Error: 34.3 → 0.1
Time: 15.4s
Precision: 64
Ground Truth: 128
\[\left(e^{x} - 2\right) + e^{-x}\]
⬇
\[\left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right) + {x}^2\]

Error

Bits error versus x

Derivation

  1. Initial program 34.3

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

  2. Applied taylor 0.1

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\frac{1}{12} \cdot {x}^{4} + \left(\frac{1}{360} \cdot {x}^{6} + {x}^2\right)}\]
  4. Using strategy rm

  5. Applied associate-+r+ 0.1

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

Runtime

Total time: 15.4s Debug log

Please report a bug with the following info:

herbie --seed '#(2665161799 3817376577 1275982065 4119664522 352114338 3907374372)'
(FPCore (x)
  :name "NMSE problem 3.3.7"
  
  :target
  (* 4 (sqr (sinh (/ x 2))))(+ (- (exp x) 2) (exp (- x))))