(/ (exp (/ (- (pow (- x m) 2)) (* 2 s))) (sqrt (* (* 2 PI) m)))

Average Error: 0.1 → 0.1

Time: 3.3s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Bits error versus m

Bits error versus s

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x m s)
  :name "(/ (exp (/ (- (pow (- x m) 2)) (* 2 s))) (sqrt (* (* 2 PI) m)))"
  :precision binary64
  (/ (exp (/ (neg (pow (- x m) 2.0)) (* 2.0 s))) (sqrt (* (* 2.0 PI) m))))