Average Error: 34.2 → 0.1
Time: 10.1s
Precision: 64
Internal precision: 1408
\[\left(e^{x} - 2\right) + e^{-x}\]
⬇
\[{x}^2 + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 34.2

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

  2. Applied taylor 0.1

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

  3. Taylor expanded around 0 0.1

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

Runtime

Time bar (total: 10.1s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x)
  :name "NMSE problem 3.3.7"
  (+ (- (exp x) 2) (exp (- x))))