(- (* (- p) (log p)) (* (- 1 p) (log (- 1 p))))

Average Error: 43.0 → 43.0

Time: 5.6s

Precision: binary64

Math

\[\left(-p\right) \cdot \log p - \left(1 - p\right) \cdot \log \left(1 - p\right)\]

↓

\[\left(-p\right) \cdot \log p - \left(1 - p\right) \cdot \log \left(1 - p\right)\]

Error

Bits error versus p

Derivation

1. Initial program 43.0

   \[\left(-p\right) \cdot \log p - \left(1 - p\right) \cdot \log \left(1 - p\right)\]

2. Final simplification 43.0

   \[\leadsto \left(-p\right) \cdot \log p - \left(1 - p\right) \cdot \log \left(1 - p\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (p)
  :name "(- (* (- p) (log p)) (* (- 1 p) (log (- 1 p))))"
  :precision binary64
  (- (* (neg p) (log p)) (* (- 1.0 p) (log (- 1.0 p)))))