Average Error: 0.5 → 0.5
Time: 16.7s
Precision: 64
\[\sqrt{x - 1.0} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1.0} \cdot \sqrt{x}\]
\sqrt{x - 1.0} \cdot \sqrt{x}
↓
\sqrt{x - 1.0} \cdot \sqrt{x}
double f(double x) {
        double r394417 = x;
        double r394418 = 1.0;
        double r394419 = r394417 - r394418;
        double r394420 = sqrt(r394419);
        double r394421 = sqrt(r394417);
        double r394422 = r394420 * r394421;
        return r394422;
}
↓
double f(double x) {
        double r394423 = x;
        double r394424 = 1.0;
        double r394425 = r394423 - r394424;
        double r394426 = sqrt(r394425);
        double r394427 = sqrt(r394423);
        double r394428 = r394426 * r394427;
        return r394428;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1.0} \cdot \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \sqrt{x - 1.0} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1.0)) (sqrt x)))