Average Error: 14.3 → 0.4
Time: 1.4m
Precision: 64
Internal Precision: 896
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\left(-1\right) - 1}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Applied simplify0.4

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

  5. Applied simplify0.4

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))