Average Error: 0.0 → 0.0
Time: 7.3s
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 r1215538 = 1.0;
        double r1215539 = x;
        double r1215540 = r1215538 / r1215539;
        double r1215541 = r1215539 * r1215539;
        double r1215542 = r1215538 - r1215541;
        double r1215543 = sqrt(r1215542);
        double r1215544 = r1215543 / r1215539;
        double r1215545 = r1215540 + r1215544;
        double r1215546 = log(r1215545);
        return r1215546;
}
↓
double f(double x) {
        double r1215547 = 1.0;
        double r1215548 = x;
        double r1215549 = r1215547 / r1215548;
        double r1215550 = r1215548 * r1215548;
        double r1215551 = r1215547 - r1215550;
        double r1215552 = sqrt(r1215551);
        double r1215553 = r1215552 / r1215548;
        double r1215554 = r1215549 + r1215553;
        double r1215555 = log(r1215554);
        return r1215555;
}

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 2019134 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))