Average Error: 0.5 → 0.4
Time: 6.3s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\frac{\frac{-1}{8}}{x} - \left(\frac{1}{2} - x\right)\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\frac{\frac{-1}{8}}{x} - \left(\frac{1}{2} - x\right)
double f(double x) {
        double r78838 = x;
        double r78839 = 1.0;
        double r78840 = r78838 - r78839;
        double r78841 = sqrt(r78840);
        double r78842 = sqrt(r78838);
        double r78843 = r78841 * r78842;
        return r78843;
}
↓
double f(double x) {
        double r78844 = -0.125;
        double r78845 = x;
        double r78846 = r78844 / r78845;
        double r78847 = 0.5;
        double r78848 = r78847 - r78845;
        double r78849 = r78846 - r78848;
        return r78849;
}

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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019133 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))