Average Error: 0.5 → 0.5
Time: 6.1s
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 r58329 = x;
        double r58330 = 1.0;
        double r58331 = r58329 - r58330;
        double r58332 = sqrt(r58331);
        double r58333 = sqrt(r58329);
        double r58334 = r58332 * r58333;
        return r58334;
}
↓
double f(double x) {
        double r58335 = x;
        double r58336 = 1.0;
        double r58337 = r58335 - r58336;
        double r58338 = sqrt(r58337);
        double r58339 = sqrt(r58335);
        double r58340 = r58338 * r58339;
        return r58340;
}

Error

Bits error versus x

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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 2019153 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))