Average Error: 0.0 → 0.0
Time: 12.6s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
\[\sqrt{1 - x \cdot x}\]
\sqrt{1 - x \cdot x}
\sqrt{1 - x \cdot x}
double f(double x) {
        double r49135778 = 1.0;
        double r49135779 = x;
        double r49135780 = r49135779 * r49135779;
        double r49135781 = r49135778 - r49135780;
        double r49135782 = sqrt(r49135781);
        return r49135782;
}

double f(double x) {
        double r49135783 = 1.0;
        double r49135784 = x;
        double r49135785 = r49135784 * r49135784;
        double r49135786 = r49135783 - r49135785;
        double r49135787 = sqrt(r49135786);
        return r49135787;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]
  2. Final simplification0.0

    \[\leadsto \sqrt{1 - x \cdot x}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(1-x*x)"
  (sqrt (- 1 (* x x))))