Try testing this in your tax software. Create an experimental return with $100,000 income and $13,000 in long-term capital gains. Now edit the $13,000 down to $3,000 and see how much less you would owe. I would expect $1,500.
When you earn about $100,000, then the $12,500 of long-term capital gains is taxed at the 15% rate. It should be impossible to pay double that. The highest capital gains rate kicks in over $400,000 and is roughly 24% last year. Even AMT doesn't charge 30%, if that applies. So because of that, I suspect a misunderstanding or mistake is involved.