Average Error: 0.0 → 0.0
Time: 5.4s
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 r63182 = 1.0;
        double r63183 = x;
        double r63184 = r63182 / r63183;
        double r63185 = r63183 * r63183;
        double r63186 = r63182 - r63185;
        double r63187 = sqrt(r63186);
        double r63188 = r63187 / r63183;
        double r63189 = r63184 + r63188;
        double r63190 = log(r63189);
        return r63190;
}
↓
double f(double x) {
        double r63191 = 1.0;
        double r63192 = x;
        double r63193 = r63191 / r63192;
        double r63194 = r63192 * r63192;
        double r63195 = r63191 - r63194;
        double r63196 = sqrt(r63195);
        double r63197 = r63196 / r63192;
        double r63198 = r63193 + r63197;
        double r63199 = log(r63198);
        return r63199;
}

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 2019354 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  :precision binary64
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))