(+ (- (sinh x) (cosh x)) (tanh x))

Average Error: 0.1 → 0.0

Time: 2.0s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 2.7279434923395366e+116

Math

\[\left(\sinh x - \cosh x\right) + \tanh x\]

↓

\[\tanh x - e^{-x}\]

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\left(\sinh x - \cosh x\right) + \tanh x\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\tanh x - e^{-x}}\]

3. Final simplification 0.0

   \[\leadsto \tanh x - e^{-x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (- (sinh x) (cosh x)) (tanh x))"
  :precision binary64
  (+ (- (sinh x) (cosh x)) (tanh x)))