Average Error: 0.5 → 0.5
Time: 14.3s
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 r528493 = x;
        double r528494 = 1.0;
        double r528495 = r528493 - r528494;
        double r528496 = sqrt(r528495);
        double r528497 = sqrt(r528493);
        double r528498 = r528496 * r528497;
        return r528498;
}
↓
double f(double x) {
        double r528499 = x;
        double r528500 = 1.0;
        double r528501 = r528499 - r528500;
        double r528502 = sqrt(r528501);
        double r528503 = sqrt(r528499);
        double r528504 = r528502 * r528503;
        return r528504;
}

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