diff --git a/src/bin/flat/main.rs b/src/bin/flat/main.rs
index 58fdee2..ec89f8c 100644
--- a/src/bin/flat/main.rs
+++ b/src/bin/flat/main.rs
@@ -675,25 +675,32 @@ mod fns {
 		let margin = 1.0 / 16.0;
 		let mul = 1.0 + margin;
 		for x in itertools_num::linspace(-mul * testee.external, mul * testee.external, 100) {
-			let u = testee.u(x);
-			assert!(abs_diff_eq!(x, testee.x(u), epsilon = ε), "At x={}:\nu(x):    {}\nx(u(x)): {}\n", x, u, testee.x(u));
+			let ux = testee.u(x);
+			let xux = testee.x(ux);
+			assert!(abs_diff_eq!(x, xux, epsilon = ε), "At x={}:\nu(x):    {}\nx(u(x)): {}\n", x, ux, xux);
 
-			let du = (testee.u(x + δ) - testee.u(x - δ)) / (2. * δ);
-			assert!(abs_diff_eq!(du, testee.du(x), epsilon = ε), "At x={}, u':\nexpected: {}\nactual:   {}\n", x, du, testee.du(x));
+			let du_num = (testee.u(x + δ) - testee.u(x - δ)) / (2. * δ);
+			let du_expl = testee.du(x);
+			assert!(abs_diff_eq!(du_expl, du_num, epsilon = ε), "At x={}, du/dx:\nnumerical: {}\nexplicit:  {}\n", x, du_num, du_expl);
 
-			assert!(abs_diff_eq!(testee.du(x) * testee.dx(u), 1.0, epsilon = ε), "At x={}:\nu'x': {}\n", x, testee.du(x) * testee.dx(u));
+			let dudx = du_expl * testee.dx(ux);
+			assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At x={}:\ndu/dx * dx/du: {}\n", x, dudx);
 
-			let d2u = (testee.du(x + δ) - testee.du(x - δ)) / (2. * δ);
-			assert!(abs_diff_eq!(d2u, testee.d2u(x), epsilon = ε), "At x={}, u'':\nexpected: {}\nactual:   {}\n", x, d2u, testee.d2u(x));
+			let d2u_num = (testee.du(x + δ) - testee.du(x - δ)) / (2. * δ);
+			let d2u_expl = testee.d2u(x);
+			assert!(abs_diff_eq!(d2u_expl, d2u_num, epsilon = ε), "At x={}, d^2u/dx^2:\nnumerical: {}\nexplicit:  {}\n", x, d2u_num, d2u_expl);
 		}
 		for u in itertools_num::linspace(-mul * testee.internal, mul * testee.internal, 100) {
-			let x = testee.x(u);
-			assert!(abs_diff_eq!(x, testee.x(u), epsilon = ε), "At u={}:\nx(u):    {}\nu(x(u)): {}\n", u, x, testee.u(x));
+			let xu = testee.x(u);
+			let uxu = testee.u(xu);
+			assert!(abs_diff_eq!(u, uxu, epsilon = ε), "At u={}:\nx(u):    {}\nu(x(u)): {}\n", u, xu, uxu);
 
-			let dx = (testee.x(u + δ) - testee.x(u - δ)) / (2. * δ);
-			assert!(abs_diff_eq!(dx, testee.dx(u), epsilon = ε), "At u={}, x':\nexpected: {}\nactual:   {}\n", u, dx, testee.dx(u));
+			let dx_num = (testee.x(u + δ) - testee.x(u - δ)) / (2. * δ);
+			let dx_expl = testee.dx(u);
+			assert!(abs_diff_eq!(dx_expl, dx_num, epsilon = ε), "At u={}, dx/du:\nnumerical: {}\nexplicit:  {}\n", u, dx_num, dx_expl);
 
-			assert!(abs_diff_eq!(testee.du(x) * testee.dx(u), 1.0, epsilon = ε), "At u={}:\nu'x': {}\n", u, testee.du(x) * testee.dx(u));
+			let dudx = testee.du(xu) * dx_expl;
+			assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At u={}:\ndu/dx * dx/du: {}\n", u, dudx);
 		}
 	}
 }