Average Error: 0.0 → 0.0
Time: 2.4s
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 r67071 = 1.0;
        double r67072 = x;
        double r67073 = r67071 / r67072;
        double r67074 = r67072 * r67072;
        double r67075 = r67071 - r67074;
        double r67076 = sqrt(r67075);
        double r67077 = r67076 / r67072;
        double r67078 = r67073 + r67077;
        double r67079 = log(r67078);
        return r67079;
}
↓
double f(double x) {
        double r67080 = 1.0;
        double r67081 = x;
        double r67082 = r67080 / r67081;
        double r67083 = r67081 * r67081;
        double r67084 = r67080 - r67083;
        double r67085 = sqrt(r67084);
        double r67086 = r67085 / r67081;
        double r67087 = r67082 + r67086;
        double r67088 = log(r67087);
        return r67088;
}

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 2020002 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  :precision binary64
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))