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 r4073579 = 1.0;
        double r4073580 = x;
        double r4073581 = r4073579 / r4073580;
        double r4073582 = r4073580 * r4073580;
        double r4073583 = r4073579 - r4073582;
        double r4073584 = sqrt(r4073583);
        double r4073585 = r4073584 / r4073580;
        double r4073586 = r4073581 + r4073585;
        double r4073587 = log(r4073586);
        return r4073587;
}
↓
double f(double x) {
        double r4073588 = 1.0;
        double r4073589 = x;
        double r4073590 = r4073588 / r4073589;
        double r4073591 = r4073589 * r4073589;
        double r4073592 = r4073588 - r4073591;
        double r4073593 = sqrt(r4073592);
        double r4073594 = r4073593 / r4073589;
        double r4073595 = r4073590 + r4073594;
        double r4073596 = log(r4073595);
        return r4073596;
}

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 2019124 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))