(/ (- (exp (/ (- (exp2 x)) 2))) (sqrt (* 2 PI)))

Average Error: 0.5 → 0.5

Time: 1.2s

Precision: binary64

Math

\[\frac{-e^{\frac{-2^{x}}{2}}}{\sqrt{2 \cdot \pi}}\]

↓

\[\frac{-e^{\frac{-2^{x}}{2}}}{\sqrt{2 \cdot \pi}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.5

   \[\frac{-e^{\frac{-2^{x}}{2}}}{\sqrt{2 \cdot \pi}}\]

2. Final simplification 0.5

   \[\leadsto \frac{-e^{\frac{-2^{x}}{2}}}{\sqrt{2 \cdot \pi}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- (exp (/ (- (exp2 x)) 2))) (sqrt (* 2 PI)))"
  :precision binary64
  (/ (neg (exp (/ (neg (exp2 x)) 2.0))) (sqrt (* 2.0 PI))))