Average Error: 0.5 → 0.5
Time: 2.3s
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 r1799 = x;
        double r1800 = 1.0;
        double r1801 = r1799 - r1800;
        double r1802 = sqrt(r1801);
        double r1803 = sqrt(r1799);
        double r1804 = r1802 * r1803;
        return r1804;
}
↓
double f(double x) {
        double r1805 = x;
        double r1806 = 1.0;
        double r1807 = r1805 - r1806;
        double r1808 = sqrt(r1807);
        double r1809 = sqrt(r1805);
        double r1810 = r1808 * r1809;
        return r1810;
}

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 2020001 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))