Average Error: 0.0 → 0.0
Time: 6.5m
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 r23519441 = 1.0;
        double r23519442 = x;
        double r23519443 = r23519441 / r23519442;
        double r23519444 = r23519442 * r23519442;
        double r23519445 = r23519441 - r23519444;
        double r23519446 = sqrt(r23519445);
        double r23519447 = r23519446 / r23519442;
        double r23519448 = r23519443 + r23519447;
        double r23519449 = log(r23519448);
        return r23519449;
}
↓
double f(double x) {
        double r23519450 = 1.0;
        double r23519451 = x;
        double r23519452 = r23519450 / r23519451;
        double r23519453 = r23519451 * r23519451;
        double r23519454 = r23519450 - r23519453;
        double r23519455 = sqrt(r23519454);
        double r23519456 = r23519455 / r23519451;
        double r23519457 = r23519452 + r23519456;
        double r23519458 = log(r23519457);
        return r23519458;
}

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 2019158 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))