Average Error: 0.5 → 0.5
Time: 2.6s
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 r7363 = x;
        double r7364 = 1.0;
        double r7365 = r7363 - r7364;
        double r7366 = sqrt(r7365);
        double r7367 = sqrt(r7363);
        double r7368 = r7366 * r7367;
        return r7368;
}
↓
double f(double x) {
        double r7369 = x;
        double r7370 = 1.0;
        double r7371 = r7369 - r7370;
        double r7372 = sqrt(r7371);
        double r7373 = sqrt(r7369);
        double r7374 = r7372 * r7373;
        return r7374;
}

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 2020060 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))