Average Error: 0.0 → 0.0
Time: 9.9s
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 r1984661 = 1.0;
        double r1984662 = x;
        double r1984663 = r1984661 / r1984662;
        double r1984664 = r1984662 * r1984662;
        double r1984665 = r1984661 - r1984664;
        double r1984666 = sqrt(r1984665);
        double r1984667 = r1984666 / r1984662;
        double r1984668 = r1984663 + r1984667;
        double r1984669 = log(r1984668);
        return r1984669;
}
↓
double f(double x) {
        double r1984670 = 1.0;
        double r1984671 = x;
        double r1984672 = r1984670 / r1984671;
        double r1984673 = r1984671 * r1984671;
        double r1984674 = r1984670 - r1984673;
        double r1984675 = sqrt(r1984674);
        double r1984676 = r1984675 / r1984671;
        double r1984677 = r1984672 + r1984676;
        double r1984678 = log(r1984677);
        return r1984678;
}

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 2019149 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))