
nachlassen
to lessen
To lose intensity, strength, quality, or performance; to become weaker or stop.
Gegen Abend ließ der starke Wind endlich nach.
Toward evening, the strong wind finally lessened.
to lessen / to reduce
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to lessen
To lose intensity, strength, quality, or performance; to become weaker or stop.
Gegen Abend ließ der starke Wind endlich nach.
Toward evening, the strong wind finally lessened.

to reduce
To reduce a price or give a discount.
Auf dem Flohmarkt konnte ich den Verkäufer überreden, beim Preis noch etwas nachzulassen.
At the flea market, I was able to persuade the seller to reduce the price a little more.
'Nachlassen' (to lessen / to reduce) is a separable verb. The prefix 'nach-' comes at the end in a main clause. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Der Sturm hat endlich nachgelassen.
The storm has finally let up.
The meaning depends strongly on the context. If it is about weather, feelings, pain, or performance, 'nachlassen' usually means 'to become weaker'. If it is about money or prices, it means 'to give a discount'.
Meine Kopfschmerzen lassen langsam nach.
My headache is slowly easing.
The meaning 'to become weaker' is often used for things that lose intensity by themselves. Typical subjects are: pain, rain, wind, heat, strength, or concentration.
Nach einer Stunde ließ seine Konzentration deutlich nach.
After an hour, his concentration lessened noticeably.
When talking about a price reduction, the phrasing 'im Preis nachlassen' or 'beim Preis nachlassen' is often used. You can also simply ask: 'Können Sie noch etwas nachlassen?' (Can you reduce it a little more?)
Vielleicht lässt der Verkäufer noch etwas nach, wenn Sie bar bezahlen.
Maybe the seller will reduce the price a little more if you pay in cash.
to reduce
Both words can express a price reduction. „Reduzieren“ usually takes the price or amount as its direct object and describes the reduction objectively. „Nachlassen“ emphasizes that the seller is giving the customer a discount. „Reduzieren“ is appropriate for a neutral statement about a price; „nachlassen“ is used when negotiating.

Der Händler lässt beim Preis des Fahrrads zehn Prozent nach.
The dealer gives ten percent off the price of the bicycle.
Der Händler reduziert den Preis des Fahrrads um zehn Prozent.
The dealer reduces the price of the bicycle by ten percent.