Average Error: 0.0 → 0.0
Time: 12.8s
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 r3280626 = 1.0;
        double r3280627 = x;
        double r3280628 = r3280626 / r3280627;
        double r3280629 = r3280627 * r3280627;
        double r3280630 = r3280626 - r3280629;
        double r3280631 = sqrt(r3280630);
        double r3280632 = r3280631 / r3280627;
        double r3280633 = r3280628 + r3280632;
        double r3280634 = log(r3280633);
        return r3280634;
}
↓
double f(double x) {
        double r3280635 = 1.0;
        double r3280636 = x;
        double r3280637 = r3280635 / r3280636;
        double r3280638 = r3280636 * r3280636;
        double r3280639 = r3280635 - r3280638;
        double r3280640 = sqrt(r3280639);
        double r3280641 = r3280640 / r3280636;
        double r3280642 = r3280637 + r3280641;
        double r3280643 = log(r3280642);
        return r3280643;
}

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))))