diff --git a/src/bin/flat.rs b/src/bin/flat.rs
index 4cad63f..b5b870b 100644
--- a/src/bin/flat.rs
+++ b/src/bin/flat.rs
@@ -548,18 +548,20 @@ impl Rect {
 
 	pub fn x(&self, u: f32) -> f32 { self.fy().x(u) }
 	pub fn u(&self, x: f32) -> f32 { self.fy().u(x) }
-	pub fn dx(&self, u: f32, du: f32) -> f32 { self.fy().dx(u, du) }
-	pub fn du(&self, x: f32, dx: f32) -> f32 { self.fy().du(x, dx) }
+	pub fn dx(&self, u: f32, du: f32) -> f32 { self.fy().dx(u) * du }
+	pub fn du(&self, x: f32, dx: f32) -> f32 { self.fy().du(x) * dx }
 }
 
 mod fns {
+	use crate::FloatExt2;
+
 	pub struct RectX {
 		pub min: f32,
 		pub max: f32,
 	}
 
 	impl RectX {
-		pub fn value(&self, x: f32) -> f32 { ((x.abs() - self.min) / (self.max - self.min)).clamp(0.0, 1.0) }
+		pub fn value(&self, x: f32) -> f32 { (self.min, self.max).inverse_lerp(x.abs()).clamp(0.0, 1.0) }
 		pub fn derivative(&self, x: f32) -> f32 { if x.abs() > self.min && x.abs() < self.max { x.signum() / (self.max - self.min) } else { 0.0 } }
 	}
 
@@ -569,19 +571,17 @@ mod fns {
 	}
 
 	impl RectY {
-		fn γ(&self) -> f32 { self.external / self.internal }
-		fn a(&self) -> f32 { -(self.γ() - 1.0) / self.internal }
-		fn b(&self) -> f32 { 2.0 * self.γ() - 1.0 }
+		fn a(&self) -> f32 { -(self.external - self.internal) / self.internal.powi(2) }
+		fn b(&self) -> f32 { 2.0 * self.external / self.internal - 1.0 }
+		fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x.abs()).sqrt() }
 
-		fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x).sqrt() }
-		fn d(&self, u: f32) -> f32 { 2.0 * self.a() * u + self.b() }
 		pub fn x(&self, u: f32) -> f32 { (self.a() * u.abs() + self.b()) * u }
-		pub fn u(&self, x: f32) -> f32 { 0.5 * x.signum() * (-self.b() + self.root(x.abs())) / self.a() }
-		pub fn dx(&self, u: f32, du: f32) -> f32 { du * self.d(u.abs()) }
-		pub fn du(&self, x: f32, dx: f32) -> f32 { dx / self.root(x.abs()) }
+		pub fn u(&self, x: f32) -> f32 { 0.5 * x.signum() * (-self.b() + self.root(x)) / self.a() }
+		pub fn dx(&self, u: f32) -> f32 { 2.0 * self.a() * u.abs() + self.b() }
+		pub fn du(&self, x: f32) -> f32 { 1.0 / self.root(x) }
 
-		pub fn value(&self, x: f32) -> f32 { if x.abs() <= self.external { 1.0 / self.root(x.abs()) } else { 1.0 } }
-		pub fn derivative(&self, x: f32) -> f32 { if x.abs() <= self.external { -2.0 * x.signum() * self.a() * self.root(x.abs()).powi(-3) } else { 0.0 } }
+		pub fn value(&self, x: f32) -> f32 { if x.abs() <= self.external { 1.0 / self.root(x) } else { 1.0 } }
+		pub fn derivative(&self, x: f32) -> f32 { if x.abs() <= self.external { -2.0 * x.signum() * self.a() * self.root(x).powi(-3) } else { 0.0 } }
 	}
 }
 
@@ -611,9 +611,6 @@ fn test_rect() {
 	assert_abs_diff_eq!(r.x(r.u(50.0)), 50.0, epsilon = 1.0e-5);
 	assert_abs_diff_eq!(r.x(r.u(-50.0)), -50.0, epsilon = 1.0e-5);
 	assert_abs_diff_eq!(r.x(r.u(100.0)), 100.0, epsilon = 1.0e-5);
-	assert_abs_diff_eq!(r.d(r.u(10.0)), r.root(10.0), epsilon = 1.0e-5);
-	assert_abs_diff_eq!(r.d(r.u(50.0)), r.root(50.0), epsilon = 1.0e-5);
-	assert_abs_diff_eq!(r.d(r.u(100.0)), r.root(100.0), epsilon = 1.0e-5);
 	assert_abs_diff_eq!(r.du(10.0, r.dx(r.u(10.0), 3.0)), 3.0, epsilon = 1.0e-5);
 	assert_abs_diff_eq!(r.du(50.0, r.dx(r.u(50.0), 3.0)), 3.0, epsilon = 1.0e-5);
 	assert_abs_diff_eq!(r.du(-50.0, r.dx(r.u(-50.0), 3.0)), 3.0, epsilon = 1.0e-5);
@@ -626,10 +623,12 @@ fn test_rect() {
 
 trait FloatExt2 {
 	fn lerp(&self, t: f32) -> f32;
+	fn inverse_lerp(&self, y: f32) -> f32;
 }
 
 impl FloatExt2 for (f32, f32) {
 	fn lerp(&self, t: f32) -> f32 { f32::lerp(self.0, self.1, t) }
+	fn inverse_lerp(&self, y: f32) -> f32 { f32::inverse_lerp(self.0, self.1, y) }
 }
 
 impl Metric for Rect {