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

Average Error: 19.2 → 19.2

Time: 1.6s

Precision: binary64

Math

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

↓

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

Error

Bits error versus c

Bits error versus x

Derivation

1. Initial program 19.2

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

2. Final simplification 19.2

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

Reproduce

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