Average Error: 0.0 → 0.0
Time: 13.5s
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 r3631031 = 1.0;
        double r3631032 = x;
        double r3631033 = r3631031 / r3631032;
        double r3631034 = r3631032 * r3631032;
        double r3631035 = r3631031 - r3631034;
        double r3631036 = sqrt(r3631035);
        double r3631037 = r3631036 / r3631032;
        double r3631038 = r3631033 + r3631037;
        double r3631039 = log(r3631038);
        return r3631039;
}
↓
double f(double x) {
        double r3631040 = 1.0;
        double r3631041 = x;
        double r3631042 = r3631040 / r3631041;
        double r3631043 = r3631041 * r3631041;
        double r3631044 = r3631040 - r3631043;
        double r3631045 = sqrt(r3631044);
        double r3631046 = r3631045 / r3631041;
        double r3631047 = r3631042 + r3631046;
        double r3631048 = log(r3631047);
        return r3631048;
}

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 2019163 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))