Assuming an algorithm $A$ known to both Alice and Bob.
Alice runs the algorithm and gets a result $R$. How can Alice prove to Bob that $R$ is the result of the execution of $A$ and not some random value (without having Bob run the algorithm himself)?
The goal is for Bob to perform less calculations checking Alice proof than running the algorithm itself. A probabilistic scheme for the proof is fine.
Please note that Alice does not have to prove correctness of $R$, just that she ran $A$ to obtain $R$.
The algorithm and its inputs can be modified to build the proof if necessary
Note: from the discussions below. I am happy with heuristics or techniques to obtain the proof. This is not a rhetorical question on algorithms.
Note2: @DavidRicherby suggests providing an execution trace, which seems perfectly reasonable. This leads to two sub-questions
How does Alice practically build a trace which proves to Bob with high probability that the trace is the one linked to the result ? (Bob should run less calculations checking the trace, than running the calculation himself)
Could such a mechanism be generic i.e. work with any algorithm ? For instance by confining execution inside a Virtual Machine which could record all operations.