Average Error: 0.0 → 0.0
Time: 4.8s
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 r938039 = 1.0;
        double r938040 = x;
        double r938041 = r938039 / r938040;
        double r938042 = r938040 * r938040;
        double r938043 = r938039 - r938042;
        double r938044 = sqrt(r938043);
        double r938045 = r938044 / r938040;
        double r938046 = r938041 + r938045;
        double r938047 = log(r938046);
        return r938047;
}
↓
double f(double x) {
        double r938048 = 1.0;
        double r938049 = x;
        double r938050 = r938048 / r938049;
        double r938051 = r938049 * r938049;
        double r938052 = r938048 - r938051;
        double r938053 = sqrt(r938052);
        double r938054 = r938053 / r938049;
        double r938055 = r938050 + r938054;
        double r938056 = log(r938055);
        return r938056;
}

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 2019154 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))