Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
Internal Precision: 320
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\log_* (1 + (e^{\sqrt{1 - x \cdot x}} - 1)^*)}{x}\right)\]

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 log1p-expm1-u0.0

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

Runtime

Time bar (total: 22.7s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))