Average Error: 13.9 → 0.1
Time: 3.0m
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

Derivation

  1. Initial program 13.9

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

  3. Applied frac-sub13.4

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

  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 associate-/r*0.1

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

  7. Applied simplify0.1

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

Runtime

Time bar (total: 3.0m)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))