Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{\frac{x}{\sqrt{1 - x \cdot x}}} + \frac{1}{x}\right)\]
\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)
↓
\log \left(\frac{1}{\frac{x}{\sqrt{1 - x \cdot x}}} + \frac{1}{x}\right)
double f(double x) {
        double r2753821 = 1.0;
        double r2753822 = x;
        double r2753823 = r2753821 / r2753822;
        double r2753824 = r2753822 * r2753822;
        double r2753825 = r2753821 - r2753824;
        double r2753826 = sqrt(r2753825);
        double r2753827 = r2753826 / r2753822;
        double r2753828 = r2753823 + r2753827;
        double r2753829 = log(r2753828);
        return r2753829;
}
↓
double f(double x) {
        double r2753830 = 1.0;
        double r2753831 = x;
        double r2753832 = r2753831 * r2753831;
        double r2753833 = r2753830 - r2753832;
        double r2753834 = sqrt(r2753833);
        double r2753835 = r2753831 / r2753834;
        double r2753836 = r2753830 / r2753835;
        double r2753837 = r2753830 / r2753831;
        double r2753838 = r2753836 + r2753837;
        double r2753839 = log(r2753838);
        return r2753839;
}

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. Using strategy rm

  3. Applied clear-num0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))