Average Error: 0.5 → 0.4
Time: 10.0s
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 r194922 = x;
        double r194923 = 1.0;
        double r194924 = r194922 - r194923;
        double r194925 = sqrt(r194924);
        double r194926 = sqrt(r194922);
        double r194927 = r194925 * r194926;
        return r194927;
}
↓
double f(double x) {
        double r194928 = -0.125;
        double r194929 = x;
        double r194930 = r194928 / r194929;
        double r194931 = 0.5;
        double r194932 = r194931 - r194929;
        double r194933 = r194930 - r194932;
        return r194933;
}

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 2019125 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))