Average Error: 14.3 → 0.1
Time: 6.2s
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 14.3

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

  3. Applied frac-sub 13.7

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

  4. Applied simplify 13.7

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

  6. Applied associate-/r* 13.7

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

  7. Applied simplify 0.1

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

  8. Applied simplify 0.1

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

Runtime

Time bar (total: 6.2s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x)
  :name "NMSE problem 3.3.1"
  :pre (!= x 0)
  (- (/ 1 (+ x 1)) (/ 1 x)))