Okay, I try to make it clearer. Your main calculation error is that you add your base value 666 three times - but you have only one base value.
Base value (for quarry level 32, on an island with reduced stone production): 666
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Base value + merchant bonus (30%):
666 * 1.3 = ~866
This means a bonus of 200 stone per hour is added to the base value of 666 stone.
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Base value + merchant bonus (30%) + production bonus for Andromeda level 10 (30%):
666 * 1.6 = ~1066
This means that a bonus of 200 stone per hour is added to the base value of 666 stone due to the merchant bonus,
and another 200 stone per hour are added to the base value due to Andromeda´s 30% bonus.
The bonuses add up to 60%, that´s why you can multiply your base value by 1.6 to calculate your total production.
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Base value + merchant bonus (30%) + production bonus for Andromeda level 10 (30%) + "Happiness" (50%):
666 * 2.1 = ~1399
This means that a bonus of 200 stone per hour is added to the base value of 666 stone due to the merchant bonus,
and another 200 stone per hour are added to the base value due to Andromeda´s 30% bonus,
and another 333 stone are added to the base value due to the spell "Happiness".
And as already stated by dev-grepo, 200+200+333 = 733, and that´s your additional production, when the bonuses of merchant, hero and spell are active in your city. The bonuses add up to 110%, that´s why you can multiply your base value by 2.1 to calculate your total production.
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In your calculation you did not only add the bonuses to the base value, but you added the base value(s) all over again.