Average Error: 0.5 → 0.5
Time: 7.8s
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 r111129 = x;
        double r111130 = 1.0;
        double r111131 = r111129 - r111130;
        double r111132 = sqrt(r111131);
        double r111133 = sqrt(r111129);
        double r111134 = r111132 * r111133;
        return r111134;
}
↓
double f(double x) {
        double r111135 = x;
        double r111136 = 1.0;
        double r111137 = r111135 - r111136;
        double r111138 = sqrt(r111137);
        double r111139 = sqrt(r111135);
        double r111140 = r111138 * r111139;
        return r111140;
}

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 2019112 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))