Toxicity prediction of chemical compounds is a grand challenge. Lately, it achieved significant progress in accuracy but using a huge set of features, implementing a complex blackbox technique such as a deep neural network, and exploiting enormous computational resources. In this paper, we strongly argue for the models and methods that are simple in machine learning characteristics, efficient in computing resource usage, and powerful to achieve very high accuracy levels. To demonstrate this, we develop a single task-based chemical toxicity prediction framework using only 2D features that are less compute intensive. We effectively use a decision tree to obtain an optimum number of features from a collection of thousands of them. We use a shallow neural network and jointly optimize it with decision tree taking both network parameters and input features into account. Our model needs only a minute on a single CPU for its training while existing methods using deep neural networks need about 10 min on NVidia Tesla K40 GPU. However, we obtain similar or better performance on several toxicity benchmark tasks. We also develop a cumulative feature ranking method which enables us to identify features that can help chemists perform prescreening of toxic compounds effectively.