Average Error: 29.6 → 0.3
Time: 55.5s
Precision: 64
Internal Precision: 1408
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{1}{x + 1} \cdot \frac{\left(\left(-x\right) + \left(-x\right)\right) - \left(x + 1\right)}{x - 1}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.6

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

  3. Applied frac-sub30.4

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

  5. Applied distribute-lft-in30.4

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

  6. Applied associate--r+28.4

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

  7. Applied simplify27.0

    \[\leadsto \frac{\color{blue}{x \cdot \left(x - \left(x + 2\right)\right)} - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity27.0

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(x - \left(x + 2\right)\right) - \left(x + 1\right) \cdot 1\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  10. Applied times-frac25.3

    \[\leadsto \color{blue}{\frac{1}{x + 1} \cdot \frac{x \cdot \left(x - \left(x + 2\right)\right) - \left(x + 1\right) \cdot 1}{x - 1}}\]

  11. Applied simplify0.3

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

Runtime

Time bar (total: 55.5s)Debug log

herbie shell --seed '#(4187538376 1520029361 2786545844 1568991248 4244367449 2261141537)' 
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))