Average Error: 0.0 → 0.0
Time: 14.6s
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 r1755523 = 1.0;
        double r1755524 = x;
        double r1755525 = r1755523 / r1755524;
        double r1755526 = r1755524 * r1755524;
        double r1755527 = r1755523 - r1755526;
        double r1755528 = sqrt(r1755527);
        double r1755529 = r1755528 / r1755524;
        double r1755530 = r1755525 + r1755529;
        double r1755531 = log(r1755530);
        return r1755531;
}
↓
double f(double x) {
        double r1755532 = 1.0;
        double r1755533 = x;
        double r1755534 = r1755532 / r1755533;
        double r1755535 = r1755533 * r1755533;
        double r1755536 = r1755532 - r1755535;
        double r1755537 = sqrt(r1755536);
        double r1755538 = r1755537 / r1755533;
        double r1755539 = r1755534 + r1755538;
        double r1755540 = log(r1755539);
        return r1755540;
}

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 2019143 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))