diff --git a/Cargo.lock b/Cargo.lock
index 737a762d88f0d..1905090baa10a 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -131,9 +131,9 @@ checksum = "afddf7f520a80dbf76e6f50a35bca42a2331ef227a28b3b6dc5c2e2338d114b1"
 
 [[package]]
 name = "approx"
-version = "0.3.2"
+version = "0.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f0e60b75072ecd4168020818c0107f2857bb6c4e64252d8d3983f6263b40a5c3"
+checksum = "072df7202e63b127ab55acfe16ce97013d5b97bf160489336d3f1840fd78e99e"
 dependencies = [
  "num-traits",
 ]
@@ -2189,15 +2189,6 @@ dependencies = [
  "typenum",
 ]
 
-[[package]]
-name = "generic-array"
-version = "0.13.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f797e67af32588215eaaab8327027ee8e71b9dd0b2b26996aedf20c030fce309"
-dependencies = [
- "typenum",
-]
-
 [[package]]
 name = "generic-array"
 version = "0.14.4"
@@ -3656,9 +3647,9 @@ dependencies = [
 
 [[package]]
 name = "linregress"
-version = "0.4.0"
+version = "0.4.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0d0ad4b5cc8385a881c561fac3501353d63d2a2b7a357b5064d71815c9a92724"
+checksum = "1e6e407dadb4ca4b31bc69c27aff00e7ca4534fdcee855159b039a7cebb5f395"
 dependencies = [
  "nalgebra",
  "statrs",
@@ -3766,9 +3757,9 @@ checksum = "7ffc5c5338469d4d3ea17d269fa8ea3512ad247247c30bd2df69e68309ed0a08"
 
 [[package]]
 name = "matrixmultiply"
-version = "0.2.4"
+version = "0.3.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "916806ba0031cd542105d916a97c8572e1fa6dd79c9c51e7eb43a09ec2dd84c1"
+checksum = "5a8a15b776d9dfaecd44b03c5828c2199cddff5247215858aac14624f8d6b741"
 dependencies = [
  "rawpointer",
 ]
@@ -4050,22 +4041,33 @@ dependencies = [
 
 [[package]]
 name = "nalgebra"
-version = "0.21.1"
+version = "0.27.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d6b6147c3d50b4f3cdabfe2ecc94a0191fd3d6ad58aefd9664cf396285883486"
+checksum = "462fffe4002f4f2e1f6a9dcf12cc1a6fc0e15989014efc02a941d3e0f5dc2120"
 dependencies = [
  "approx",
- "generic-array 0.13.3",
  "matrixmultiply",
+ "nalgebra-macros",
  "num-complex",
- "num-rational",
+ "num-rational 0.4.0",
  "num-traits",
- "rand 0.7.3",
+ "rand 0.8.3",
  "rand_distr",
  "simba",
  "typenum",
 ]
 
+[[package]]
+name = "nalgebra-macros"
+version = "0.1.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "01fcc0b8149b4632adc89ac3b7b31a12fb6099a0317a4eb2ebff574ef7de7218"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "names"
 version = "0.11.0"
@@ -4587,11 +4589,10 @@ dependencies = [
 
 [[package]]
 name = "num-complex"
-version = "0.2.4"
+version = "0.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b6b19411a9719e753aff12e5187b74d60d3dc449ec3f4dc21e3989c3f554bc95"
+checksum = "26873667bbbb7c5182d4a37c1add32cdf09f841af72da53318fdb81543c15085"
 dependencies = [
- "autocfg",
  "num-traits",
 ]
 
@@ -4617,6 +4618,17 @@ dependencies = [
  "num-traits",
 ]
 
+[[package]]
+name = "num-rational"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d41702bd167c2df5520b384281bc111a4b5efcf7fbc4c9c222c815b07e0a6a6a"
+dependencies = [
+ "autocfg",
+ "num-integer",
+ "num-traits",
+]
+
 [[package]]
 name = "num-traits"
 version = "0.2.14"
@@ -6571,11 +6583,12 @@ dependencies = [
 
 [[package]]
 name = "rand_distr"
-version = "0.2.2"
+version = "0.4.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "96977acbdd3a6576fb1d27391900035bf3863d4a16422973a409b488cf29ffb2"
+checksum = "051b398806e42b9cd04ad9ec8f81e355d0a382c543ac6672c62f5a5b452ef142"
 dependencies = [
- "rand 0.7.3",
+ "num-traits",
+ "rand 0.8.3",
 ]
 
 [[package]]
@@ -7280,7 +7293,7 @@ dependencies = [
  "log",
  "merlin",
  "num-bigint",
- "num-rational",
+ "num-rational 0.2.4",
  "num-traits",
  "parity-scale-codec",
  "parking_lot 0.11.1",
@@ -8565,14 +8578,14 @@ checksum = "0f0242b8e50dd9accdd56170e94ca1ebd223b098eb9c83539a6e367d0f36ae68"
 
 [[package]]
 name = "simba"
-version = "0.1.5"
+version = "0.5.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "fb931b1367faadea6b1ab1c306a860ec17aaa5fa39f367d0c744e69d971a1fb2"
+checksum = "8e82063457853d00243beda9952e910b82593e4b07ae9f721b9278a99a0d3d5c"
 dependencies = [
  "approx",
  "num-complex",
  "num-traits",
- "paste 0.1.18",
+ "paste 1.0.4",
 ]
 
 [[package]]
@@ -9512,11 +9525,15 @@ checksum = "a2eb9349b6444b326872e140eb1cf5e7c522154d69e7a0ffb0fb81c06b37543f"
 
 [[package]]
 name = "statrs"
-version = "0.12.0"
+version = "0.15.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cce16f6de653e88beca7bd13780d08e09d4489dbca1f9210e041bc4852481382"
+checksum = "05bdbb8e4e78216a85785a85d3ec3183144f98d0097b9281802c019bb07a6f05"
 dependencies = [
- "rand 0.7.3",
+ "approx",
+ "lazy_static",
+ "nalgebra",
+ "num-traits",
+ "rand 0.8.3",
 ]
 
 [[package]]
@@ -11037,7 +11054,7 @@ dependencies = [
  "errno",
  "libc",
  "memory_units",
- "num-rational",
+ "num-rational 0.2.4",
  "num-traits",
  "parity-wasm 0.42.2",
  "wasmi-validation",
diff --git a/frame/benchmarking/Cargo.toml b/frame/benchmarking/Cargo.toml
index 3b20cf7dd048c..beff930161a08 100644
--- a/frame/benchmarking/Cargo.toml
+++ b/frame/benchmarking/Cargo.toml
@@ -13,7 +13,7 @@ readme = "README.md"
 targets = ["x86_64-unknown-linux-gnu"]
 
 [dependencies]
-linregress = { version = "0.4.0", optional = true }
+linregress = { version = "0.4.3", optional = true }
 paste = "1.0"
 codec = { package = "parity-scale-codec", version = "2.0.0", default-features = false }
 sp-api = { version = "3.0.0", path = "../../primitives/api", default-features = false }
@@ -31,7 +31,7 @@ hex-literal = "0.3.1"
 serde = "1.0.101"
 
 [features]
-default = [ "std" ]
+default = ["std"]
 std = [
 	"codec/std",
 	"sp-runtime-interface/std",