Average Error: 0.0 → 0.0
Time: 6.4s
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 r2849399 = 1.0;
        double r2849400 = x;
        double r2849401 = r2849399 / r2849400;
        double r2849402 = r2849400 * r2849400;
        double r2849403 = r2849399 - r2849402;
        double r2849404 = sqrt(r2849403);
        double r2849405 = r2849404 / r2849400;
        double r2849406 = r2849401 + r2849405;
        double r2849407 = log(r2849406);
        return r2849407;
}
↓
double f(double x) {
        double r2849408 = 1.0;
        double r2849409 = x;
        double r2849410 = r2849408 / r2849409;
        double r2849411 = r2849409 * r2849409;
        double r2849412 = r2849408 - r2849411;
        double r2849413 = sqrt(r2849412);
        double r2849414 = r2849413 / r2849409;
        double r2849415 = r2849410 + r2849414;
        double r2849416 = log(r2849415);
        return r2849416;
}

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 2019172 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))