Average Error: 0.0 → 0.0
Time: 55.8s
Precision: 64
Internal Precision: 384
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\log \left(e^{\sqrt{1 - x \cdot x}}\right)}{x}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

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

Runtime

Time bar (total: 55.8s)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))