Average Error: 0.5 → 0.5
Time: 21.7s
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 r351135 = x;
        double r351136 = 1.0;
        double r351137 = r351135 - r351136;
        double r351138 = sqrt(r351137);
        double r351139 = sqrt(r351135);
        double r351140 = r351138 * r351139;
        return r351140;
}
↓
double f(double x) {
        double r351141 = x;
        double r351142 = 1.0;
        double r351143 = r351141 - r351142;
        double r351144 = sqrt(r351143);
        double r351145 = sqrt(r351141);
        double r351146 = r351144 * r351145;
        return r351146;
}

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 2019107 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))