Average Error: 0.0 → 0.0
Time: 8.2s
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 r2591676 = 1.0;
        double r2591677 = x;
        double r2591678 = r2591676 / r2591677;
        double r2591679 = r2591677 * r2591677;
        double r2591680 = r2591676 - r2591679;
        double r2591681 = sqrt(r2591680);
        double r2591682 = r2591681 / r2591677;
        double r2591683 = r2591678 + r2591682;
        double r2591684 = log(r2591683);
        return r2591684;
}
↓
double f(double x) {
        double r2591685 = 1.0;
        double r2591686 = x;
        double r2591687 = r2591685 / r2591686;
        double r2591688 = r2591686 * r2591686;
        double r2591689 = r2591685 - r2591688;
        double r2591690 = sqrt(r2591689);
        double r2591691 = r2591690 / r2591686;
        double r2591692 = r2591687 + r2591691;
        double r2591693 = log(r2591692);
        return r2591693;
}

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

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))