Float Precision Problems

Description	float64	float16	Symbolic Term
Small Numbers	1.000e-08	0.000e+00	$10^{-8}$
Big Numbers	7.000e+04	inf	$70000$
Long Sum	1.000e+04	9.992e+03	$\sum_{k=1}^{10^{5}} 0.1$
Catastrophic Cancellation	1.000e-04	0.000e+00	$1 - (1 - 10^{-4})$