Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
\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 r3021350 = 1.0;
        double r3021351 = x;
        double r3021352 = r3021350 / r3021351;
        double r3021353 = r3021351 * r3021351;
        double r3021354 = r3021350 - r3021353;
        double r3021355 = sqrt(r3021354);
        double r3021356 = r3021355 / r3021351;
        double r3021357 = r3021352 + r3021356;
        double r3021358 = log(r3021357);
        return r3021358;
}
↓
double f(double x) {
        double r3021359 = 1.0;
        double r3021360 = x;
        double r3021361 = r3021359 / r3021360;
        double r3021362 = r3021360 * r3021360;
        double r3021363 = r3021359 - r3021362;
        double r3021364 = sqrt(r3021363);
        double r3021365 = r3021364 / r3021360;
        double r3021366 = r3021361 + r3021365;
        double r3021367 = log(r3021366);
        return r3021367;
}

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 2019163 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))