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In Wolfram Alpha:
plot -EXP(t)/2 LN((EXP(t)-1)/(EXP(t)+1)) from t=0 to t=40
Is this how round off errors appear in solutions when subtraction operand orders of magnitude differ more than 2^24 (32-bit float) ?
Link: Equation Plot
Link: What Every Computer Scientist Should Know About Floating-Point Arithmetic
Basically, yes, though the subtraction is hidden in the computation, and the datatype is double, not float.
For large
t,(exp(t)-1)/(exp(t)+1)is essentially1 - 2exp(-t), the logarithm of which is very nearly-2exp(-t). However, because2exp(-t)is so small compared to1, most of the bits of precision are lost in the value passed to the logarithm, which results in all the noise you are observing.