Average Error: 0.0 → 0.0
Time: 10.0s
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 r4225926 = 1.0;
        double r4225927 = x;
        double r4225928 = r4225926 / r4225927;
        double r4225929 = r4225927 * r4225927;
        double r4225930 = r4225926 - r4225929;
        double r4225931 = sqrt(r4225930);
        double r4225932 = r4225931 / r4225927;
        double r4225933 = r4225928 + r4225932;
        double r4225934 = log(r4225933);
        return r4225934;
}
↓
double f(double x) {
        double r4225935 = 1.0;
        double r4225936 = x;
        double r4225937 = r4225935 / r4225936;
        double r4225938 = r4225936 * r4225936;
        double r4225939 = r4225935 - r4225938;
        double r4225940 = sqrt(r4225939);
        double r4225941 = r4225940 / r4225936;
        double r4225942 = r4225937 + r4225941;
        double r4225943 = log(r4225942);
        return r4225943;
}

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 2019112 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))