Schubert introduced the partnership ability φ-index relying on a researcher's number of co-authors and collaboration rate. As a Hirsch-type index, φ was expected to be consistent with Schubert-Glänzel's model of h-index. Schubert demonstrated this relationship with the 34 awardees of the Hevesy medal in the field of nuclear and radiochemistry (r² = 0.8484). In this paper, we upscale this study by testing the φ-index on a million researchers in computer science. We found that the Schubert-Glänzel's model correlates with the million empirical φ values (r² = 0.8695). In addition, machine learning through symbolic regression produces models whose accuracy does not exceed a 6.1% gain (r² = 0.9227). These results suggest that the Schubert-Glänzel's model of φ-index is accurate and robust on the domain-wide bibliographic dataset of computer science.