In this short excerpt from the preface to Bunyan’s The Acceptable Sacrifice, written by George Cokayn, we are instructed on the believer’s response to their sin. 

Now, therefore, surely such a heart as this is must needs be very delightful to God. He says to us, ‘My son, give me thine heart’ (Prov 23:26). But, doubtless, he means there a broken heart: an unbroken heart we may keep to ourselves; it is the broken heart which God will have us to give to him; for, indeed, it is all the amends that the best of us are capable of making, for all the injury we have done to God in sinning against him.

We are not able to give better satisfaction for breaking God’s laws, than by breaking our own hearts; this is all that we can do of that kind; for the blood of Christ only must give the due and full satisfaction to the justice of God for what provocations we are at any time guilty of; but all that we can do is to accompany the acknowledgments we make of miscarriages with a broken and contrite spirit.

Therefore we find, that when David had committed those two foul sins of adultery and murder, against God, he saw that all his sacrifices signified nothing to the expiating of his guilt; therefore he brings to God a broken heart, which carried in it the best expression of indignation against himself, as of the highest respect he could show to God (2 Cor 7:11).

Bunyan, John (2011-03-24). Works of John Bunyan — Complete (Kindle Locations 28901-28909). . Kindle Edition.