Average Error: 14.5 → 0.1
Time: 2.6m
Precision: 64
Internal Precision: 832
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[-\frac{\frac{1 + 1}{1 + x}}{x - 1}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  4. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed 2018215 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))