diff --git a/crates/egui/src/layout.rs b/crates/egui/src/layout.rs
index c97652e8d..15152f47b 100644
--- a/crates/egui/src/layout.rs
+++ b/crates/egui/src/layout.rs
@@ -1,4 +1,4 @@
-use emath::GuiRounding as _;
+use emath::{GuiRounding as _, fast_midpoint};
 
 use crate::{
     Align, Direction,
@@ -477,12 +477,12 @@ impl Layout {
 
         // Make sure it isn't negative:
         if avail.max.x < avail.min.x {
-            let x = 0.5 * (avail.min.x + avail.max.x);
+            let x = fast_midpoint(avail.min.x, avail.max.x);
             avail.min.x = x;
             avail.max.x = x;
         }
         if avail.max.y < avail.min.y {
-            let y = 0.5 * (avail.min.y + avail.max.y);
+            let y = fast_midpoint(avail.min.y, avail.max.y);
             avail.min.y = y;
             avail.max.y = y;
         }
diff --git a/crates/egui_demo_lib/src/demo/misc_demo_window.rs b/crates/egui_demo_lib/src/demo/misc_demo_window.rs
index d035f5186..6b9584dd2 100644
--- a/crates/egui_demo_lib/src/demo/misc_demo_window.rs
+++ b/crates/egui_demo_lib/src/demo/misc_demo_window.rs
@@ -143,9 +143,7 @@ impl View for MiscDemoWindow {
                     )
                     .changed()
                 {
-                    for check in &mut self.checklist {
-                        *check = all_checked;
-                    }
+                    self.checklist.fill(all_checked);
                 }
                 for (i, checked) in self.checklist.iter_mut().enumerate() {
                     ui.checkbox(checked, format!("Item {}", i + 1));
diff --git a/crates/emath/src/easing.rs b/crates/emath/src/easing.rs
index 95fc7250d..6a98cad80 100644
--- a/crates/emath/src/easing.rs
+++ b/crates/emath/src/easing.rs
@@ -7,6 +7,8 @@
 //! Derived from <https://github.com/warrenm/AHEasing/blob/master/AHEasing/easing.c>.
 use std::f32::consts::PI;
 
+use crate::fast_midpoint;
+
 #[inline]
 fn powf(base: f32, exp: f32) -> f32 {
     base.powf(exp)
@@ -116,7 +118,7 @@ pub fn circular_in_out(t: f32) -> f32 {
     if t < 0.5 {
         0.5 * (1. - (1. - 4. * t * t).sqrt())
     } else {
-        0.5 * ((-(2. * t - 3.) * (2. * t - 1.)).sqrt() + 1.)
+        fast_midpoint((-(2. * t - 3.) * (2. * t - 1.)).sqrt(), 1.)
     }
 }
 
diff --git a/crates/emath/src/range.rs b/crates/emath/src/range.rs
index 26d5f6f2c..be6072c71 100644
--- a/crates/emath/src/range.rs
+++ b/crates/emath/src/range.rs
@@ -1,5 +1,7 @@
 use std::ops::{RangeFrom, RangeFull, RangeInclusive, RangeToInclusive};
 
+use crate::fast_midpoint;
+
 /// Inclusive range of floats, i.e. `min..=max`, but more ergonomic than [`RangeInclusive`].
 #[repr(C)]
 #[derive(Clone, Copy, Debug, PartialEq)]
@@ -52,7 +54,7 @@ impl Rangef {
     /// The center of the range
     #[inline]
     pub fn center(self) -> f32 {
-        0.5 * (self.min + self.max)
+        fast_midpoint(self.min, self.max)
     }
 
     #[inline]
diff --git a/crates/epaint/src/shapes/bezier_shape.rs b/crates/epaint/src/shapes/bezier_shape.rs
index dfeaae5ec..b8c78f273 100644
--- a/crates/epaint/src/shapes/bezier_shape.rs
+++ b/crates/epaint/src/shapes/bezier_shape.rs
@@ -3,7 +3,7 @@
 use std::ops::Range;
 
 use crate::{Color32, PathShape, PathStroke, Shape};
-use emath::{Pos2, Rect, RectTransform};
+use emath::{Pos2, Rect, RectTransform, fast_midpoint};
 
 // ----------------------------------------------------------------------------
 
@@ -689,8 +689,8 @@ fn single_curve_approximation(curve: &CubicBezierShape) -> QuadraticBezierShape
     let c2_x = (curve.points[2].x * 3.0 - curve.points[3].x) * 0.5;
     let c2_y = (curve.points[2].y * 3.0 - curve.points[3].y) * 0.5;
     let c = Pos2 {
-        x: (c1_x + c2_x) * 0.5,
-        y: (c1_y + c2_y) * 0.5,
+        x: fast_midpoint(c1_x, c2_x),
+        y: fast_midpoint(c1_y, c2_y),
     };
     QuadraticBezierShape {
         points: [curve.points[0], c, curve.points[3]],
diff --git a/crates/epaint/src/tessellator.rs b/crates/epaint/src/tessellator.rs
index 9a90636a4..716fe5424 100644
--- a/crates/epaint/src/tessellator.rs
+++ b/crates/epaint/src/tessellator.rs
@@ -5,7 +5,9 @@
 
 #![expect(clippy::identity_op)]
 
-use emath::{GuiRounding as _, NumExt as _, Pos2, Rect, Rot2, Vec2, pos2, remap, vec2};
+use emath::{
+    GuiRounding as _, NumExt as _, Pos2, Rect, Rot2, Vec2, fast_midpoint, pos2, remap, vec2,
+};
 
 use crate::{
     CircleShape, ClippedPrimitive, ClippedShape, Color32, CornerRadiusF32, CubicBezierShape,
@@ -1074,7 +1076,7 @@ fn stroke_and_fill_path(
             */
 
             let inner_rad = 0.5 * (stroke.width - feathering);
-            let outer_rad = 0.5 * (stroke.width + feathering);
+            let outer_rad = fast_midpoint(stroke.width, feathering);
 
             match path_type {
                 PathType::Closed => {