Average Error: 0.0 → 0.0
Time: 1.3s
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 r165820 = 1.0;
        double r165821 = x;
        double r165822 = r165821 * r165821;
        double r165823 = r165820 - r165822;
        double r165824 = sqrt(r165823);
        return r165824;
}
↓
double f(double x) {
        double r165825 = 1.0;
        double r165826 = x;
        double r165827 = r165826 * r165826;
        double r165828 = r165825 - r165827;
        double r165829 = sqrt(r165828);
        return r165829;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

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 2019209 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))