In order to balance the renting quantity of cloud computing resources and the accuracy of data mining in cloud, the optimum cost performance ratio is obtained. Taking the convolution neural network (CNN) as an example, the evolution patterns of the number of iterations and accuracy of CNN was explored. A lot of experiments were performed upon the image dataset MNIST and the text dataset IMDB. The results show that in different types of data sets, the machine time consumed increases sharply with a small increase in accuracy when the optimal solution is approached, which is called the long tail phenomena. Correspondingly, in the real cloud environment, when the long tail phenomenon of big data mining occurs and the accuracy is satisfied, terminating the performance of CNN in cloud in advance rather than at the convergence time can save a lot of cloud resource costs. The results have practical value and practical significance for the rational use of cloud computing resources and the reduction of cloud rental cost.