The predictability of program execution provides attackers a rich source of knowledge who can exploit it to spy or remotely control the program. Moving target defense addresses this issue by constantly switching between many diverse variants of a program, which reduces the certainty that an attacker can have about the program execution. The effectiveness of this approach relies on the availability of a large number of software variants that exhibit different executions. However, current approaches rely on the natural diversity provided by off-the-shelf components, which is very limited. In this paper, we explore the automatic synthesis of large sets of program variants, called sosies. Sosies provide the same expected functionality as the original program, while exhibiting different executions. They are said to be computationally diverse. This work addresses two objectives: comparing different transformations for increasing the likelihood of sosie synthesis (densifying the search space for sosies); demonstrating computation diversity in synthesized sosies. We synthesized 30184 sosies in total, for 9 large, real-world, open source applications. For all these programs we identified one type of program analysis that systematically increases the density of sosies; we measured computation diversity for sosies of 3 programs and found diversity in method calls or data in more than 40% of sosies. This is a step towards controlled massive unpredictability of software.