(/ (exp (/ (- (* x x)) (* (* 2.0 sigma) sigma))) (* sigma (sqrt (* 2.0 PI))))

Average Error: 8.0 → 8.0

Time: 1.0s

Precision: binary64

Math

\[\frac{e^{\frac{-x \cdot x}{\left(2 \cdot sigma\right) \cdot sigma}}}{sigma \cdot \sqrt{2 \cdot \pi}}\]

↓

\[\frac{e^{\frac{-x \cdot x}{\left(2 \cdot sigma\right) \cdot sigma}}}{sigma \cdot \sqrt{2 \cdot \pi}}\]

Error

Bits error versus x

Bits error versus sigma

Derivation

1. Initial program 8.0

   \[\frac{e^{\frac{-x \cdot x}{\left(2 \cdot sigma\right) \cdot sigma}}}{sigma \cdot \sqrt{2 \cdot \pi}}\]

2. Final simplification 8.0

   \[\leadsto \frac{e^{\frac{-x \cdot x}{\left(2 \cdot sigma\right) \cdot sigma}}}{sigma \cdot \sqrt{2 \cdot \pi}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x sigma)
  :name "(/ (exp (/ (- (* x x)) (* (* 2.0 sigma) sigma))) (* sigma (sqrt (* 2.0 PI))))"
  :precision binary64
  (/ (exp (/ (neg (* x x)) (* (* 2.0 sigma) sigma))) (* sigma (sqrt (* 2.0 PI)))))