The overall elimination half-life of Mirtazapine is 20–40 hours, so the old dose will be roughly half by the time you take your first Fluoxetine tablet the next day, so doesn’t look like you need to taper.
From Wikipedia
Concurrent use with inhibitors or inducers of the cytochrome (CYP) P450 isoenzymes CYP1A2, CYP2D6, and/or CYP3A4 can result in altered concentrations of mirtazapine, as these are the main enzymes responsible for its metabolism.[3][7] As examples, fluoxetine and paroxetine, inhibitors of these enzymes, are known to modestly increase mirtazapine levels, while carbamazepine, an inducer, considerably decreases them.[3] Liver impairment and moderate renal impairment have been reported to decrease the oral clearance of mirtazapine by about 30%; severe renal impairment decreases it by 50%.[3]
According to information from the manufacturers, mirtazapine should not be started within two weeks of any monoamine oxidase inhibitor (MAOI) usage; likewise, MAOIs should not be administered within two weeks of discontinuing mirtazapine.[8] Mirtazapine in combination with an SSRI, SNRI, or TCA as an augmentation strategy is considered to be relatively safe and is often employed therapeutically,[42] with a combination of venlafaxine and mirtazapine, sometimes referred to as “California rocket fuel”.[58][59] Several case reports document serotonin syndrome induced by the combination of mirtazapine with other agents (olanzapine,[60] quetiapine,[61] tramadol and venlafaxine[62]).
Fluoxetine is an SSRI, so taking them both together is considered to be relatively safe..