Average Error: 0.5 → 0.5
Time: 6.7s
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 r58826 = x;
        double r58827 = 1.0;
        double r58828 = r58826 - r58827;
        double r58829 = sqrt(r58828);
        double r58830 = sqrt(r58826);
        double r58831 = r58829 * r58830;
        return r58831;
}
↓
double f(double x) {
        double r58832 = x;
        double r58833 = 1.0;
        double r58834 = r58832 - r58833;
        double r58835 = sqrt(r58834);
        double r58836 = sqrt(r58832);
        double r58837 = r58835 * r58836;
        return r58837;
}

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 2019153 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))