Average Error: 0.0 → 0.0
Time: 9.8s
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 r2506561 = 1.0;
        double r2506562 = x;
        double r2506563 = r2506561 / r2506562;
        double r2506564 = r2506562 * r2506562;
        double r2506565 = r2506561 - r2506564;
        double r2506566 = sqrt(r2506565);
        double r2506567 = r2506566 / r2506562;
        double r2506568 = r2506563 + r2506567;
        double r2506569 = log(r2506568);
        return r2506569;
}
↓
double f(double x) {
        double r2506570 = 1.0;
        double r2506571 = x;
        double r2506572 = r2506570 / r2506571;
        double r2506573 = r2506571 * r2506571;
        double r2506574 = r2506570 - r2506573;
        double r2506575 = sqrt(r2506574);
        double r2506576 = r2506575 / r2506571;
        double r2506577 = r2506572 + r2506576;
        double r2506578 = log(r2506577);
        return r2506578;
}

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 2019165 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))