Average Error: 14.2 → 0.1
Time: 4.1s
Precision: 64
Internal precision: 896
\[\frac{1}{x + 1} - \frac{1}{x}\]
⬇
\[\frac{\frac{-1}{1 + x}}{x}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub 13.6

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

  4. Applied simplify 13.6

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

  5. Applied taylor 13.6

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

  6. Taylor expanded around 0 13.6

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

  7. Applied simplify 0.1

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

Runtime

Time bar (total: 4.1s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067901057 3396600083 3715501224 3126139233 3908045574 1593683916)'
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))