\[\left(e^{x} - 2\right) + e^{-x}\]
Test:
NMSE problem 3.3.7
Bits:
128 bits
Bits error versus x
Time: 9.8 s
Input Error: 13.8
Output Error: 1.0
Log: ⚲
Profile: 🕒
\({x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \log \left(e^{\frac{1}{360} \cdot {x}^{6}}\right)\right)\)
  1. Started with
    \[\left(e^{x} - 2\right) + e^{-x}\]
    13.8
  2. Applied taylor to get
    \[\left(e^{x} - 2\right) + e^{-x} \leadsto {x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)\]
    0.0
  3. Taylor expanded around 0 to get
    \[\color{red}{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)} \leadsto \color{blue}{{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)}\]
    0.0
  4. Using strategy rm
    0.0
  5. Applied add-log-exp to get
    \[{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \color{red}{\frac{1}{360} \cdot {x}^{6}}\right) \leadsto {x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \color{blue}{\log \left(e^{\frac{1}{360} \cdot {x}^{6}}\right)}\right)\]
    1.0
  6. Removed slow pow expressions

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.3.7"
  (+ (- (exp x) 2) (exp (- x)))
  #:target
  (* 4 (sqr (sinh (/ x 2)))))