Input Error: 34.6b
Output Error: 0.1b
Time: 15.4s
Precision: 64b
Ground Truth: 128b
\[\left(e^{x} - 2\right) + e^{-x}\]
⬇
\[\frac{1}{360} \cdot {x}^{6} + \left(\frac{1}{12} \cdot {x}^{4} + {x}^2\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 34.6b

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

  2. Applied taylor 0.1b

    \[\leadsto \frac{1}{360} \cdot {x}^{6} + \left(\frac{1}{12} \cdot {x}^{4} + {x}^2\right)\]

  3. Taylor expanded around 0 0.1b

    \[\leadsto \color{blue}{\frac{1}{360} \cdot {x}^{6} + \left(\frac{1}{12} \cdot {x}^{4} + {x}^2\right)}\]
  4. Removed slow pow expressions

Runtime

Total time: 15.4s Debug log

herbie --seed '#(829581554 979068679 1633572420 3492881794 3238434126 3740004167)'
(FPCore (x)
  :name "NMSE problem 3.3.7"
  
  :target
  (* 4 (sqr (sinh (/ x 2))))(+ (- (exp x) 2) (exp (- x))))