Average Error: 0.0 → 0.0
Time: 8.6s
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 r4253131 = 1.0;
        double r4253132 = x;
        double r4253133 = r4253131 / r4253132;
        double r4253134 = r4253132 * r4253132;
        double r4253135 = r4253131 - r4253134;
        double r4253136 = sqrt(r4253135);
        double r4253137 = r4253136 / r4253132;
        double r4253138 = r4253133 + r4253137;
        double r4253139 = log(r4253138);
        return r4253139;
}
↓
double f(double x) {
        double r4253140 = 1.0;
        double r4253141 = x;
        double r4253142 = r4253140 / r4253141;
        double r4253143 = r4253141 * r4253141;
        double r4253144 = r4253140 - r4253143;
        double r4253145 = sqrt(r4253144);
        double r4253146 = r4253145 / r4253141;
        double r4253147 = r4253142 + r4253146;
        double r4253148 = log(r4253147);
        return r4253148;
}

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 2019121 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))