Interchange loops

  for (i = 0; i < 500; i++)
    for (k = 0; k < 500; k++){
      r = A[i][k];
      for (j = 0; j < 500; j++)
        C[i][j] += r * B[k][j];
    }

• 45 seconds (5.5 MFLOPS).
• Why is this such a good idea?
• How might a compiler perform this transformation?
• Can we do better still?