Average Error: 0.0 → 0.0
Time: 11.8s
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 r2145221 = 1.0;
        double r2145222 = x;
        double r2145223 = r2145221 / r2145222;
        double r2145224 = r2145222 * r2145222;
        double r2145225 = r2145221 - r2145224;
        double r2145226 = sqrt(r2145225);
        double r2145227 = r2145226 / r2145222;
        double r2145228 = r2145223 + r2145227;
        double r2145229 = log(r2145228);
        return r2145229;
}
↓
double f(double x) {
        double r2145230 = 1.0;
        double r2145231 = x;
        double r2145232 = r2145230 / r2145231;
        double r2145233 = r2145231 * r2145231;
        double r2145234 = r2145230 - r2145233;
        double r2145235 = sqrt(r2145234);
        double r2145236 = r2145235 / r2145231;
        double r2145237 = r2145232 + r2145236;
        double r2145238 = log(r2145237);
        return r2145238;
}

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 2019135 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))