Average Error: 0.0 → 0.0
Time: 14.0s
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 r2820159 = 1.0;
        double r2820160 = x;
        double r2820161 = r2820159 / r2820160;
        double r2820162 = r2820160 * r2820160;
        double r2820163 = r2820159 - r2820162;
        double r2820164 = sqrt(r2820163);
        double r2820165 = r2820164 / r2820160;
        double r2820166 = r2820161 + r2820165;
        double r2820167 = log(r2820166);
        return r2820167;
}
↓
double f(double x) {
        double r2820168 = 1.0;
        double r2820169 = x;
        double r2820170 = r2820168 / r2820169;
        double r2820171 = r2820169 * r2820169;
        double r2820172 = r2820168 - r2820171;
        double r2820173 = sqrt(r2820172);
        double r2820174 = r2820173 / r2820169;
        double r2820175 = r2820170 + r2820174;
        double r2820176 = log(r2820175);
        return r2820176;
}

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 2019158 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))