Average Error: 0.0 → 0.0
Time: 28.8s
Precision: 64
Internal Precision: 384
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{x}{x + 1} + \frac{1}{x - 1}}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied add-log-exp0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied sum-log0.0

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

  6. Applied simplify0.0

    \[\leadsto \log \color{blue}{\left(e^{\frac{x}{x + 1} + \frac{1}{x - 1}}\right)}\]
  7. Removed slow pow expressions.

Runtime

Time bar (total: 28.8s)Debug log

herbie shell --seed '#(2961832646 520228599 1275628947 1047906571 1774476463 2890033825)' 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))