How do I compare CPUs on my own application without buying them? Is there some kind of daily-billed cloud computing service where I can choose any CPU and run my app on it?
Sort of. If you look at EC2 instance types [1], about 1/2 of them have a specific CPU related to them. Same thing with Microsoft's Azure instances [2].
There are a limited number of cpus available - they typically are xenons or AMD equivalents, so if you want data on consumer CPUS, the best you can do is try your app out in the cloud and then look at published benchmarks and try to estimate what your expected performance should be.
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1. https://aws.amazon.com/ec2/instance-types/
2. https://azure.microsoft.com/en-us/pricing/details/virtual-ma...
The correlation of bare-metal cores vs cloud vCPUs is very much nonlinear.