Average Error: 0.0 → 0.0
Time: 6.1s
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 r2644198 = 1.0;
        double r2644199 = x;
        double r2644200 = r2644198 / r2644199;
        double r2644201 = r2644199 * r2644199;
        double r2644202 = r2644198 - r2644201;
        double r2644203 = sqrt(r2644202);
        double r2644204 = r2644203 / r2644199;
        double r2644205 = r2644200 + r2644204;
        double r2644206 = log(r2644205);
        return r2644206;
}
↓
double f(double x) {
        double r2644207 = 1.0;
        double r2644208 = x;
        double r2644209 = r2644207 / r2644208;
        double r2644210 = r2644208 * r2644208;
        double r2644211 = r2644207 - r2644210;
        double r2644212 = sqrt(r2644211);
        double r2644213 = r2644212 / r2644208;
        double r2644214 = r2644209 + r2644213;
        double r2644215 = log(r2644214);
        return r2644215;
}

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 2019172 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))