A large class of data questions can be modeled as identifying important slices of data driven by user defined metrics. This paper presents TRACE, a Time-Relational Approximate Cubing Engine that enables interactive analysis on such slices with a low upfront cost - both in space and computation. It does this by materializing the most important parts of the cube over time enabling interactive querying for a large class of analytical queries e.g. what part of my business has the highest revenue growth ([SubCategory=Sports Equipment, Gender=Female]), what slices are lagging in revenue per user ([State=CA, Age=20-30]). Many user defined metrics are supported including common aggregations such as SUM, COUNT, DISTINCT COUNT and more complex ones such as AVERAGE. We implemented and deployed TRACE for a variety of business use cases.