Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
\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 r505238 = 1.0;
        double r505239 = x;
        double r505240 = r505238 / r505239;
        double r505241 = r505239 * r505239;
        double r505242 = r505238 - r505241;
        double r505243 = sqrt(r505242);
        double r505244 = r505243 / r505239;
        double r505245 = r505240 + r505244;
        double r505246 = log(r505245);
        return r505246;
}
↓
double f(double x) {
        double r505247 = 1.0;
        double r505248 = x;
        double r505249 = r505247 / r505248;
        double r505250 = r505248 * r505248;
        double r505251 = r505247 - r505250;
        double r505252 = sqrt(r505251);
        double r505253 = r505252 / r505248;
        double r505254 = r505249 + r505253;
        double r505255 = log(r505254);
        return r505255;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019128 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))