, _ -> {
       let xarr_length = list.length(xarr)
       let yarr_length = list.length(yarr)
       case xarr_length == yarr_length, weights {
-        False, _ ->
-          "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
-          |> Error
+        False, _ -> Error(Nil)
         True, option.None -> {
           True
           |> Ok
@@ -97,9 +92,7 @@ fn validate_lists(
             True -> {
               validate_weights(warr)
             }
-            False ->
-              "Invalid input argument: length(weights) != length(xarr) and length(weights) != length(yarr). Valid input is when length(weights) == length(xarr) == length(yarr)."
-              |> Error
+            False -> Error(Nil)
           }
         }
       }
@@ -107,16 +100,12 @@ fn validate_lists(
   }
 }
 
-fn validate_weights(warr: List(Float)) -> Result(Bool, String) {
+fn validate_weights(warr: List(Float)) -> Result(Bool, Nil) {
   // Check that all the given weights are positive
   let assert Ok(minimum) = piecewise.list_minimum(warr, float.compare)
   case minimum >=. 0.0 {
-    False ->
-      "Invalid input argument: One or more weights are negative. Valid input is when all weights are >= 0."
-      |> Error
-    True ->
-      True
-      |> Ok
+    False -> Error(Nil)
+    True -> Ok(True)
   }
 }
 
@@ -174,7 +163,7 @@ pub fn norm(
   arr: List(Float),
   p: Float,
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case arr, weights {
     [], _ ->
       0.0
@@ -221,10 +210,7 @@ pub fn norm(
               |> Error
           }
         }
-        False -> {
-          "Invalid input argument: length(weights) != length(arr). Valid input is when length(weights) == length(arr)."
-          |> Error
-        }
+        False -> Error(Nil)
       }
     }
   }
@@ -286,7 +272,7 @@ pub fn manhattan_distance(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   minkowski_distance(xarr, yarr, 1.0, weights)
 }
 
@@ -354,26 +340,17 @@ pub fn minkowski_distance(
   yarr: List(Float),
   p: Float,
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
-  case validate_lists(xarr, yarr, weights) {
-    Error(msg) ->
-      msg
-      |> Error
-    Ok(_) -> {
-      case p <. 1.0 {
-        True ->
-          "Invalid input argument: p < 1. Valid input is p >= 1."
-          |> Error
-        False -> {
-          let differences =
-            list.zip(xarr, yarr)
-            |> list.map(fn(tuple) { pair.first(tuple) -. pair.second(tuple) })
-
-          let assert Ok(result) = norm(differences, p, weights)
-          result
-          |> Ok
-        }
-      }
+) -> Result(Float, Nil) {
+  use _ <- result.try(validate_lists(xarr, yarr, weights))
+  case p <. 1.0 {
+    True -> Error(Nil)
+    False -> {
+      let differences: List(Float) =
+        list.zip(xarr, yarr)
+        |> list.map(fn(tuple: #(Float, Float)) -> Float {
+          pair.first(tuple) -. pair.second(tuple)
+        })
+      norm(differences, p, weights)
     }
   }
 }
@@ -434,7 +411,7 @@ pub fn euclidean_distance(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   minkowski_distance(xarr, yarr, 2.0, weights)
 }
 
@@ -484,7 +461,7 @@ pub fn euclidean_distance(
 pub fn chebyshev_distance(
   xarr: List(Float),
   yarr: List(Float),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case validate_lists(xarr, yarr, option.None) {
     Error(msg) ->
       msg
@@ -540,11 +517,9 @@ pub fn chebyshev_distance(
 ///     </a>
 /// </div>
 ///
-pub fn mean(arr: List(Float)) -> Result(Float, String) {
+pub fn mean(arr: List(Float)) -> Result(Float, Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     _ ->
       arr
       |> arithmetics.float_sum(option.None)
@@ -664,34 +639,27 @@ fn do_median(
 ///     </a>
 /// </div>
 ///
-pub fn variance(arr: List(Float), ddof: Int) -> Result(Float, String) {
-  case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
-    _ ->
-      case ddof < 0 {
-        True ->
-          "Invalid input argument: ddof < 0. Valid input is ddof >= 0."
-          |> Error
-        False -> {
-          let assert Ok(mean) = mean(arr)
-          arr
-          |> list.map(fn(a) {
-            let assert Ok(result) = elementary.power(a -. mean, 2.0)
-            result
-          })
-          |> arithmetics.float_sum(option.None)
-          |> fn(a) {
-            a
-            /. {
-              conversion.int_to_float(list.length(arr))
-              -. conversion.int_to_float(ddof)
-            }
-          }
-          |> Ok
+pub fn variance(arr: List(Float), ddof: Int) -> Result(Float, Nil) {
+  case arr, ddof {
+    [], _ -> Error(Nil)
+    _, _ if ddof < 0 -> Error(Nil)
+    _, _ -> {
+      let assert Ok(mean) = mean(arr)
+      arr
+      |> list.map(fn(a: Float) -> Float {
+        let assert Ok(result) = elementary.power(a -. mean, 2.0)
+        result
+      })
+      |> arithmetics.float_sum(option.None)
+      |> fn(a: Float) -> Float {
+        a
+        /. {
+          conversion.int_to_float(list.length(arr))
+          -. conversion.int_to_float(ddof)
         }
       }
+      |> Ok
+    }
   }
 }
 
@@ -741,25 +709,18 @@ pub fn variance(arr: List(Float), ddof: Int) -> Result(Float, String) {
 ///     </a>
 /// </div>
 ///
-pub fn standard_deviation(arr: List(Float), ddof: Int) -> Result(Float, String) {
-  case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
-    _ ->
-      case ddof < 0 {
-        True ->
-          "Invalid input argument: ddof < 0. Valid input is ddof >= 0."
-          |> Error
-        False -> {
-          let assert Ok(variance) = variance(arr, ddof)
-          // The computed variance will always be positive
-          // So an error should never be returned
-          let assert Ok(stdev) = elementary.square_root(variance)
-          stdev
-          |> Ok
-        }
-      }
+pub fn standard_deviation(arr: List(Float), ddof: Int) -> Result(Float, Nil) {
+  case arr, ddof {
+    [], _ -> Error(Nil)
+    _, _ if ddof < 0 -> Error(Nil)
+    _, _ -> {
+      let assert Ok(variance) = variance(arr, ddof)
+      // The computed variance will always be positive
+      // So an error should never be returned
+      let assert Ok(stdev) = elementary.square_root(variance)
+      stdev
+      |> Ok
+    }
   }
 }
 
@@ -924,7 +885,7 @@ pub fn tversky_index(
   yset: set.Set(a),
   alpha: Float,
   beta: Float,
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case alpha >=. 0.0, beta >=. 0.0 {
     True, True -> {
       let intersection =
@@ -943,18 +904,7 @@ pub fn tversky_index(
       /. { intersection +. alpha *. difference1 +. beta *. difference2 }
       |> Ok
     }
-    False, True -> {
-      "Invalid input argument: alpha < 0. Valid input is alpha >= 0."
-      |> Error
-    }
-    True, False -> {
-      "Invalid input argument: beta < 0. Valid input is beta >= 0."
-      |> Error
-    }
-    _, _ -> {
-      "Invalid input argument: alpha < 0 and beta < 0. Valid input is alpha >= 0 and beta >= 0."
-      |> Error
-    }
+    _, _ -> Error(Nil)
   }
 }
 
@@ -1077,7 +1027,7 @@ pub fn cosine_similarity(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case validate_lists(xarr, yarr, weights) {
     Error(msg) ->
       msg
@@ -1173,7 +1123,7 @@ pub fn canberra_distance(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case validate_lists(xarr, yarr, weights) {
     Error(msg) ->
       msg
@@ -1266,7 +1216,7 @@ pub fn braycurtis_distance(
   xarr: List(Float),
   yarr: List(Float),
   weights: option.Option(List(Float)),
-) -> Result(Float, String) {
+) -> Result(Float, Nil) {
   case validate_lists(xarr, yarr, weights) {
     Error(msg) ->
       msg
diff --git a/src/gleam_community/maths/piecewise.gleam b/src/gleam_community/maths/piecewise.gleam
index fdfc4fb..cebdc38 100644
--- a/src/gleam_community/maths/piecewise.gleam
+++ b/src/gleam_community/maths/piecewise.gleam
@@ -949,11 +949,9 @@ pub fn minmax(x: a, y: a, compare: fn(a, a) -> order.Order) {
 pub fn list_minimum(
   arr: List(a),
   compare: fn(a, a) -> order.Order,
-) -> Result(a, String) {
+) -> Result(a, Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     [x, ..rest] ->
       Ok(
         list.fold(rest, x, fn(acc, element) {
@@ -1003,11 +1001,9 @@ pub fn list_minimum(
 pub fn list_maximum(
   arr: List(a),
   compare: fn(a, a) -> order.Order,
-) -> Result(a, String) {
+) -> Result(a, Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     [x, ..rest] ->
       Ok(
         list.fold(rest, x, fn(acc, element) {
@@ -1063,11 +1059,9 @@ pub fn list_maximum(
 pub fn arg_minimum(
   arr: List(a),
   compare: fn(a, a) -> order.Order,
-) -> Result(List(Int), String) {
+) -> Result(List(Int), Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     _ -> {
       let assert Ok(min) =
         arr
@@ -1133,11 +1127,9 @@ pub fn arg_minimum(
 pub fn arg_maximum(
   arr: List(a),
   compare: fn(a, a) -> order.Order,
-) -> Result(List(Int), String) {
+) -> Result(List(Int), Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     _ -> {
       let assert Ok(max) =
         arr
@@ -1203,11 +1195,9 @@ pub fn arg_maximum(
 pub fn extrema(
   arr: List(a),
   compare: fn(a, a) -> order.Order,
-) -> Result(#(a, a), String) {
+) -> Result(#(a, a), Nil) {
   case arr {
-    [] ->
-      "Invalid input argument: The list is empty."
-      |> Error
+    [] -> Error(Nil)
     [x, ..rest] ->
       Ok(
         list.fold(rest, #(x, x), fn(acc, element) {
diff --git a/src/gleam_community/maths/predicates.gleam b/src/gleam_community/maths/predicates.gleam
index 4681e3b..73e5743 100644
--- a/src/gleam_community/maths/predicates.gleam
+++ b/src/gleam_community/maths/predicates.gleam
@@ -135,7 +135,7 @@ fn float_absolute_difference(a: Float, b: Float) -> Float {
 ///       let rtol = 0.01
 ///       let atol = 0.10
 ///       predicates.all_close(xarr, yarr, rtol, atol)
-///       |> fn(zarr), String)) {
+///       |> fn(zarr: Result(List(Bool), Nil)) -> Result(Bool, Nil) {
 ///         case zarr {
 ///           Ok(arr) ->
 ///             arr
@@ -159,13 +159,11 @@ pub fn all_close(
   yarr: List(Float),
   rtol: Float,
   atol: Float,
-) -> Result(List(Bool), String) {
+) -> Result(List(Bool), Nil) {
   let xlen = list.length(xarr)
   let ylen = list.length(yarr)
   case xlen == ylen {
-    False ->
-      "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
-      |> Error
+    False -> Error(Nil)
     True ->
       list.zip(xarr, yarr)
       |> list.map(fn(z) { is_close(pair.first(z), pair.second(z), rtol, atol) })
diff --git a/src/gleam_community/maths/sequences.gleam b/src/gleam_community/maths/sequences.gleam
index 62c5301..c801184 100644
--- a/src/gleam_community/maths/sequences.gleam
+++ b/src/gleam_community/maths/sequences.gleam
@@ -160,7 +160,7 @@ pub fn linear_space(
   stop: Float,
   num: Int,
   endpoint: Bool,
-) -> Result(iterator.Iterator(Float), String) {
+) -> Result(iterator.Iterator(Float), Nil) {
   let direction = case start <=. stop {
     True -> 1.0
     False -> -1.0
@@ -184,9 +184,7 @@ pub fn linear_space(
       })
       |> Ok
     }
-    False ->
-      "Invalid input: num < 1. Valid input is num >= 1."
-      |> Error
+    False -> Error(Nil)
   }
 }
 
@@ -241,7 +239,7 @@ pub fn logarithmic_space(
   num: Int,
   endpoint: Bool,
   base: Float,
-) -> Result(iterator.Iterator(Float), String) {
+) -> Result(iterator.Iterator(Float), Nil) {
   case num > 0 {
     True -> {
       let assert Ok(linspace) = linear_space(start, stop, num, endpoint)
@@ -252,9 +250,7 @@ pub fn logarithmic_space(
       })
       |> Ok
     }
-    False ->
-      "Invalid input: num < 1. Valid input is num >= 1."
-      |> Error
+    False -> Error(Nil)
   }
 }
 
@@ -316,11 +312,9 @@ pub fn geometric_space(
   stop: Float,
   num: Int,
   endpoint: Bool,
-) -> Result(iterator.Iterator(Float), String) {
+) -> Result(iterator.Iterator(Float), Nil) {
   case start == 0.0 || stop == 0.0 {
-    True ->
-      "Invalid input: Neither 'start' nor 'stop' can be zero, as they must be non-zero for logarithmic calculations."
-      |> Error
+    True -> Error(Nil)
     False ->
       case num > 0 {
         True -> {
@@ -328,9 +322,7 @@ pub fn geometric_space(
           let assert Ok(log_stop) = elementary.logarithm_10(stop)
           logarithmic_space(log_start, log_stop, num, endpoint, 10.0)
         }
-        False ->
-          "Invalid input: num < 1. Valid input is num >= 1."
-          |> Error
+        False -> Error(Nil)
       }
   }
 }
diff --git a/src/gleam_community/maths/special.gleam b/src/gleam_community/maths/special.gleam
index a3f0136..6422709 100644
--- a/src/gleam_community/maths/special.gleam
+++ b/src/gleam_community/maths/special.gleam
@@ -163,7 +163,7 @@ fn gamma_lanczos(x: Float) -> Float {
 ///     </a>
 /// </div>
 ///
-pub fn incomplete_gamma(a: Float, x: Float) -> Result(Float, String) {
+pub fn incomplete_gamma(a: Float, x: Float) -> Result(Float, Nil) {
   case a >. 0.0 && x >=. 0.0 {
     True -> {
       let assert Ok(v) = elementary.power(x, a)
@@ -173,9 +173,7 @@ pub fn incomplete_gamma(a: Float, x: Float) -> Result(Float, String) {
       |> Ok
     }
 
-    False ->
-      "Invalid input argument: a <= 0 or x < 0. Valid input is a > 0 and x >= 0."
-      |> Error
+    False -> Error(Nil)
   }
 }
 
diff --git a/test/gleam_community/maths/predicates_test.gleam b/test/gleam_community/maths/predicates_test.gleam
index c9e2c5f..e544eb5 100644
--- a/test/gleam_community/maths/predicates_test.gleam
+++ b/test/gleam_community/maths/predicates_test.gleam
@@ -23,7 +23,7 @@ pub fn float_list_all_close_test() {
   let rtol = 0.01
   let atol = 0.1
   predicates.all_close(xarr, yarr, rtol, atol)
-  |> fn(zarr) {
+  |> fn(zarr: Result(List(Bool), Nil)) -> Result(Bool, Nil) {
     case zarr {
       Ok(arr) ->
         arr