Average Error: 0.5 → 0.4
Time: 21.7s
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 r824400 = x;
        double r824401 = 1.0;
        double r824402 = r824400 - r824401;
        double r824403 = sqrt(r824402);
        double r824404 = sqrt(r824400);
        double r824405 = r824403 * r824404;
        return r824405;
}
↓
double f(double x) {
        double r824406 = -0.125;
        double r824407 = x;
        double r824408 = r824406 / r824407;
        double r824409 = 0.5;
        double r824410 = r824409 - r824407;
        double r824411 = r824408 - r824410;
        return r824411;
}

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 2019128 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))