Average Error: 14.4 → 0.1
Time: 1.7m
Precision: 64
Internal Precision: 832
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{1}{x + 1} \cdot \frac{\left(-1\right) + \left(-1\right)}{x - 1}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Applied simplify0.4

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

  6. Applied *-un-lft-identity0.4

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

  7. Applied times-frac0.1

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))