For $X \sim \mathcal{N}(\mu, \sigma^2)$, return $P(a \leq X \leq b)$.

Standardise both ends and difference the CDF, which you can write with the error function:

$$\Phi(z) = \tfrac{1}{2}\left(1 + \mathrm{erf}\!\left(\tfrac{z}{\sqrt{2}}\right)\right)$$

Input

mu = 0.0
sigma = 1.0
a = -1.0
b = 1.0

Output

0.6826894921370859