First, you have to be very careful how you express it. To say that something is twice as fast is the same as saying that it has improved 100%, which means the same thing as saying that it is 200% of what it was (whatever that says) ) When you say "improved" or "increased", you have a hidden link to the original amount + improvement.
Example: You have 3 dollars. You double your money up to $ 6. This is a 100% improvement (or a 100% increase) because you have the original $ 3 + new $ 3 (which is 100% of the original amount). But you can also say that you have 200% as much as it was before, because $ 3 * 200% = $ 3 * 2 = $ 6.
Now, as far as speed goes, think about it in terms of the old algebra equation: Speed * Time = distance. Except for us, "Distance" is more like "Doing the job."
So, if a specific task takes 1 second, and you changed it to make it do the same job in 0.5 seconds: Original
R * 1sec = 1job
R = 1job / 1sec = 1 job / sec
New R * 0.5sec = 1job
R = 1job / 0.5sec = 2 job / sec
Thus, your speed doubled. You can say that the rate has increased by 100% or that the rate has doubled or that it is 200% as fast as before.
-------------------- edit to use OP numbers ------
Original
R * 34sec = 1job
R = 1job / 34sec = 1/34 job / sec = 0.029 job / sec
New
R * 2sec = 1job
R = 1job / 2sec = 1/2 job / sec = 0.5 job / sec
So, to compare rates of 0,029 tasks / second to 0,5 tasks / second
0.5 / 0.029 = 17
Thus, the new code runs 17 times faster or 1700% faster, or increases by 1600%.
nurdyguy
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