Average Error: 0.0 → 0.0
Time: 948.0ms
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 r198687 = 1.0;
        double r198688 = x;
        double r198689 = r198688 * r198688;
        double r198690 = r198687 - r198689;
        double r198691 = sqrt(r198690);
        return r198691;
}
↓
double f(double x) {
        double r198692 = 1.0;
        double r198693 = x;
        double r198694 = r198693 * r198693;
        double r198695 = r198692 - r198694;
        double r198696 = sqrt(r198695);
        return r198696;
}

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 2020036 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))