Average Error: 0.0 → 0.0
Time: 1.1s
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 r123681 = 1.0;
        double r123682 = x;
        double r123683 = r123682 * r123682;
        double r123684 = r123681 - r123683;
        double r123685 = sqrt(r123684);
        return r123685;
}
↓
double f(double x) {
        double r123686 = 1.0;
        double r123687 = x;
        double r123688 = r123687 * r123687;
        double r123689 = r123686 - r123688;
        double r123690 = sqrt(r123689);
        return r123690;
}

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 2019303 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))