Average Error: 0.0 → 0.0
Time: 14.6s
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 r5647349 = 1.0;
        double r5647350 = x;
        double r5647351 = r5647349 / r5647350;
        double r5647352 = r5647350 * r5647350;
        double r5647353 = r5647349 - r5647352;
        double r5647354 = sqrt(r5647353);
        double r5647355 = r5647354 / r5647350;
        double r5647356 = r5647351 + r5647355;
        double r5647357 = log(r5647356);
        return r5647357;
}
↓
double f(double x) {
        double r5647358 = 1.0;
        double r5647359 = x;
        double r5647360 = r5647358 / r5647359;
        double r5647361 = r5647359 * r5647359;
        double r5647362 = r5647358 - r5647361;
        double r5647363 = sqrt(r5647362);
        double r5647364 = r5647363 / r5647359;
        double r5647365 = r5647360 + r5647364;
        double r5647366 = log(r5647365);
        return r5647366;
}

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 2019173 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))