Average Error: 14.5 → 0.1
Time: 19.1s
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 14.5

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

  3. Applied frac-sub13.8

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

  4. Applied simplify13.8

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

  5. Taylor expanded around 0 13.8

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

  6. Applied simplify0.1

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

Runtime

Time bar (total: 19.1s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))