Average Error: 0.0 → 0.0
Time: 1.6s
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 r183766 = 1.0;
        double r183767 = x;
        double r183768 = r183767 * r183767;
        double r183769 = r183766 - r183768;
        double r183770 = sqrt(r183769);
        return r183770;
}
↓
double f(double x) {
        double r183771 = 1.0;
        double r183772 = x;
        double r183773 = r183772 * r183772;
        double r183774 = r183771 - r183773;
        double r183775 = sqrt(r183774);
        return r183775;
}

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 2019356 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))