Average Error: 0.5 → 0.5
Time: 2.6s
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 r1190 = x;
        double r1191 = 1.0;
        double r1192 = r1190 - r1191;
        double r1193 = sqrt(r1192);
        double r1194 = sqrt(r1190);
        double r1195 = r1193 * r1194;
        return r1195;
}
↓
double f(double x) {
        double r1196 = x;
        double r1197 = 1.0;
        double r1198 = r1196 - r1197;
        double r1199 = sqrt(r1198);
        double r1200 = sqrt(r1196);
        double r1201 = r1199 * r1200;
        return r1201;
}

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 2020036 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))