Average Error: 34.5 → 0.2
Time: 52.2s
Precision: 64
Ground Truth: 128
\[\left(e^{x} - 2\right) + e^{-x}\]
⬇
\[\left(\frac{1}{360} \cdot {x}^{6} + \frac{1}{12} \cdot {x}^{4}\right) + {x}^2\]

Error

Bits error versus x

Target

Original34.5
Comparison8.9
Herbie0.2
\[ 4 \cdot {\left(\sinh \left(\frac{x}{2}\right)\right)}^2 \]

Derivation

  1. Initial program 34.5

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

  2. Applied taylor 0.2

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

  3. Taylor expanded around 0 0.2

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

  5. Applied associate-+r+ 0.2

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

Runtime

Total time: 52.2s Debug log

Please include this information when filing a bug report:

herbie --seed '#(1243583531 2921907369 2562593981 2570033246 2288809704 3678089512)'
(FPCore (x)
  :name "NMSE problem 3.3.7"

  :target
  (* 4 (sqr (sinh (/ x 2))))

  (+ (- (exp x) 2) (exp (- x))))