Average Error: 0.0 → 0.0
Time: 21.1s
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 r2337339 = 1.0;
        double r2337340 = x;
        double r2337341 = r2337339 / r2337340;
        double r2337342 = r2337340 * r2337340;
        double r2337343 = r2337339 - r2337342;
        double r2337344 = sqrt(r2337343);
        double r2337345 = r2337344 / r2337340;
        double r2337346 = r2337341 + r2337345;
        double r2337347 = log(r2337346);
        return r2337347;
}
↓
double f(double x) {
        double r2337348 = 1.0;
        double r2337349 = x;
        double r2337350 = r2337348 / r2337349;
        double r2337351 = r2337349 * r2337349;
        double r2337352 = r2337348 - r2337351;
        double r2337353 = sqrt(r2337352);
        double r2337354 = r2337353 / r2337349;
        double r2337355 = r2337350 + r2337354;
        double r2337356 = log(r2337355);
        return r2337356;
}

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 2019144 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))