Average Error: 0.0 → 0.0
Time: 26.5s
Precision: 64
Internal Precision: 320
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\sqrt{e^{\log \left(1 - x \cdot x\right)}}}{x}\right)\]

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-exp-log0.0

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

Runtime

Time bar (total: 26.5s)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))))