Average Error: 0.0 → 0.0
Time: 30.4s
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 r12651837 = 1.0;
        double r12651838 = x;
        double r12651839 = r12651837 / r12651838;
        double r12651840 = r12651838 * r12651838;
        double r12651841 = r12651837 - r12651840;
        double r12651842 = sqrt(r12651841);
        double r12651843 = r12651842 / r12651838;
        double r12651844 = r12651839 + r12651843;
        double r12651845 = log(r12651844);
        return r12651845;
}
↓
double f(double x) {
        double r12651846 = 1.0;
        double r12651847 = x;
        double r12651848 = r12651846 / r12651847;
        double r12651849 = r12651847 * r12651847;
        double r12651850 = r12651846 - r12651849;
        double r12651851 = sqrt(r12651850);
        double r12651852 = r12651851 / r12651847;
        double r12651853 = r12651848 + r12651852;
        double r12651854 = log(r12651853);
        return r12651854;
}

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 2019125 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))