(exp (/ (* (- 0.5) (+ (* x x) (* y y))) s))

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

Math

\[e^{\frac{\left(-0.5\right) \cdot \left(x \cdot x + y \cdot y\right)}{s}}\]

↓

\[e^{\frac{\left(-0.5\right) \cdot \left(x \cdot x + y \cdot y\right)}{s}}\]

Error

Bits error versus x

Bits error versus y

Bits error versus s

Derivation

1. Initial program 0.0

   \[e^{\frac{\left(-0.5\right) \cdot \left(x \cdot x + y \cdot y\right)}{s}}\]

2. Final simplification 0.0

   \[\leadsto e^{\frac{\left(-0.5\right) \cdot \left(x \cdot x + y \cdot y\right)}{s}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y s)
  :name "(exp (/ (* (- 0.5) (+ (* x x) (* y y))) s))"
  :precision binary64
  (exp (/ (* (neg 0.5) (+ (* x x) (* y y))) s)))