Average Error: 0.5 → 0.4
Time: 7.4s
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 r101315 = x;
        double r101316 = 1.0;
        double r101317 = r101315 - r101316;
        double r101318 = sqrt(r101317);
        double r101319 = sqrt(r101315);
        double r101320 = r101318 * r101319;
        return r101320;
}
↓
double f(double x) {
        double r101321 = x;
        double r101322 = 0.5;
        double r101323 = -0.125;
        double r101324 = r101323 / r101321;
        double r101325 = r101322 - r101324;
        double r101326 = r101321 - r101325;
        return r101326;
}

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 2019104 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))