Average Error: 0.0 → 0.0
Time: 6.6s
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 r2456377 = 1.0;
        double r2456378 = x;
        double r2456379 = r2456377 / r2456378;
        double r2456380 = r2456378 * r2456378;
        double r2456381 = r2456377 - r2456380;
        double r2456382 = sqrt(r2456381);
        double r2456383 = r2456382 / r2456378;
        double r2456384 = r2456379 + r2456383;
        double r2456385 = log(r2456384);
        return r2456385;
}
↓
double f(double x) {
        double r2456386 = 1.0;
        double r2456387 = x;
        double r2456388 = r2456386 / r2456387;
        double r2456389 = r2456387 * r2456387;
        double r2456390 = r2456386 - r2456389;
        double r2456391 = sqrt(r2456390);
        double r2456392 = r2456391 / r2456387;
        double r2456393 = r2456388 + r2456392;
        double r2456394 = log(r2456393);
        return r2456394;
}

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))))