Average Error: 0.0 → 0.0
Time: 24.4s
Precision: 64
\[\log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)\]
\log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)
↓
\log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)
double f(double x) {
        double r3148068 = 1.0;
        double r3148069 = x;
        double r3148070 = r3148068 / r3148069;
        double r3148071 = r3148069 * r3148069;
        double r3148072 = r3148068 - r3148071;
        double r3148073 = sqrt(r3148072);
        double r3148074 = r3148073 / r3148069;
        double r3148075 = r3148070 + r3148074;
        double r3148076 = log(r3148075);
        return r3148076;
}
↓
double f(double x) {
        double r3148077 = 1.0;
        double r3148078 = x;
        double r3148079 = r3148077 / r3148078;
        double r3148080 = r3148078 * r3148078;
        double r3148081 = r3148077 - r3148080;
        double r3148082 = sqrt(r3148081);
        double r3148083 = r3148082 / r3148078;
        double r3148084 = r3148079 + r3148083;
        double r3148085 = log(r3148084);
        return r3148085;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)\]

  2. Final simplification0.0

    \[\leadsto \log \left(\frac{1.0}{x} + \frac{\sqrt{1.0 - x \cdot x}}{x}\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))