Gems-to-materials "exchange rate"?

Has anyone figured out what the "exchange rate" (or ratio) is in terms of the numbers of gems required to replace each material if you don't have enough to upgrade? For example, I was able to work out that 25 Gems = 1 SR, albeit I only had two data points (200 Gems = 8 SR and 250 Gems = 10 SR) so it's possible that the same ratio may not hold at lower or higher numbers of SRs required if the scale is non-linear.
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