Average Error: 0.0 → 0.0
Time: 14.6s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log_* (1 + (e^{\frac{1}{x - 1} + \frac{x}{x + 1}} - 1)^*)\]

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 log1p-expm1-u0.0

    \[\leadsto \color{blue}{\log_* (1 + (e^{\frac{1}{x - 1} + \frac{x}{x + 1}} - 1)^*)}\]

  4. Final simplification0.0

    \[\leadsto \log_* (1 + (e^{\frac{1}{x - 1} + \frac{x}{x + 1}} - 1)^*)\]

Reproduce

herbie shell --seed 2019093 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))