Average Error: 0.5 → 0.5
Time: 9.2s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{x - 1} \cdot \sqrt{x}
double f(double x) {
        double r11286 = x;
        double r11287 = 1.0;
        double r11288 = r11286 - r11287;
        double r11289 = sqrt(r11288);
        double r11290 = sqrt(r11286);
        double r11291 = r11289 * r11290;
        return r11291;
}
↓
double f(double x) {
        double r11292 = x;
        double r11293 = 1.0;
        double r11294 = r11292 - r11293;
        double r11295 = sqrt(r11294);
        double r11296 = sqrt(r11292);
        double r11297 = r11295 * r11296;
        return r11297;
}

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. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))