Error

Derivation

1. Split input into 2 regimes

2. if x < -23.06066892739458 or 2.3990114478591055e-05 < x

   1. Initial program 28.8

      \[\frac{1}{x + 1} - \frac{1}{x}\]

   2. Initial simplification28.8

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

   4. Applied frac-sub27.7

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

   5. Simplified0.7

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

   6. Simplified0.7

      \[\leadsto \frac{-1}{\color{blue}{(x \cdot x + x)_*}}\]
   7. Using strategy rm

   8. Applied add-sqr-sqrt0.7

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

   9. Applied associate-/r*0.7

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

   if -23.06066892739458 < x < 2.3990114478591055e-05

   1. Initial program 0.0

      \[\frac{1}{x + 1} - \frac{1}{x}\]

   2. Initial simplification0.0

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

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -23.06066892739458 \lor \neg \left(x \le 2.3990114478591055 \cdot 10^{-05}\right):\\ \;\;\;\;\frac{\frac{-1}{\sqrt{(x \cdot x + x)_*}}}{\sqrt{(x \cdot x + x)_*}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} - \frac{1}{x}\\ \end{array}\]

Runtime

Time bar (total: 13.7s)Debug logProfile

herbie shell --seed 2018353 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))