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 r6635 = x;
        double r6636 = 1.0;
        double r6637 = r6635 - r6636;
        double r6638 = sqrt(r6637);
        double r6639 = sqrt(r6635);
        double r6640 = r6638 * r6639;
        return r6640;
}
↓
double f(double x) {
        double r6641 = x;
        double r6642 = 1.0;
        double r6643 = r6641 - r6642;
        double r6644 = sqrt(r6643);
        double r6645 = sqrt(r6641);
        double r6646 = r6644 * r6645;
        return r6646;
}

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 2020020 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))