Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
double f(double x) {
        double r7602211 = 1.0;
        double r7602212 = x;
        double r7602213 = r7602211 / r7602212;
        double r7602214 = r7602212 * r7602212;
        double r7602215 = r7602211 - r7602214;
        double r7602216 = sqrt(r7602215);
        double r7602217 = r7602216 / r7602212;
        double r7602218 = r7602213 + r7602217;
        double r7602219 = log(r7602218);
        return r7602219;
}
↓
double f(double x) {
        double r7602220 = 1.0;
        double r7602221 = x;
        double r7602222 = r7602220 / r7602221;
        double r7602223 = r7602221 * r7602221;
        double r7602224 = r7602220 - r7602223;
        double r7602225 = sqrt(r7602224);
        double r7602226 = r7602225 / r7602221;
        double r7602227 = r7602222 + r7602226;
        double r7602228 = log(r7602227);
        return r7602228;
}


\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)
↓
\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))