Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{\sqrt{1 - x \cdot x}}{x} + \frac{1}{x}\right)\]
\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)
↓
\log \left(\frac{\sqrt{1 - x \cdot x}}{x} + \frac{1}{x}\right)
double f(double x) {
        double r3385682 = 1.0;
        double r3385683 = x;
        double r3385684 = r3385682 / r3385683;
        double r3385685 = r3385683 * r3385683;
        double r3385686 = r3385682 - r3385685;
        double r3385687 = sqrt(r3385686);
        double r3385688 = r3385687 / r3385683;
        double r3385689 = r3385684 + r3385688;
        double r3385690 = log(r3385689);
        return r3385690;
}
↓
double f(double x) {
        double r3385691 = 1.0;
        double r3385692 = x;
        double r3385693 = r3385692 * r3385692;
        double r3385694 = r3385691 - r3385693;
        double r3385695 = sqrt(r3385694);
        double r3385696 = r3385695 / r3385692;
        double r3385697 = r3385691 / r3385692;
        double r3385698 = r3385696 + r3385697;
        double r3385699 = log(r3385698);
        return r3385699;
}

Error

Bits error versus x

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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

    \[\leadsto \log \left(\frac{\sqrt{1 - x \cdot x}}{x} + \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))