(/ (- (exp (/ (- (exp2 bmin)) 2))) (sqrt (* 2 pi)))

Average Error: 0.2 → 0.2

Time: 2.1s

Precision: binary64

Math

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

↓

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

Error

Bits error versus bmin

Bits error versus pi

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

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