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The application of next-generation sequencing in research and particularly in clinical routine requires highly accurate variant calling. Here we describe UVC, a method for calling small variants of germline or somatic origin. By unifying opposite assumptions with sublation, we discovered the following two empirical laws to improve variant calling: allele fraction at high sequencing depth is inversely proportional to the cubic root of variant-calling error rate, and odds ratios adjusted with Bayes factors can model various sequencing biases. UVC outperformed other variant callers on the GIAB germline truth sets, 192 scenarios of in silico mixtures simulating 192 combinations of tumor/normal sequencing depths and tumor/normal purities, the GIAB somatic truth sets derived from physical mixture, and the SEQC2 somatic reference sets derived from the breast-cancer cell-line HCC1395. UVC achieved 100% concordance with the manual review conducted by multiple independent researchers on a Qiagen 71-gene-panel dataset derived from 16 patients with colon adenoma. UVC outperformed other unique molecular identifier (UMI)-aware variant callers on the datasets used for publishing these variant callers. Performance was measured with sensitivity-specificity trade off for called variants. The improved variant calls generated by UVC from previously published UMI-based sequencing data provided additional insight about DNA damage repair. UVC is open-sourced under the BSD 3-Clause license at https://github.com/genetronhealth/uvc and quay.io/genetronhealth/gcc-6-3-0-uvc-0-6-0-441a694 [ABSTRACT FROM AUTHOR]