(- (/ (- (pow (- x m) 2)) (* 2 s)) (/ (log (* (* 2 PI) s)) 2))

Average Error: 12.0 → 12.0

Time: 3.7s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Bits error versus m

Bits error versus s

Derivation

1. Initial program 12.0

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

2. Final simplification 12.0

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

Reproduce

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