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I have some function f[x,y], with x ranging from 0.5 to 62.5 and y ranging from 10^-20 to 10^-5. Near x = 62 the function starts to increase very fast and takes at x = 62.5 some large finite value.

I want to find a domain in which f[x,y]>=2.3 using RegionPlot. Knowing the behavior of f[x,y], I increase the number of PlotPoints:

RegionPlot[f[10^x,10^y]>=2.3,{x,Log10[0.5],Log10[62.5]},{y,-20,-5},PlotPoints->170] 

However, the result I get is still not accurate in the domain x > 62 (the red domain, with the light blue showing what the result must be): enter image description here

I can either increase the number of PlotPoints or the value of MaxRecursion. However, the RegionPlot works very slow with f[x,y], and by simply increasing PlotPoints I would have a problem. I have few questions.

1) Should increasing MaxRecursion also slow down the computation? 2) Taking into account that the behavior of the function is smooth in the domain 5 < x < 60, is there any way to optimize the RegionPlot options in order to make the computations faster without making the plot worse?

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