Average Error: 0.0 → 0.0
Time: 17.6s
Precision: 64
Internal Precision: 320
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log_* (1 + \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}} - 1\right))\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]

  2. Initial simplification0.0

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

  4. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\log_* (1 + (e^{\frac{1}{x - 1} + \frac{x}{x + 1}} - 1)^*)}\]
  5. Using strategy rm

  6. Applied expm1-udef0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 17.6s)Debug logProfile

herbie shell --seed 2018230 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))