(- (+ 0.5 (* c (exp (- x)))) (* (exp (* (- 2) x)) 0.5))

Average Error: 19.1 → 19.1

Time: 1.6s

Precision: binary64

Math

\[\left(0.5 + c \cdot e^{-x}\right) - e^{\left(-2\right) \cdot x} \cdot 0.5\]

↓

\[\left(0.5 + c \cdot e^{-x}\right) - e^{\left(-2\right) \cdot x} \cdot 0.5\]

Error

Bits error versus c

Bits error versus x

Derivation

1. Initial program 19.1

   \[\left(0.5 + c \cdot e^{-x}\right) - e^{\left(-2\right) \cdot x} \cdot 0.5\]

2. Final simplification 19.1

   \[\leadsto \left(0.5 + c \cdot e^{-x}\right) - e^{\left(-2\right) \cdot x} \cdot 0.5\]

Reproduce

herbie shell --seed 2020153 
(FPCore (c x)
  :name "(- (+ 0.5 (* c (exp (- x)))) (* (exp (* (- 2) x)) 0.5))"
  :precision binary64
  (- (+ 0.5 (* c (exp (neg x)))) (* (exp (* (neg 2.0) x)) 0.5)))