Average Error: 0.5 → 0.5
Time: 6.3s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\[\sqrt{x - 1} \cdot \sqrt{x}\]
double f(double x) {
        double r77108 = x;
        double r77109 = 1.0;
        double r77110 = r77108 - r77109;
        double r77111 = sqrt(r77110);
        double r77112 = sqrt(r77108);
        double r77113 = r77111 * r77112;
        return r77113;
}

double f(double x) {
        double r77114 = x;
        double r77115 = 1.0;
        double r77116 = r77114 - r77115;
        double r77117 = sqrt(r77116);
        double r77118 = sqrt(r77114);
        double r77119 = r77117 * r77118;
        return r77119;
}

\sqrt{x - 1} \cdot \sqrt{x}
\sqrt{x - 1} \cdot \sqrt{x}

Error

Bits error versus x

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 2019102 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))