Average Error: 0.0 → 0.0
Time: 12.1s
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 r3095619 = 1.0;
        double r3095620 = x;
        double r3095621 = r3095619 / r3095620;
        double r3095622 = r3095620 * r3095620;
        double r3095623 = r3095619 - r3095622;
        double r3095624 = sqrt(r3095623);
        double r3095625 = r3095624 / r3095620;
        double r3095626 = r3095621 + r3095625;
        double r3095627 = log(r3095626);
        return r3095627;
}
↓
double f(double x) {
        double r3095628 = 1.0;
        double r3095629 = x;
        double r3095630 = r3095629 * r3095629;
        double r3095631 = r3095628 - r3095630;
        double r3095632 = sqrt(r3095631);
        double r3095633 = r3095632 / r3095629;
        double r3095634 = r3095628 / r3095629;
        double r3095635 = r3095633 + r3095634;
        double r3095636 = log(r3095635);
        return r3095636;
}

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

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

Reproduce

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