Average Error: 14.7 → 0.1
Time: 1.3m
Precision: 64
Internal Precision: 832
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{\left(-1\right) - 1}{x + 1}}{x - 1}\]

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  2. Initial simplification14.7

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

  4. Applied frac-sub14.0

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

  5. Simplified0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2018227 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))