Average Error: 0.0 → 0.0
Time: 6.9s
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 r6818513 = 1.0;
        double r6818514 = x;
        double r6818515 = r6818513 / r6818514;
        double r6818516 = r6818514 * r6818514;
        double r6818517 = r6818513 - r6818516;
        double r6818518 = sqrt(r6818517);
        double r6818519 = r6818518 / r6818514;
        double r6818520 = r6818515 + r6818519;
        double r6818521 = log(r6818520);
        return r6818521;
}
↓
double f(double x) {
        double r6818522 = 1.0;
        double r6818523 = x;
        double r6818524 = r6818522 / r6818523;
        double r6818525 = r6818523 * r6818523;
        double r6818526 = r6818522 - r6818525;
        double r6818527 = sqrt(r6818526);
        double r6818528 = r6818527 / r6818523;
        double r6818529 = r6818524 + r6818528;
        double r6818530 = log(r6818529);
        return r6818530;
}

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 2019107 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))