Average Error: 0.5 → 0.5
Time: 11.5s
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 r544160 = x;
        double r544161 = 1.0;
        double r544162 = r544160 - r544161;
        double r544163 = sqrt(r544162);
        double r544164 = sqrt(r544160);
        double r544165 = r544163 * r544164;
        return r544165;
}
↓
double f(double x) {
        double r544166 = x;
        double r544167 = 1.0;
        double r544168 = r544166 - r544167;
        double r544169 = sqrt(r544168);
        double r544170 = sqrt(r544166);
        double r544171 = r544169 * r544170;
        return r544171;
}

Error

Bits error versus x

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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 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))