Error

Derivation

1. Initial program 31.1

   \[\log \left(x + \sqrt{x \cdot x - 1}\right)\]

2. Initial simplification31.1

   \[\leadsto \log \left(x + \sqrt{(x \cdot x + -1)_*}\right)\]

3. Taylor expanded around inf 0.2

   \[\leadsto \log \color{blue}{\left(2 \cdot x - \left(\frac{1}{8} \cdot \frac{1}{{x}^{3}} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)}\]

4. Simplified0.2

   \[\leadsto \log \color{blue}{\left((2 \cdot x + \left(\frac{\frac{-1}{2}}{x}\right))_* - \frac{\frac{\frac{1}{8}}{x}}{x \cdot x}\right)}\]

5. Final simplification0.2

   \[\leadsto \log \left((2 \cdot x + \left(\frac{\frac{-1}{2}}{x}\right))_* - \frac{\frac{\frac{1}{8}}{x}}{x \cdot x}\right)\]

Runtime

Time bar (total: 18.6s)Debug logProfile

herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-cosine"
  (log (+ x (sqrt (- (* x x) 1)))))