Average Error: 14.2 → 0.1
Time: 45.0s
Precision: 64
Internal Precision: 896
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[{\left(\frac{\frac{-2}{x + 1}}{x - 1}\right)}^{1}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.2

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

  3. Applied flip--29.1

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

  4. Applied associate-/r/29.2

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

  5. Applied flip-+14.3

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

  6. Applied associate-/r/14.2

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

  7. Applied distribute-lft-out--13.6

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

  8. Applied simplify0.5

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\left(\left(0 - 1\right) - 1\right)}\]
  9. Using strategy rm

  10. Applied difference-of-squares0.5

    \[\leadsto \frac{1}{\color{blue}{\left(x + 1\right) \cdot \left(x - 1\right)}} \cdot \left(\left(0 - 1\right) - 1\right)\]

  11. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{x + 1}}{x - 1}} \cdot \left(\left(0 - 1\right) - 1\right)\]
  12. Using strategy rm

  13. Applied pow10.1

    \[\leadsto \frac{\frac{1}{x + 1}}{x - 1} \cdot \color{blue}{{\left(\left(0 - 1\right) - 1\right)}^{1}}\]

  14. Applied pow10.1

    \[\leadsto \color{blue}{{\left(\frac{\frac{1}{x + 1}}{x - 1}\right)}^{1}} \cdot {\left(\left(0 - 1\right) - 1\right)}^{1}\]

  15. Applied pow-prod-down0.1

    \[\leadsto \color{blue}{{\left(\frac{\frac{1}{x + 1}}{x - 1} \cdot \left(\left(0 - 1\right) - 1\right)\right)}^{1}}\]

  16. Applied simplify0.1

    \[\leadsto {\color{blue}{\left(\frac{\frac{-2}{x + 1}}{x - 1}\right)}}^{1}\]
  17. Removed slow pow expressions.

Runtime

Time bar (total: 45.0s)Debug log

herbie shell --seed '#(2961832646 520228599 1275628947 1047906571 1774476463 2890033825)' 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))