Average Error: 0.5 → 0.5
Time: 21.9s
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 r332869 = x;
        double r332870 = 1.0;
        double r332871 = r332869 - r332870;
        double r332872 = sqrt(r332871);
        double r332873 = sqrt(r332869);
        double r332874 = r332872 * r332873;
        return r332874;
}
↓
double f(double x) {
        double r332875 = x;
        double r332876 = 1.0;
        double r332877 = r332875 - r332876;
        double r332878 = sqrt(r332877);
        double r332879 = sqrt(r332875);
        double r332880 = r332878 * r332879;
        return r332880;
}

Error

Bits error versus x

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Results

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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 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1.0)) (sqrt x)))