(- 1 (exp (/ (- (pow x 2)) (* 2 (pow a 2)))))

Average Error: 17.7 → 17.7

Time: 2.1s

Precision: binary64

Math

\[1 - e^{\frac{-{x}^{2}}{2 \cdot {a}^{2}}}\]

↓

\[1 - e^{\frac{-{x}^{2}}{2 \cdot {a}^{2}}}\]

Error

Bits error versus x

Bits error versus a

Derivation

1. Initial program 17.7

   \[1 - e^{\frac{-{x}^{2}}{2 \cdot {a}^{2}}}\]

2. Final simplification 17.7

   \[\leadsto 1 - e^{\frac{-{x}^{2}}{2 \cdot {a}^{2}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x a)
  :name "(- 1 (exp (/ (- (pow x 2)) (* 2 (pow a 2)))))"
  :precision binary64
  (- 1.0 (exp (/ (neg (pow x 2.0)) (* 2.0 (pow a 2.0))))))