(log (+ 1 (exp (* (- a) b))))

Average Error: 0.5 → 0.5

Time: 2.4s

Precision: binary64

Math

\[\log \left(1 + e^{\left(-a\right) \cdot b}\right)\]

↓

\[\log \left(1 + e^{\left(-a\right) \cdot b}\right)\]

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.5

   \[\log \left(1 + e^{\left(-a\right) \cdot b}\right)\]

2. Final simplification 0.5

   \[\leadsto \log \left(1 + e^{\left(-a\right) \cdot b}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(log (+ 1 (exp (* (- a) b))))"
  :precision binary64
  (log (+ 1.0 (exp (* (neg a) b)))))