Average Error: 0.0 → 0.0
Time: 13.0s
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 r7282288 = 1.0;
        double r7282289 = x;
        double r7282290 = r7282288 / r7282289;
        double r7282291 = r7282289 * r7282289;
        double r7282292 = r7282288 - r7282291;
        double r7282293 = sqrt(r7282292);
        double r7282294 = r7282293 / r7282289;
        double r7282295 = r7282290 + r7282294;
        double r7282296 = log(r7282295);
        return r7282296;
}
↓
double f(double x) {
        double r7282297 = 1.0;
        double r7282298 = x;
        double r7282299 = r7282297 / r7282298;
        double r7282300 = r7282298 * r7282298;
        double r7282301 = r7282297 - r7282300;
        double r7282302 = sqrt(r7282301);
        double r7282303 = r7282302 / r7282298;
        double r7282304 = r7282299 + r7282303;
        double r7282305 = log(r7282304);
        return r7282305;
}

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 2019128 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))