(/ (exp (* (* x x) (- 0.5))) (sqrt (* 2 PI)))

Average Error: 0.0 → 0.0

Time: 762.0ms

Precision: binary64

Math

\[\frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]

↓

\[\frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]

2. Final simplification 0.0

   \[\leadsto \frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (exp (* (* x x) (- 0.5))) (sqrt (* 2 PI)))"
  :precision binary64
  (/ (exp (* (* x x) (neg 0.5))) (sqrt (* 2.0 PI))))