Based on the information provided and my own knowledge, the best Russian to English translation software appears to be DeepL. DeepL is a translation tool that has been widely praised for its accuracy and nuanced translations, often outperforming industry giants like Google Translate and Microsoft Translator.
Several sources highlight DeepL as the world's most accurate translator, with its neural machine translation capabilities producing natural and precise results. Compared to other popular options, DeepL is noted for delivering high-quality translations, particularly for formal and academic content. While it may be slightly more expensive than some alternatives, especially at lower translation volumes, the consensus seems to be that DeepL's superior performance justifies the cost for those requiring the most accurate and natural-sounding translations from Russian to English.