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 r2564 = x;
        double r2565 = 1.0;
        double r2566 = r2564 - r2565;
        double r2567 = sqrt(r2566);
        double r2568 = sqrt(r2564);
        double r2569 = r2567 * r2568;
        return r2569;
}
↓
double f(double x) {
        double r2570 = x;
        double r2571 = 1.0;
        double r2572 = r2570 - r2571;
        double r2573 = sqrt(r2572);
        double r2574 = sqrt(r2570);
        double r2575 = r2573 * r2574;
        return r2575;
}

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)))