(+ (- (sqrt (+ x 1)) (exp (- x))) (cos (* (* 2 pi) x)))

Average Error: 15.1 → 15.1

Time: 1.8s

Precision: binary64

Math

\[\left(\sqrt{x + 1} - e^{-x}\right) + \cos \left(\left(2 \cdot pi\right) \cdot x\right)\]

↓

\[\left(\sqrt{x + 1} - e^{-x}\right) + \cos \left(\left(2 \cdot pi\right) \cdot x\right)\]

Error

Bits error versus x

Bits error versus pi

Derivation

1. Initial program 15.1

   \[\left(\sqrt{x + 1} - e^{-x}\right) + \cos \left(\left(2 \cdot pi\right) \cdot x\right)\]

2. Final simplification 15.1

   \[\leadsto \left(\sqrt{x + 1} - e^{-x}\right) + \cos \left(\left(2 \cdot pi\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x pi)
  :name "(+ (- (sqrt (+ x 1)) (exp (- x))) (cos (* (* 2 pi) x)))"
  :precision binary64
  (+ (- (sqrt (+ x 1.0)) (exp (neg x))) (cos (* (* 2.0 pi) x))))