Average Error: 0.5 → 0.4
Time: 6.4s
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 r59324 = x;
        double r59325 = 1.0;
        double r59326 = r59324 - r59325;
        double r59327 = sqrt(r59326);
        double r59328 = sqrt(r59324);
        double r59329 = r59327 * r59328;
        return r59329;
}
↓
double f(double x) {
        double r59330 = -0.125;
        double r59331 = x;
        double r59332 = r59330 / r59331;
        double r59333 = 0.5;
        double r59334 = r59333 - r59331;
        double r59335 = r59332 - r59334;
        return r59335;
}

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 2019124 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))