Average Error: 0.5 → 0.5
Time: 2.2s
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 r2459 = x;
        double r2460 = 1.0;
        double r2461 = r2459 - r2460;
        double r2462 = sqrt(r2461);
        double r2463 = sqrt(r2459);
        double r2464 = r2462 * r2463;
        return r2464;
}
↓
double f(double x) {
        double r2465 = x;
        double r2466 = 1.0;
        double r2467 = r2465 - r2466;
        double r2468 = sqrt(r2467);
        double r2469 = sqrt(r2465);
        double r2470 = r2468 * r2469;
        return r2470;
}

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)))