# How to avoid getting different results in exponential and trigonometric forms [closed]

I have a complicated numerical complex expression which depends on 6 parameters (Alpha, Beta, Gamma, Delta41, Delta43, Delta). It is too long to put it all here but this is what it looks like:

Expr = -(1/2) Re[4.21789*10^-16 ((2.14978*10^-11 E^(-2 I δ) +
1.00004*10^-9 (-0.644842 E^(I α) + 0.0000146636 E^(I α - I δ + I δ41))^2 +
1000 E^(2 I γ) (0.00750167 E^(I δ43) + 0.99995 (0.00644906 +
0.00146621 E^(-I δ + I δ41)))^2 + 1.00125*10^-9 E^(2 I β) (-0.750054 +
0.010001 E^(-I δ43) (0.00644906 + 0.00146621 E^(-I δ + I δ41)))^2)
(1.216*10^-10 E^(-I δ) + 1.00004*10^-9 (0.644842 E^(-I α) -
0.0000146636 E^(-I α - I δ + I δ41)) (-0.000082943 E^(-I α + I δ41) -
0.99995 E^(-I α) (0.413249 + 0.0801478 E^(I δ))) -
1000 E^(-2 I γ) (0.00750167 E^(I δ43) + 0.99995 (0.00644906 +
0.00146621 E^(-I δ + I δ41))) (E^(I δ43) (-0.00355317 + 0.00093234 E^(I δ)) +
0.99995 (0.0041327 + 0.000801518 E^(I δ) - 0.00829347 E^(I δ41))) +
1.00125*10^-9 E^(-2 I β) (0.750054 - 0.010001 E^(-I δ43) (0.00644906 +
0.00146621 E^(-I δ + ........


My problem is the following, when I evaluate this expression for some numerical values of the parameters, I do not get the same result whether I use the exponential form or the trigonometric one whereas they are supposed to be exactly the same.

Expr /. {α -> 1, β -> 2, γ -> 3, δ43 -> 4, δ41 -> 5, δ -> 6}


1.68977*10^-38

ExpToTrig[Expr] /. {α -> 1, β -> 2, γ -> 3, δ43 -> 4, δ41 -> 5, δ -> 6}


2.7918*10^-38

Question: How can I get the same result using both forms?

## closed as off-topic by MarcoB, Henrik Schumacher, m_goldberg, Alex Trounev, Daniel LichtblauMar 15 at 16:45

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• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – MarcoB, Henrik Schumacher, m_goldberg, Alex Trounev, Daniel Lichtblau
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• Rounding errors. – Henrik Schumacher Mar 14 at 17:26
• @HenrikSchumacher Thanks, but what is the difference between Expr and ExpToTrig[Expr] regarding the errors ? – Pon Mar 15 at 0:42
• A good answer to this question would show, how to use Precision to avoid this from happening. – Johu Mar 15 at 13:12
• @Johu Thanks for the clarification. Do you mean I must increase the numerical precision of all numbers that I put in the code in order to avoid this ? – Pon Mar 15 at 14:33
• @Pon, I recommend you change your question from "why does it happen" (happens because of rounding errors in different analytic forms of the experssion) to "how to avoid it from happening". It should be possible to change the precision of the evaluation locally. After changing the question, it might get opened again. I don't think it is a bad question. – Johu Mar 15 at 21:02