Average Error: 0.5 → 0.4
Time: 7.7s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[x - \left(\frac{1}{2} - \frac{\frac{-1}{8}}{x}\right)\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
x - \left(\frac{1}{2} - \frac{\frac{-1}{8}}{x}\right)
double f(double x) {
        double r118828 = x;
        double r118829 = 1.0;
        double r118830 = r118828 - r118829;
        double r118831 = sqrt(r118830);
        double r118832 = sqrt(r118828);
        double r118833 = r118831 * r118832;
        return r118833;
}
↓
double f(double x) {
        double r118834 = x;
        double r118835 = 0.5;
        double r118836 = -0.125;
        double r118837 = r118836 / r118834;
        double r118838 = r118835 - r118837;
        double r118839 = r118834 - r118838;
        return r118839;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Taylor expanded around inf 0.4

    \[\leadsto \color{blue}{x - \left(\frac{1}{8} \cdot \frac{1}{x} + \frac{1}{2}\right)}\]

  3. Simplified0.4

    \[\leadsto \color{blue}{x - \left(\frac{1}{2} - \frac{\frac{-1}{8}}{x}\right)}\]

  4. Final simplification0.4

    \[\leadsto x - \left(\frac{1}{2} - \frac{\frac{-1}{8}}{x}\right)\]

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))