Gauss-Kronrod quadrature

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I am writing a thesis on the adaptive Gauss-Kronrod quadrature rule. In the last part I am exposing some numerical results, and I found this little problem: since in the adaptive algorithm we use as an estimate for the error the absolute value of the difference between the Gauss formula and the Gauss-Kronrod formula, in the results I found that the estimate is bigger than the actual error (the difference between the exact result and the Gauss-Kronrod result). Is this result plausible?