Average Error: 0.1 → 0.1
Time: 5.9s
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 r36521 = 1.0;
        double r36522 = x;
        double r36523 = r36521 / r36522;
        double r36524 = r36522 * r36522;
        double r36525 = r36521 - r36524;
        double r36526 = sqrt(r36525);
        double r36527 = r36526 / r36522;
        double r36528 = r36523 + r36527;
        double r36529 = log(r36528);
        return r36529;
}
↓
double f(double x) {
        double r36530 = 1.0;
        double r36531 = x;
        double r36532 = r36530 / r36531;
        double r36533 = r36531 * r36531;
        double r36534 = r36530 - r36533;
        double r36535 = sqrt(r36534);
        double r36536 = r36535 / r36531;
        double r36537 = r36532 + r36536;
        double r36538 = log(r36537);
        return r36538;
}

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 2019196 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))