Average Error: 0.5 → 0.5
Time: 15.4s
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 r443932 = x;
        double r443933 = 1.0;
        double r443934 = r443932 - r443933;
        double r443935 = sqrt(r443934);
        double r443936 = sqrt(r443932);
        double r443937 = r443935 * r443936;
        return r443937;
}
↓
double f(double x) {
        double r443938 = x;
        double r443939 = 1.0;
        double r443940 = r443938 - r443939;
        double r443941 = sqrt(r443940);
        double r443942 = sqrt(r443938);
        double r443943 = r443941 * r443942;
        return r443943;
}

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 2019169 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1.0)) (sqrt x)))