Average Error: 0.0 → 0.0
Time: 5.7s
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 r1339310 = 1.0;
        double r1339311 = x;
        double r1339312 = r1339310 / r1339311;
        double r1339313 = r1339311 * r1339311;
        double r1339314 = r1339310 - r1339313;
        double r1339315 = sqrt(r1339314);
        double r1339316 = r1339315 / r1339311;
        double r1339317 = r1339312 + r1339316;
        double r1339318 = log(r1339317);
        return r1339318;
}
↓
double f(double x) {
        double r1339319 = 1.0;
        double r1339320 = x;
        double r1339321 = r1339319 / r1339320;
        double r1339322 = r1339320 * r1339320;
        double r1339323 = r1339319 - r1339322;
        double r1339324 = sqrt(r1339323);
        double r1339325 = r1339324 / r1339320;
        double r1339326 = r1339321 + r1339325;
        double r1339327 = log(r1339326);
        return r1339327;
}

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 2019172 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))