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 r1518411 = 1.0;
        double r1518412 = x;
        double r1518413 = r1518411 / r1518412;
        double r1518414 = r1518412 * r1518412;
        double r1518415 = r1518411 - r1518414;
        double r1518416 = sqrt(r1518415);
        double r1518417 = r1518416 / r1518412;
        double r1518418 = r1518413 + r1518417;
        double r1518419 = log(r1518418);
        return r1518419;
}
↓
double f(double x) {
        double r1518420 = 1.0;
        double r1518421 = x;
        double r1518422 = r1518420 / r1518421;
        double r1518423 = r1518421 * r1518421;
        double r1518424 = r1518420 - r1518423;
        double r1518425 = sqrt(r1518424);
        double r1518426 = r1518425 / r1518421;
        double r1518427 = r1518422 + r1518426;
        double r1518428 = log(r1518427);
        return r1518428;
}

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 2019170 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))