How to create per-function memory profile of a multithreaded C++ program?

Question

Problem:

I have a multi-threaded C++ program, which handles quite some data (a few GB). At some point, my program runs out of main memory, which is something that I want to avoid. Theoretically, this should not happen, since the amount of data that this program analyzes is still much less than my main memory.

Assumed problem root:

My guess is that at some point I am passing all of that data by value to some function or some similar stupid mistake. This than ramps up my memory usage and I run out of main memory.

How can I find the code that causes the problem?

I would like to profile the memory usage of my program on a per-function basis. So the outcome should be something like (where both f and g are functions):

f    used 10% of total memory used
g    used  1% of total memory used

As suggested in this post, I had a look at massif by Valgrind. Looks like an amazing tool, but valgrind --tool=massif ./myProgram takes forever (even if I reduce the amount of data substantially).

Question:

What tool can I use to find the "bug" in my source code? I am looking for something that does not take forever to run, but still gives me the insight I need. I am also willing to do this programmatically by somehow changing my source code.

Env:

Compiler: Clang 9

OS: RHEL

C++: std=17