Average Error: 0.5 → 0.5
Time: 9.6s
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 r355841 = x;
        double r355842 = 1.0;
        double r355843 = r355841 - r355842;
        double r355844 = sqrt(r355843);
        double r355845 = sqrt(r355841);
        double r355846 = r355844 * r355845;
        return r355846;
}
↓
double f(double x) {
        double r355847 = x;
        double r355848 = 1.0;
        double r355849 = r355847 - r355848;
        double r355850 = sqrt(r355849);
        double r355851 = sqrt(r355847);
        double r355852 = r355850 * r355851;
        return r355852;
}

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

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))