diff --git a/Detectors/Base/include/DetectorsBase/Ray.h b/Detectors/Base/include/DetectorsBase/Ray.h
index 9f087363707c4..1701e65c2d638 100644
--- a/Detectors/Base/include/DetectorsBase/Ray.h
+++ b/Detectors/Base/include/DetectorsBase/Ray.h
@@ -46,7 +46,7 @@ class Ray
   static constexpr float InvalidT = -1e9;
   static constexpr float Tiny = 1e-9;
 
-  GPUd() Ray() : mP{0.f}, mD{0.f}, mDistXY2(0.f), mDistXY2i(0.f), mDistXYZ(0.f), mXDxPlusYDy(0.f), mXDxPlusYDyRed(0.f), mXDxPlusYDy2(0.f), mR02(0.f), mR12(0.f), mInvDz(Tiny)
+  GPUd() Ray() : mP{0.f}, mD{0.f}, mDistXY2(0.f), mDistXY2i(0.f), mDistXYZ(0.f), mXDxPlusYDy(0.f), mXDxPlusYDyRed(0.f), mXDxPlusYDy2(0.f), mR02(0.f), mR12(0.f)
   {
   }
   GPUdDefault() ~Ray() CON_DEFAULT;
@@ -61,7 +61,6 @@ class Ray
   GPUd() float crossRadial(const MatLayerCyl& lr, int sliceID) const;
   GPUd() float crossRadial(float cs, float sn) const;
   GPUd() float crossZ(float z) const;
-  GPUd() float crossZ_fast(float z) const; // without check
 
   GPUd() void getCrossParams(int i, float& par1, float& par2) const
   {
@@ -85,49 +84,6 @@ class Ray
     return p;
   }
 
-  // fast, approximate arctan calculation - sufficient for phi sector determination in material budget layers
-  // source of inspirations:
-  // - https://mazzo.li/posts/vectorized-atan2.html
-  // - https://www.coranac.com/documents/arctangent/
-  GPUd() float atan_approx_5terms(float x) const
-  {
-    // fast atan implementation
-    // function has a max error of ~1.16825e-05f
-    float a1 = 0.9998660f;
-    float a3 = -0.3302995f;
-    float a5 = 0.1801410f;
-    float a7 = -0.0851330f;
-    float a9 = 0.0208351f;
-
-    float x_sq = x * x;
-    // todo: force fuse-multiply add
-    return x * (a1 + x_sq * (a3 + x_sq * (a5 + x_sq * (a7 + x_sq * a9))));
-  }
-
-  GPUd() float atan2_approx(float y, float x) const
-  {
-    const bool swap = fabs(x) < fabs(y);
-    const float atan_input = (swap ? x : y) / (swap ? y : x);
-    const float pi2 = M_PI_2;
-    const float pi = M_PI;
-    float res = atan_approx_5terms(atan_input);
-
-    // if swapped, adjust atan output
-    res = swap ? (atan_input >= 0.0f ? pi2 : -pi2) - res : res;
-    // adjust quadrants
-    if (x < 0.0f) {
-      res = ((y < 0.0f) ? -pi : pi) + res;
-    }
-    return res;
-  }
-
-  GPUd() float getPhi_approx(float t) const
-  {
-    float p = atan2_approx(mP[1] + t * mD[1], mP[0] + t * mD[0]);
-    o2::math_utils::bringTo02Pi(p);
-    return p;
-  }
-
   GPUd() float getZ(float t) const { return mP[2] + t * mD[2]; }
 
   GPUd() bool validateZRange(float& cpar1, float& cpar2, const MatLayerCyl& lr) const;
@@ -145,7 +101,6 @@ class Ray
   float mR12;             ///< radius^2 of mP1
   float mCrossParams1[2]; ///< parameters of crossing the layer (first parameter)
   float mCrossParams2[2]; ///< parameters of crossing the layer (second parameter)
-  float mInvDz;
 
   ClassDefNV(Ray, 1);
 };
@@ -164,7 +119,6 @@ inline Ray::Ray(const math_utils::Point3D<float> point0, const math_utils::Point
   mXDxPlusYDy2 = mXDxPlusYDy * mXDxPlusYDy;
   mR02 = point0.Perp2();
   mR12 = point1.Perp2();
-  mInvDz = 1.f / mD[2];
 }
 #endif // !GPUCA_ALIGPUCODE
 
@@ -180,7 +134,6 @@ GPUdi() Ray::Ray(float x0, float y0, float z0, float x1, float y1, float z1)
   mXDxPlusYDy2 = mXDxPlusYDy * mXDxPlusYDy;
   mR02 = x0 * x0 + y0 * y0;
   mR12 = x1 * x1 + y1 * y1;
-  mInvDz = 1.f / mD[2];
 }
 
 //______________________________________________________
@@ -222,13 +175,6 @@ GPUdi() float Ray::crossZ(float z) const
   return mD[2] != 0. ? (z - mP[2]) / mD[2] : InvalidT;
 }
 
-//______________________________________________________
-GPUdi() float Ray::crossZ_fast(float z) const
-{
-  // calculate t of crossing XY plane at Z
-  return (z - mP[2]) * mInvDz;
-}
-
 //______________________________________________________
 GPUdi() bool Ray::validateZRange(float& cpar1, float& cpar2, const MatLayerCyl& lr) const
 {
diff --git a/Detectors/Base/src/MatLayerCylSet.cxx b/Detectors/Base/src/MatLayerCylSet.cxx
index 6ee8a006db002..fb2e720427016 100644
--- a/Detectors/Base/src/MatLayerCylSet.cxx
+++ b/Detectors/Base/src/MatLayerCylSet.cxx
@@ -294,8 +294,8 @@ GPUd() MatBudget MatLayerCylSet::getMatBudget(float x0, float y0, float z0, floa
     for (int ic = nc; ic--;) {
       float cross1, cross2;
       ray.getCrossParams(ic, cross1, cross2); // tmax,tmin of crossing the layer
-      auto phi0 = ray.getPhi_approx(cross1), phi1 = ray.getPhi_approx(cross2), dPhi = phi0 - phi1;
-      // auto phi0 = ray.getPhi(cross1), phi1 = ray.getPhi(cross2), dPhi = phi0 - phi1;
+
+      auto phi0 = ray.getPhi(cross1), phi1 = ray.getPhi(cross2), dPhi = phi0 - phi1;
       auto phiID = lr.getPhiSliceID(phi0), phiIDLast = lr.getPhiSliceID(phi1);
       // account for eventual wrapping around 0
       if (dPhi > 0.f) {
@@ -339,7 +339,10 @@ GPUd() MatBudget MatLayerCylSet::getMatBudget(float x0, float y0, float z0, floa
               tEndZ = tEndPhi;
               checkMoreZ = false;
             } else {
-              tEndZ = ray.crossZ_fast(lr.getZBinMin(stepZID > 0 ? zID + 1 : zID));
+              tEndZ = ray.crossZ(lr.getZBinMin(stepZID > 0 ? zID + 1 : zID));
+              if (tEndZ == Ray::InvalidT) { // track normal to Z axis, abandon Zbin change test
+                break;
+              }
             }
             // account materials of this step
             float step = tEndZ > tStartZ ? tEndZ - tStartZ : tStartZ - tEndZ; // the real step is ray.getDist(tEnd-tStart), will rescale all later