Average Error: 0.5 → 0.5
Time: 10.6s
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 r14521 = x;
        double r14522 = 1.0;
        double r14523 = r14521 - r14522;
        double r14524 = sqrt(r14523);
        double r14525 = sqrt(r14521);
        double r14526 = r14524 * r14525;
        return r14526;
}
↓
double f(double x) {
        double r14527 = x;
        double r14528 = 1.0;
        double r14529 = r14527 - r14528;
        double r14530 = sqrt(r14529);
        double r14531 = sqrt(r14527);
        double r14532 = r14530 * r14531;
        return r14532;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.5

    \[\leadsto \color{blue}{\sqrt{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \sqrt{\sqrt{x - 1} \cdot \sqrt{x}}}\]

  4. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))