Why does setting a const variable (which will be stored with the same value) lead to a different result once divided?

The "issue" is due to the -freciprocal-math switch (implied by -Ofast):

Allow the reciprocal of a value to be used instead of dividing by the value if this enables optimizations. For example x / y can be replaced with x * (1/y), which is useful if (1/y) is subject to common subexpression elimination. Note that this loses precision and increases the number of flops operating on the value.

The compiler can calculate d = 1/bConst at compile time and change from:

c/bConst

to

c * d

but multiplication and division are different instructions with different performance and precision.

See: http://coliru.stacked-crooked.com/a/ba9770ec39ec5ac2

You are using -Ofast in your link, which enables all -O3 optimizations and includes both -ffast-math, which in turns includes -funsafe-math-optimizations.

From what I could glean, with optimizations enabled, -funsafe-math-optimizations allows the compiler to reduce the precision of some computations. This seems to be what happens in the c/bConst case.