Average Error: 0.8 → 0.3
Time: 6.7s
Precision: 64
Internal precision: 384
\[\frac{x - 1}{x \cdot x - 1}\]
\[\frac{1}{x + 1} \cdot 1\]

Error

Bits error versus x

Derivation

  1. Initial program 0.8

    \[\frac{x - 1}{x \cdot x - 1}\]
  2. Using strategy rm
  3. Applied square-unmult 0.8

    \[\leadsto \frac{x - 1}{\color{blue}{{x}^2} - 1}\]
  4. Applied difference-of-sqr-1 0.5

    \[\leadsto \frac{x - 1}{\color{blue}{\left(x + 1\right) \cdot \left(x - 1\right)}}\]
  5. Applied *-un-lft-identity 0.5

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - 1\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  6. Applied times-frac 0.3

    \[\leadsto \color{blue}{\frac{1}{x + 1} \cdot \frac{x - 1}{x - 1}}\]
  7. Applied simplify 0.3

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

Runtime

Time bar (total: 6.7s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x)
  :name "test05_nonlin1, r4"
  :pre (< 1.00001 x 2)
  (/ (- x 1) (- (* x x) 1)))