diff --git a/wtracer.cpp b/wtracer.cpp
index 3783243..cd86a06 100644
--- a/wtracer.cpp
+++ b/wtracer.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 disciminant = 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 disciminant = half_b*half_b - a*c;
     if (disciminant < 0) {
         return -1.0;
     } else {
-        return (-b - std::sqrt(disciminant)) / (2.0 * a);
+        return (-half_b - std::sqrt(disciminant)) / a;
     }
 }