Average Error: 0.5 → 0.5
Time: 13.3s
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 r509068 = x;
        double r509069 = 1.0;
        double r509070 = r509068 - r509069;
        double r509071 = sqrt(r509070);
        double r509072 = sqrt(r509068);
        double r509073 = r509071 * r509072;
        return r509073;
}
↓
double f(double x) {
        double r509074 = x;
        double r509075 = 1.0;
        double r509076 = r509074 - r509075;
        double r509077 = sqrt(r509076);
        double r509078 = sqrt(r509074);
        double r509079 = r509077 * r509078;
        return r509079;
}

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 2019158 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))