Average Error: 0.0 → 0.0
Time: 20.1s
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 r2236407 = 1.0;
        double r2236408 = x;
        double r2236409 = r2236407 / r2236408;
        double r2236410 = r2236408 * r2236408;
        double r2236411 = r2236407 - r2236410;
        double r2236412 = sqrt(r2236411);
        double r2236413 = r2236412 / r2236408;
        double r2236414 = r2236409 + r2236413;
        double r2236415 = log(r2236414);
        return r2236415;
}
↓
double f(double x) {
        double r2236416 = 1.0;
        double r2236417 = x;
        double r2236418 = r2236416 / r2236417;
        double r2236419 = r2236417 * r2236417;
        double r2236420 = r2236416 - r2236419;
        double r2236421 = sqrt(r2236420);
        double r2236422 = r2236421 / r2236417;
        double r2236423 = r2236418 + r2236422;
        double r2236424 = log(r2236423);
        return r2236424;
}

Error

Bits error versus x

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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 2019142 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))