Average Error: 0.5 → 0.5
Time: 9.2s
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 r12388 = x;
        double r12389 = 1.0;
        double r12390 = r12388 - r12389;
        double r12391 = sqrt(r12390);
        double r12392 = sqrt(r12388);
        double r12393 = r12391 * r12392;
        return r12393;
}
↓
double f(double x) {
        double r12394 = x;
        double r12395 = 1.0;
        double r12396 = r12394 - r12395;
        double r12397 = sqrt(r12396);
        double r12398 = sqrt(r12394);
        double r12399 = r12397 * r12398;
        return r12399;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))