Average Error: 0.0 → 0.0
Time: 12.7s
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 r6673726 = 1.0;
        double r6673727 = x;
        double r6673728 = r6673726 / r6673727;
        double r6673729 = r6673727 * r6673727;
        double r6673730 = r6673726 - r6673729;
        double r6673731 = sqrt(r6673730);
        double r6673732 = r6673731 / r6673727;
        double r6673733 = r6673728 + r6673732;
        double r6673734 = log(r6673733);
        return r6673734;
}
↓
double f(double x) {
        double r6673735 = 1.0;
        double r6673736 = x;
        double r6673737 = r6673735 / r6673736;
        double r6673738 = r6673736 * r6673736;
        double r6673739 = r6673735 - r6673738;
        double r6673740 = sqrt(r6673739);
        double r6673741 = r6673740 / r6673736;
        double r6673742 = r6673737 + r6673741;
        double r6673743 = log(r6673742);
        return r6673743;
}

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 2019104 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))