(/ 1 (sqrt (+ 1 (pow e (- z)))))

Average Error: 0.3 → 0.3

Time: 1.2s

Precision: binary64

Math

\[\frac{1}{\sqrt{1 + {e}^{\left(-z\right)}}}\]

↓

\[\frac{1}{\sqrt{1 + {e}^{\left(-z\right)}}}\]

Error

Bits error versus e

Bits error versus z

Derivation

1. Initial program 0.3

   \[\frac{1}{\sqrt{1 + {e}^{\left(-z\right)}}}\]

2. Final simplification 0.3

   \[\leadsto \frac{1}{\sqrt{1 + {e}^{\left(-z\right)}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (e z)
  :name "(/ 1 (sqrt (+ 1 (pow e (- z)))))"
  :precision binary64
  (/ 1.0 (sqrt (+ 1.0 (pow e (neg z))))))