(/ 1 (+ 1 (exp (/ (+ (- Rw) Rb) (* 400 (log 10))))))

Average Error: 0.0 → 0.0

Time: 984.0ms

Precision: binary64

Math

\[\frac{1}{1 + e^{\frac{\left(-Rw\right) + Rb}{400 \cdot \log 10}}}\]

↓

\[\frac{1}{1 + e^{\frac{\left(-Rw\right) + Rb}{400 \cdot \log 10}}}\]

Error

Bits error versus Rw

Bits error versus Rb

Derivation

1. Initial program 0.0

   \[\frac{1}{1 + e^{\frac{\left(-Rw\right) + Rb}{400 \cdot \log 10}}}\]

2. Final simplification 0.0

   \[\leadsto \frac{1}{1 + e^{\frac{\left(-Rw\right) + Rb}{400 \cdot \log 10}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (Rw Rb)
  :name "(/ 1 (+ 1 (exp (/ (+ (- Rw) Rb) (* 400 (log 10))))))"
  :precision binary64
  (/ 1.0 (+ 1.0 (exp (/ (+ (neg Rw) Rb) (* 400.0 (log 10.0)))))))