Average Error: 0.0 → 0.0
Time: 5.8s
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 r2647639 = 1.0;
        double r2647640 = x;
        double r2647641 = r2647639 / r2647640;
        double r2647642 = r2647640 * r2647640;
        double r2647643 = r2647639 - r2647642;
        double r2647644 = sqrt(r2647643);
        double r2647645 = r2647644 / r2647640;
        double r2647646 = r2647641 + r2647645;
        double r2647647 = log(r2647646);
        return r2647647;
}
↓
double f(double x) {
        double r2647648 = 1.0;
        double r2647649 = x;
        double r2647650 = r2647648 / r2647649;
        double r2647651 = r2647649 * r2647649;
        double r2647652 = r2647648 - r2647651;
        double r2647653 = sqrt(r2647652);
        double r2647654 = r2647653 / r2647649;
        double r2647655 = r2647650 + r2647654;
        double r2647656 = log(r2647655);
        return r2647656;
}

Error

Bits error versus x

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Results

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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 2019192 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))