The core promoter, the region immediately surrounding the transcription start site, plays a central role in setting metazoan gene expression levels, but how exactly it computes expression remains poorly understood. To dissect core promoter function, we carried out a comprehensive structure-function analysis to measure synthetic promoters activities, with and without an external stimulus (hormonal activation). By using robotics and a dual-luciferase reporter assay, we tested ~3000 mutational variants representing 19 different Drosophila melanogaster promoter architectures. We explored the impact of different types of mutations, including knockout of individual sequence motifs and motif combinations, variations of motif strength, positioning, and flanking sequences. We observe strong effects of the mutations on activity, and a linear combination of the individual motif features can largely account for the combinatorial effects on core promoter activity. Our findings shed new light on the quantitative assessment of gene expression, a fundamental process in all metazoans.