diff --git a/rtiww/src/main.cpp b/rtiww/src/main.cpp
index a19ceaa..7895dae 100644
--- a/rtiww/src/main.cpp
+++ b/rtiww/src/main.cpp
@@ -7,14 +7,14 @@
 double hit_sphere(const point3 &center, double radius, const ray &r) {
     vec3 oc = r.origin() - center;
 
-    auto a = dot(r.direction(), r.direction());
-    auto b = 2.0 * dot(oc, r.direction());
-    auto c = dot(oc, oc) - radius * radius;
-    auto discriminant = b * b - 4 * a * c;
+    auto a = r.direction().length_squared();
+    auto half_b = dot(oc, r.direction());
+    auto c = oc.length_squared() - radius * radius;
+    auto discriminant = half_b * half_b - a * c;
     if (discriminant < 0) {
         return -1.0;
     } else {
-        return (-b - sqrt(discriminant)) / (2.0*a);
+        return (-half_b - sqrt(discriminant)) / a;
     }
 }