(+ (+ (exp (- x)) (exp x)) (- (exp (- x)) (exp x)))

Average Error: 0.3 → 0.0

Time: 1.2s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 2872.6372031135757

Math

\[\left(e^{-x} + e^{x}\right) + \left(e^{-x} - e^{x}\right)\]

↓

\[\frac{2}{e^{x}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.3

   \[\left(e^{-x} + e^{x}\right) + \left(e^{-x} - e^{x}\right)\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{2}{e^{x}}}\]

3. Final simplification 0.0

   \[\leadsto \frac{2}{e^{x}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (+ (exp (- x)) (exp x)) (- (exp (- x)) (exp x)))"
  :precision binary64
  (+ (+ (exp (neg x)) (exp x)) (- (exp (neg x)) (exp x))))