Average Error: 0.5 → 0.5
Time: 7.3s
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 r290785 = x;
        double r290786 = 1.0;
        double r290787 = r290785 - r290786;
        double r290788 = sqrt(r290787);
        double r290789 = sqrt(r290785);
        double r290790 = r290788 * r290789;
        return r290790;
}
↓
double f(double x) {
        double r290791 = x;
        double r290792 = 1.0;
        double r290793 = r290791 - r290792;
        double r290794 = sqrt(r290793);
        double r290795 = sqrt(r290791);
        double r290796 = r290794 * r290795;
        return r290796;
}

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 2019165 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))