Error

Derivation

1. Split input into 2 regimes

2. if x < -8.80985298240059e+48 or 126507.6676441063 < x

   1. Initial program 59.8

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

   3. Applied frac-sub61.7

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

   4. Taylor expanded around inf 0.3

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

   5. Simplified0.0

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

   if -8.80985298240059e+48 < x < 126507.6676441063

   1. Initial program 3.3

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

   3. Applied frac-sub3.3

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

   4. Taylor expanded around 0 0.0

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

   5. Simplified0.0

      \[\leadsto \frac{\color{blue}{(-3 \cdot x + -1)_*}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.80985298240059 \cdot 10^{+48} \lor \neg \left(x \le 126507.6676441063\right):\\ \;\;\;\;(\left(\frac{-1}{x \cdot x}\right) \cdot \left(\frac{3}{x}\right) + \left(\frac{-1}{x \cdot x} - \frac{3}{x}\right))_*\\ \mathbf{else}:\\ \;\;\;\;\frac{(-3 \cdot x + -1)_*}{\left(1 + x\right) \cdot \left(x - 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))

Details

Time bar (total: 2.0m)Debug log