Error

Try it out

Derivation

1. Split input into 2 regimes

2. if x < -13083.266728584855 or 11234.078675704557 < x

   1. Initial program 59.4

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
   2. Using strategy rm

   3. Applied add-log-exp59.4

      \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x + 1} - \frac{x + 1}{x - 1}}\right)}\]
   4. Using strategy rm

   5. Applied rem-log-exp59.4

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{x + 1}{x - 1}}\]

   6. Taylor expanded around -inf 0.3

      \[\leadsto \color{blue}{-\left(3 \cdot \frac{1}{{x}^{3}} + \left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)\right)}\]

   7. Simplified0.0

      \[\leadsto \color{blue}{\left(\frac{-3}{x} - \frac{1}{x \cdot x}\right) + \frac{\frac{-3}{x}}{x \cdot x}}\]

   if -13083.266728584855 < x < 11234.078675704557

   1. Initial program 0.1

      \[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
   2. Using strategy rm

   3. Applied add-log-exp0.1

      \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x + 1} - \frac{x + 1}{x - 1}}\right)}\]
   4. Using strategy rm

   5. Applied rem-log-exp0.1

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{x + 1}{x - 1}}\]
3. Recombined 2 regimes into one program.

4. Final simplification0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -13083.266728584855 \lor \neg \left(x \le 11234.078675704557\right):\\ \;\;\;\;\left(\frac{-3}{x} - \frac{1}{x \cdot x}\right) + \frac{\frac{-3}{x}}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} - \frac{1 + x}{x - 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))

Details

Time bar (total: 12.7s)Debug log