Average Error: 0.0 → 0.0
Time: 5.6s
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 r2865853 = 1.0;
        double r2865854 = x;
        double r2865855 = r2865853 / r2865854;
        double r2865856 = r2865854 * r2865854;
        double r2865857 = r2865853 - r2865856;
        double r2865858 = sqrt(r2865857);
        double r2865859 = r2865858 / r2865854;
        double r2865860 = r2865855 + r2865859;
        double r2865861 = log(r2865860);
        return r2865861;
}
↓
double f(double x) {
        double r2865862 = 1.0;
        double r2865863 = x;
        double r2865864 = r2865862 / r2865863;
        double r2865865 = r2865863 * r2865863;
        double r2865866 = r2865862 - r2865865;
        double r2865867 = sqrt(r2865866);
        double r2865868 = r2865867 / r2865863;
        double r2865869 = r2865864 + r2865868;
        double r2865870 = log(r2865869);
        return r2865870;
}

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 2019171 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))