Average Error: 0.1 → 0.1
Time: 8.3s
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 r2199695 = 1.0;
        double r2199696 = x;
        double r2199697 = r2199695 / r2199696;
        double r2199698 = r2199696 * r2199696;
        double r2199699 = r2199695 - r2199698;
        double r2199700 = sqrt(r2199699);
        double r2199701 = r2199700 / r2199696;
        double r2199702 = r2199697 + r2199701;
        double r2199703 = log(r2199702);
        return r2199703;
}
↓
double f(double x) {
        double r2199704 = 1.0;
        double r2199705 = x;
        double r2199706 = r2199704 / r2199705;
        double r2199707 = r2199705 * r2199705;
        double r2199708 = r2199704 - r2199707;
        double r2199709 = sqrt(r2199708);
        double r2199710 = r2199709 / r2199705;
        double r2199711 = r2199706 + r2199710;
        double r2199712 = log(r2199711);
        return r2199712;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))