Average Error: 0.0 → 0.0
Time: 16.6s
Precision: 64
Internal Precision: 384
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{(e^{\log_* (1 + \sqrt{1 - x \cdot x})} - 1)^*}{x}\right)\]

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 expm1-log1p-u0.0

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

Runtime

Time bar (total: 16.6s)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))