Average Error: 13.8 → 0.1
Time: 4.0s
Precision: 64
Internal precision: 896
\[\frac{1}{x + 1} - \frac{1}{x}\]
⬇
\[\frac{1}{x + 1} \cdot \frac{-1}{x}\]

Error

Bits error versus x

Derivation

  1. Initial program 13.8

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

  3. Applied frac-sub 13.2

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

  4. Applied simplify 13.2

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

  6. Applied *-un-lft-identity 13.2

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

  7. Applied times-frac 13.2

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

  8. Applied simplify 0.1

    \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\frac{0 - 1}{x}}\]

  9. Applied simplify 0.1

    \[\leadsto \frac{1}{x + 1} \cdot \frac{\color{blue}{-1}}{x}\]
  10. Removed slow pow expressions

Runtime

Time bar (total: 4.0s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))