When you use evalf, you can provide an argument n, which is "the number of
digits of precision" that you want
One straightforward interpretation of this is that Sympy's evalf interface
always returns a number whose nth significant digit is within 1 of the true
answer (in either direction).
The only examples I have seen this break are around zero. In particular, if
you have the wrong sign, then tweaking the nth significant digit is not
going to help
Here is a simple example where sp.core.evalf.evalf gives a different sign
with different precision (so at least one of them has the wrong sign)
```
expr = sp.fibonacci(27) - (sp.GoldenRatio**27)/sp.sqrt(5)
re, _, re_acc, _ = sp.core.evalf.evalf(expr, prec=1, options={"strict":
True})
sign, man, exp, bc = re
print([1, -1][sign]*man*2**exp)
print(float(expr))
```
prints
```
-128
1.0182366178305287e-06
```
I also dug into the code a bit to see what I could find, when you use
"strict=True", behind the scenes, Sympy basically just checks that
sp.core.evalf.evalf's returned re_acc (only concerned with) is at least as
high as the desired precision. (Where re_acc seems to be the number of
accurate bits in the number that re is a rounded version of)
So it isn't really clear to me what the interpretation of n/prec/re_acc is
for these cases around zero
In a perfect world, I would like to have a function which takes the
input/output of evalf and returns an upper and lower bound for the true
value of the expression.
As a related question, I would like to know how rigorous Sympy tries to be
with adhering to a specific precision guarantee (for example mpmath has
[this
page](https://mpmath.org/doc/current/technical.html#correctness-guarantees))
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